The scientific program covers a broad range of topics from the mathematical structure of General Relativity (GR) and fundamental issues of classical gravity, through mathematical models of quantum gravity, to gravitational waves and their detection. The goal of the conference is to give an account of achievements of GR. This theory has been developed in many different directions. All of them will be included in the conference. We will invite experts from the leading world centres of mathematical relativity and gravitational physics who will present the state of art in our knowledge and understanding of various areas of General Relativity:
Thanks to the spectacular observational advances since the 1990s, a 'standard model' of the early universe has now emerged. However, since it is based on quantum field theory in curved space-times, it is not applicable in the Planck regime. Using techniques from loop quantum gravity, the theory can be extended over the 12 orders of magnitude in density and curvature from the onset of inflation all the way back to the Planck regime, providing us with a candidate completion of the standard model. Contrary to a wide-spread belief, the resulting pre-inflationary dynamics can have observational consequences. Thus, two way bridge has now opened between observations and fundamental theory. The talk will provide a broad overview of these results.
We introduce Dirac fields in hybrid loop quantum cosmology and study their behavior as part of the primordial perturbations, additional to those of the geometry and the inflaton field. With a convenient ansatz for physical quantum states, we show how to deduce a Schrodinger equation that dictates the quantum evolution of these fermionic perturbations. Remarkably, such evolution is unitary, and couples the fermion field with an infinite sequence of quantum moments of the homogeneous geometry. We also discuss some issues related with the quantum backreaction produced by the Dirac fields.
Coordinates adapted to metric tensor are common tool in many areas of General Relativity. From the point of view of canonical framework they provide Dirac observables invariant with respect (ideally) to all or (practically) to most of diffeomorphisms. Recently, in that context the coordinates defined by geodesics emanating from observer were studied. In the case of the space like geodesics the symmetry group is a suitably deformed Poincare group acting on the space of the metric tensor. In the case of the null geodesics the result is surprising for additional reason: the coordinates reduce the diffeomorphism freedom much more than one could expect. Those published as well as very recent results will reported.
[1] Symetria Lorentza i zdeformowana symetria Poincarego w zakrzywionej czasoprzestrzeni, Maciej Kolanowski (Bachelor dissertation)
[2] Observer’s observables. Residual diffeomorphisms. Paweł Duch, Jerzy Lewandowski, Jedrzej Świeżewski. Class.Quant.Grav. 34 (2017) no.12, 125009.
[3] The algebra of observables in Gaußian normal spacetime coordinates. Norbert Bodendorfer, Paweł Duch, Jerzy Lewandowski, Jędrzej Świeżewski. JHEP 1601 (2016) 047.
[4] General relativity in the radial gauge: Reduced phase space and canonical structure. Norbert Bodendorfer, Jerzy Lewandowski, Jedrzej Świeżewski. Phys.Rev. D92 (2015) no.8, 084041.
The dynamics of the general (non-diagonal) Bianchi IX model, near the gravitational singularity, underlies the BKL scenario. Asymptotically, the solutions to this dynamics include some special structures named wiggles, which correspond to the oscillatory evolution of the BKL scenario. We propose the formalism, based on the affine quantization scheme, to examine the fate of the wiggles at the quantum level. We present the way of comparing the classical wiggles with their quantum counterparts. The expectation is that our work may contribute towards understanding some quantum aspects of the BKL scenario.
TBA
We examine a naive perturbative generalization of the Friedmann--Lemaitre cosmological model. We introduce at the metric level parameters which control basic properties of inhomogeneities, their profile, growth rate and density contrast. We give conditions under which the model can be considered reasonable and comment limitations of this approach. Finally, we perform an averaging procedure of the model using the notion of weak limit and propose a method to construct its background model.
As known since 1980, some light rays emitted from the Big Bang (BB) in a
Lemaitre - Tolman (L-T) model reach all observers with an infinite blueshift.
This happens when at the emission point the BB function t_B(r) has nonzero
derivative and the ray propagates radially. Some authors portrayed the existence
of blueshifts as a disaster disqualifying the L-T models. This author recently
proposed that blueshifted rays are actually observed as gamma-ray bursts (GRBs).
Two papers were published. In the first one, it was shown that L-T based models
of GRB sources successfully account for the energies of the GRBs, the large
distances to them, their multitude, and for the existence of the afterglows.
However, these models did not account for the durations of the GRBs and of the
afterglows and for their (hypothetical) collimation into narrow jets. In the
second paper, the existence and properties of blueshifts were investigated in
exemplary Szekeres models. In them, infinite blueshifts may arise only along two
opposite directions, so the collimation is accounted for. The third paper, now
submitted for publication, shows how realistic Szekeres-based models of GRBs
improve upon the L-T based models. Currently, I work on accounting for the
duration of the GRBs and their afterglows, but the work is not yet completed.
Inhomogeneous, relativistic cosmology has recently observed a rise in popularity among the cosmologists. In particular, the scalar averaging approach (Buchert formalism) has been intensively examined
both analytically and numerically, giving some new insights
into the problem of cosmological backreaction i.e. the conjectured influence of small scale density inhomogeneities on the large scale evolution of the Universe. In my talk, I will summarise these recent efforts, including multi-scale partitioning approach and some results from N-body simulations. I will also put into perspective future prospects of cosmological backreaction investigations.
We study the formation of first molecules H$_2$ and HD, negative Hydrogen ions H$^-$, molecular ions H$_2^+$ and HeH$^+$ in the pre-reionization Universe. The cosmological recombination is described within the framework of modified model of the effective 3-level atom [Seager, Sasselov $\&$ Scott, 1999; Wong, Moss $\&$ Scott, 2008], while for the kinetics of chemical reactions we restrict consideration to the minimal model of [Galli $\&$ Palla, 1998] for Hydrogen, Deuterium and Helium. It is found that the uncertainties of molecular abundances caused by the inaccuracies in description of cosmological recombination are about 2-3$\%$, comparable to those caused by the uncertainties of parameters of the $\Lambda$CDM model (up to 2.3$\%$). We investigate the effect of deviations from $\Lambda$CDM (minimally and non-minimally coupled dynamical dark energy, decaying dark matter) on the evolution of abundances of the first molecules.
I present the cosmological model which approximates the periodically distributed dust overdensities on the Einstein-de Sitter background.
The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously.
The comparison of the angular diameter distance obtained within the presented model and the angular diameter distances for the respective
average space-times is given.
We present a new geometrical inequality involving the ADM mass, the angular momentum and the size of an ordinary axially symmetric object. The main tool we use to use to prove it is the monotonicity of the Geroch quasi-local energy along the inverse mean curvature flow. We also compute numerical examples to test the robustness of our hypotheses and results.
Topological defects such as domain walls are present in many Beyond Standard Model theories and cosmological models. We investigate the behaviour of a thick domain wall in the Kerr spacetime. We simulate the transit of a light domain wall through the Kerr black hole to show how this behaviour depends on the domain walls' parameters and the black hole's spin. We also point out the presence of ringing modes.
I will report on the results of the joint numerical project with J.A. Font and P. Mach. We investigated low angular momentum accretion of inviscid fluids on black holes. The Newtonian calculation in this topic have been already done by D. Proga and M. Begelman. Our work promotes their models to fully relativistic setting. The staring point of those simulations is the Bondi-type accretion solution, perturbed by adding a small amount of angular momentum. The results of simulations will be discussed, emphasizing the similarities and differences with Newtonian models.
I will present the Idea of an inflaton without direct couplings to any additional fields. I will show a possible mechanisms of reheating together with implications of dark inflation on predictions of inflation, dark energy, dark matter, thermal history of the Universe, electro-weak phase transition and gravitational waves production.
In the paper we show that the general relativity action (and Lagrangian) in recent Einstein-Palatini formulation is equivalent to the action (and Langrangian) of a gauge field.
We begin with a bit of information of the Einstein-Palatini (EP) action, then we present how Einstein fields equations can be derived from it. In the next section, we consider Einstein-Palatini action integral for general relativity with a positive cosmological constant $\Lambda $ in terms of ''corrected curvature'' $\hat{F}$. We will see that in terms of $\hat{F}$ this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the curvature $\hat{F}$.
TBA
I shall briefly summarize recent contributions of the Polgraw-Virgo group to the effort for searches of gravitational waves by the LIGO-Virgo consortium. I shall present details of the searches for gravitational wave signals from rotating neutron stars done by the team from the Polgraw-Virgo group. I shall present both searches for known pulsars like Crab and Vela and blind searches in the whole of our Galaxy.
We show exemplary initial metrics for gravitational axial waves, that are twice differentiable but which are not $C^2$. They generate wave pulses that interact with matter in the radiation cosmological era. This forces the radiation matter to rotate. This rotation is permanent - it persists after the passage of the gravitational pulse. In contrast to that, we explicitly show that a class of smooth initial metrics that are at least $C^2$ gives rise to gravitational wave pulses that do not interact with the background during the radiation epoch.
We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman-Lemaitre-Robertson-Walker space-times. Axial gravitational waves can inuence only the azimuthal velocity. The whole gravitational dynamics reduces to the single "master equation" that has the same form as for axial modes. That allows us to conclude that the status of the Huygens principle is the same for both axial and polar modes of gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.
We are finding in class of null one-way fields solution with separated variables of Maxwell equations in Kerr space-time. Obtained solution describes left and right circularly-polarized waves. From this solution we deduce the dependence of polarization rotation angle from frequency as well as expression for phase shift.
Gravitational entropy and the cosmological “no-hair” conjecture
Gravitational entropy [1] and the “no-hair” conjectures [2, 3] are seemingly contradictory: the growth of the first one is associated with the growth of inhomogeneity [4, 5, 6], while the second one argues that the dark energy dominated Universe will asymptotically approach a homogeneous and isotropic de Sitter state[7, 8].
In my talk I will present the analysis of both of these conjectures within the silent universes [9, 10]. Irrotational silent universes belong to a class of systems where each worldline evolves independently of other worldlines - there is no communication between the worldlines, i.e. no pressure gradients, no energy flux, no gravitational radiation. In my talk I will discuss properties and evolution of the irrotational silent universe. I will focus on the gravitational entropy and future asymptotic state of the silent universe dominated by dark energy [11]. Finally, I will comment on the gravitational entropy of gravitational waves.
References
[1] T. Clifton, G. F. R. Ellis, and R. Tavakol, “A gravitational entropy proposal,” Classical and Quantum Gravity, vol. 30, p. 125009, 2013.
[2] G. Götz, “On the cosmological ’no-hair’ conjecture,” Physics Letters A, vol. 128, no. 3, pp. 129 – 132, 1988.
[3] L. G. Jensen and J. A. Stein-Schabes, “Is inflation natural?,” Phys. Rev. D, vol. 35, pp. 1146–1150, 1987.
[4] K. Bolejko and W. R. Stoeger, “Intermediate homogenization of the Universe and the problem of gravitational entropy,” Phys. Rev. D, vol. 88, no. 6, p. 063529, 2013.
[5] R. A. Sussman and J. Larena, “Gravitational entropies in LTB dust models,” Classical and Quantum Gravity, vol. 31, p. 075021, 2014.
[6] R. A. Sussman , “Gravitational entropy of cosmic expansion,” Astronomische Nachrichten, vol. 335, p. 587, 2014.
[7] R. M. Wald, “Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant,” Phys. Rev. D, vol. 28, pp. 2118–2120, 1983.
[8] T. Pacher and J. A. Stein-Schabes, “On the Locality of the No Hair Conjecture and the Measure of the Universe,” Annalen der Physik, vol. 503, pp. 518–526, 1991.
[9] M. Bruni, S. Matarrese, and O. Pantano, “Dynamics of silent universes,” Astroph. J., vol. 445, pp. 958–977, 1995.
[10] H. van Elst, C. Uggla, W. M. Lesame, G. F. R. Ellis, and R. Maartens, “Integrability of irrotational silent cosmological models,” Classical and Quantum Gravity, vol. 14, pp. 1151–1162, 1997.
[11] K. Bolejko, In preparation, 2017.
Traceless tensors with vanishing divergence (TT tensors) play a big role in the initial value problem in general relativity. They are solutions of the momentum constraints which can be extended to solutions of the full system of constraints by means of the conformal method of Lichnerowicz. First, we describe all divergence-free tensors T in flat spaces in terms of potentials which form a four index tensor R with all algebraic symmetries of the Riemann tensor. This tensor admits a big group of gauge transformations which can be used to simplify it. If T is traceless then we can choose R to be traceless too, so it has all properties of the Weyl tensor. Still it can be further reduced by means of gauge transformations.
I will present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. In particular, I will show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in $3+1$ dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a gravitational wave does make sense also beyond the linear approximation and provides a basis for a theory of nonlinear gravitational waves. The talk is based on a recent preprint http://arxiv.org/abs/1705.02258.
It is well known that the study of many-body systems in the presence of long-range interactions (1/r^a, a>1) within the context of Boltzmann-Gibbs statistical mechanics is unsuccessful. The configurational integral contained in the partition function diverges, preventing us from a proper probabilistic analysis of the system. This motivates us to describe our system by a non-additive and non-extensive entropy, i.e. the Tsallis entropy. Non-extensive statistical mechanics emerge as a powerful way to describe these systems. We present an analysis of a self-gravitating non-relativistic gas at thermal equilibrium using Tsallis non-extensive statistical mechanics, proposing an alternative more consistent way to study astronomical self-gravitational systems, and discuss the results and possible issues arising with our approach.
An intervening galaxy acts like a gravitational lens and produce multiple images of a single source such as a remote galaxy. Such galaxies have peculiar speeds in addition to the bulk motion appearing due to the expansion of the universe. There is a difference in light arriving time known as the time delay. We calculate more realistic time delays when such peculiar motions are taken into consideration.
Cosmological perturbations along with the background cosmology, in light mass Galileon scenario, will be discussed. Light mass Galileon is a cubic Galileon model with potential and nonminimal coupling. Effects of the nonminimal coupling on power spectrum and bispectrum will be discussed.
We propose and discuss a $\psi$-diagram a novel kind of a plot representing light-like geodesics. We consider spherically symmetric, static spacetimes. The general construction is illustrated with diagrams for light rays in the proximity of the Schwarzschild, Reissner–Nordstrom (charged) and Kerr (rotating) types of black holes.
The idea is developed from the phase portraits illustrating the null geodesics in Schwarzschild spacetime [1]. But our proposal puts greater emphasis on the role of observer and his/her perception of light. We consider various types of observers including local static and freely falling. The construction for freely falling one is of particular interest, since it allows analysis of an interior of the black holes.
The diagrams can improve our understanding of the peculiarities of communication outside and inside horizon of black holes [2] and issues like self-focusing or dimensional reduction [3]. What is more significant light rays of infinite angular momentum observed inside horizon seems to be pictured clearly in this picture. The diagrams can also serve as a suitable illustration of a well-known problem of a Doppler shift near the event horizon [4,5,6] and can be useful in determination of a size of a black hole (problem of black hole shadow) [7].
[1] Dean B, Am. J. Phys. 67, 78 (1999)
[2] A. Augousti et al., Eur. J. Phys 33, 1 (2012)
[3] K. Umetsu, Phys.Lett. B. Volume 692, Issue 1 (2010)
[4] Toporensky, A. et al. Eur.Phys.J. C77 (2017) no.3, 179 arXiv:1611.09807
[5] Radosz, A. et al. Phys.Lett. A373 (2009) 801-803 arXiv:0901.1470 [gr-qc]
[6] Toporensky, A. et al. arXiv:1704.08308 [gr-qc]
[7] A. Abdujabbarov et al., arXiv:1512.05206 [gr-qc]
Wave optics aspects of image formation in strong gravitational fields (in a vicinity of a black hole’s horizon) are discussed. We consider two observers A and B placed (co) radially, r(A)<r(B) within Schwarzschild spacetime. The case of an image formation of an isotropic source of light placed at A in terms of lens arranged at B is analyzed. Emission (A) and propagation (AB) of the null geodesics results in the phase distribution (B), leading to the Airy’s rings pattern on the screen. This process is discussed in detail and illustrated. The comparison with the case of flat (Minkovski) spacetime is made. Research includes both static observers as well as observers freely falling toward an event horizon of a black hole.
A linear coupling between a scalar field and the Gauss–Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. I will consider a scalar-tensor theory of gravity that includes such a coupling and present results of numerical simulations of hair formation in a static, spherically symmetric background. I will also show that backgrounds describing stellar collapse yield similar field configurations. I will then discuss the physical implications of these results and possible extensions of our work to rotating spacetimes.
Abstract
Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity.
We consider two numerical black-hole solution: by P. Kanti, et. al. in the Einstein-dilaton-Gauss-Bonnet theory [Phys.Rev. D54 (1996) 5049-5058] and
the one by H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601] in the Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent these numerical solution in the analytical forms which are accurate not only near the event horizon or far from black hole, but in the whole space. Thereby, the obtained analytical forms of the metrics allow one to study easily all the further properties of the black holes, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representations can serve in the same way as exact solutions.
We analyze spherically symmetric black holes in the general Lovelock gravity for different asymptotics (flat, dS, AdS). We find numerically the metric coefficients of the physically relevant branch of the solutions and the corresponding effective potentials for the gravitational perturbations. We also perform a comprehensive analysis of the eikonal instabilities of the black holes.
TBA
We construct a closed string field theory in the proper-time gauge which is the closed analog of the deformed cubic open string field theory and define the general closed string scattering amplitudes. Taking the zero-slope limit, we explicitly evaluate the three-graviton scattering amplitudes and the four-graviton scattering amplitudes. We discuss in the framework of the closed string field theory, the Kawai-Lewellen-Tye (KLT) relations, which relate the tree level string scattering amplitudes of closed string to those of open string.
Causal Dynamical Triangulations (CDT) is a lattice field theory of quantum gravity based on Regge calculus which can be studied using Monte Carlo techniques. The key feature of CDT is an introduction of a global proper time foliation into spatial hypersurfaces and a requirement that spatial topology is fixed. Measurements showed that CDT parametrized by bare coupling constants of the Regge action has a complicated phase structure. Under spherical topology four phases appeared, and they most likely have a common point, a so called "quadrupole" point. The phase transitions were also measured and it was shown that there exists phase transitions of second or higher order, which opens a possibility of investigating the UV limit. We recently measured the phase structure in toroidal topology that appeared to be quite similar to the one observed in spherical case. This may indicate that the phase structure is independent from the topology of the universe.
The concept of a field theory with nonlinear phase space has recently been introduced, inspired by nontrivial geometry of the particles' phase spaces appearing in several approaches to quantum gravity. In particular, it has been applied in the context of cosmological inflation, by considering a scalar field theory with spherical phase space, defined on the standard FRW background (i.e. general relativity itself is not modified). The scalar field Hamiltonian is assumed to correspond to the continuous XXZ Heisenberg model of a system of spins. For the homogenous cosmology the nonlinearity of the field phase space turns out to be relevant at late cosmological times, when it may lead to a recollapse of universe, while at early times there is a possibility of a bounce, avoiding the initial singularity. Quantum perturbations of the field have been studied in the linear approximation but taking into account the Lorentz symmetry breaking term in the field Hamiltonian. This leads to a correction to the ordinary amplitude of perturbations and a generalization of the Bunch-Davies vacuum state, while the inflationary spectral index remains unchanged in the leading order. The discussed framework is potentially able to bring cosmology and condensed matter physics closer together.
In this presentation, we investigate the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semi-classical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semi-classical quantum field theory.
The so-called state of silence has been obtained as a possible
consequence of deformed space-time structure in the models
of loop quantum gravity. The purpose of the talk is to provide
up to date status of the state of silence in cosmology. Our attention
will be focused on discussing possibility of solving various
cosmological problems employing the state of silence. In particular,
the initial value problem including the issue of initial homogeneity
will be discussed. Generation of cosmological perturbations
and the possibile non-Gaussian contributions will be analyzed.
Furthermore, our current fundamental understanding of the state
of silence and the associated change of signature will be presented.
In the cosmological scheme of conformal cyclic cosmology (CCC), the equations governing the crossover form each aeon to the next demand the creation of a dominant new scalar material, postulated to be dark matter. In order that this material does not build up from aeon to aeon, it is taken to decay away completely over the history of each aeon. The dark matter particles (erebons) may be expected to behave almost as classical particles, though with bosonic properties, being probably of about a Planck mass, and interacting only gravitationally. Their decay would be to gravitational signals, and responsible for the (~scale invariant) temperature fluctuations in the CMB of the succeeding aeon. In our own aeon, erebon decay might show up in signals discernable by gravitational wave detectors.
By applying a parabolic-hyperbolic formulation of the constraints and superposing Kerr-Schild black holes, a simple method is introduced to initialize time evolution of binary systems. As the input parameters are essentially the same as those used in the post-Newtonian (PN) setup the proposed method interrelates various physical expressions applied in PN and in fully relativistic formulations. The global ADM charges are also determined by the input parameters, and no use of boundary conditions in the strong field regime is made.
The main stages of investigations of spinning particle motions in
general relativity, that are described by the equations which appeared
in literature in 1937 due to the pioneer paper of Myron Mathisson
(1897-1940), are under consideration. Period from 1940s up today is
included. The specific properties of the highly relativistic regime of
the spin-gravity coupling and spinning particle motions in the
Schwarzschild, Kerr, and Schwarzschild-de Sitter backgrounds are
discussed.
The horizon conjecture, proved in a case by case basis, states that every supersymmetric smooth horizon admits an $sl(2, \mathbb{R})$ symmetry algebra. However it is unclear how string corrections modify the statement. In this talk I will present the analysis of supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory, and show the conditions for the horizon to admit an $sl(2, \mathbb{R})$ symmetry algebra. In the second part of the talk, I shall present a step further on answering the question how many extreme black holes posses a prescribed near-horizon geometry.
I will discuss the inverse problem of determining the spacetime near an extremal Killing horizon with a prescribed, spatially compact near-horizon geometry. I will show that in Einstein-Maxwell theory with a cosmological constant, the Einstein and Maxwell equations for the infinitesimal deformations transverse to the horizon reduce to a system of elliptic PDEs for the extrinsic curvature of a cross-section of the horizon and the vector potential on the cross-section, hence there exists a finite dimensional moduli space of such deformations. I will then discuss the most general axisymmetric transverse deformation of a Kerr-Newman horizon.
We show nonexistence of non-trivial solutions of the linearised near-horizon equations at the Kerr metric.
Recently, the existence of gravitational waves has been confirmed in experiments. It is worth then to analyze once again one of the most intriguing open problems of the general theory of relativity: the problem of vacuum type N with twist. It is well known that according to the "peeling off theorem" the graviational radiation far away from a bounded source is of the type N. All vacuum type N metrics can be divided into four classes. Three classes are explicitly known. They are characterized by the vanishing of the twist (parameter which describes the properties of the congruences of the null geodesics). All of them have singularities and this is the reason why they cannot be treated as a model of the gravitational radiation. Among the metrics with nonzero twist only one solution is known explicitly (Hauser, 1974). This solution has singularities as well. Plenty different approaches to the twisting vacuum type N problem have been presented for last 40 years. Existence of the Killing vectors (KV) or homothetic Killing vectors (HKV) simplify the problem a little. Nevertheless, even two KV or one KV and one HKV enable us to reduce the field equations to the strongly nonlinear and complicated ODE of the third order. A few forms of such equations have been proposed by different authors. For some values of the homothetic parameter these equations become easier and shorter, but we are still far from the finding the explicit solutions other than the Houser's one. In what follows we present the approach to the twisting vacuum type N problem by studying hyperheavenly spaces equipped with two KV or one KV and one HKV. The field equations are reduced to the nonlinear ODE of the fifth order. Our considerations remain valid in all 4-dimensional real spaces of arbitrary signature, as well as in the complex spaces. Finally, some new family of the metrics which admit two Killing vectors is presented. It seems, that this family does not admit any Lorentzian real slice.
A new technique is presented in order to build tetrads in four-dimensional Lorentzian spacetimes. These tetrads have special useful properties in general relativity, astrophysics and also particle physics. A new fundamental result is proved in group theory. The group SO(2) (spatial rotations) is isomorphic to the group SO(1; 1) (boosts) plus two kinds of discrete transformations. One of them is not Lorentzian. That is, a compact group is isomorphic to a non-compact group plus two different kinds of discrete transformations (1;2). The electromagnetic local gauge group is proved to be isomorphic to the local group of transformations of these particular kind of tetrads. Therefore, establishing a concrete link between internal and spacetime local groups of transformations. These new tetrads also diagonalize the electromagnetic stress-energy tensor for non-null electromagnetic fields, any stress-energy tensor, in a general, covariant and local way. These new tetrads also introduce maximum simplification in the Einstein-Maxwell differential equations, and introduce maximum
simplification in the expression of the electromagnetic field itself, in any curved four-dimensional Lorentzian spacetime, allowing for the identification of its degrees of freedom in two local scalars. These tetrads introduce simplification in spacetime evolution algorithms, specially in astrophysical situations related, for example, to neutron stars (3). This new tetrad can be applied and introduce simplification in the analysis of astrophysical relativistic problems where vorticity is present through the Carter-Lichnerowicz equation (4).
REFERENCES
(1) A. Garat, Tetrads in geometrodynamics, J. Math. Phys. 46, 102502 (2005). arXiv:gr-qc/0412037
(2) A. Garat, Tetrads in Yang-Mills geometrodynamics, Gravitation and Cosmology, (2014) Vol.20 No. 1, pp. 116-126. Pleiades Publishing Ltd. arXiv:gr-qc/0602049.
(3) A. Garat, Euler observers in geometrodynamics, Int. J. Geom. Meth. Mod. Phys., Vol. 11 (2014), 1450060. arXiv:gr-qc/1306.4005
(4) A. Garat, Covariant diagonalization of the perfect fluid stress-energy tensor, Int. J. Geom. Meth. Mod. Phys., Vol. 12 (2015), 1550031. arXiv:gr-qc/1211.2779
I will review quasi-local aspects of the gravitational field, in particular, energy as a Hamiltonian for the finite region. The considerations are closely related to the initial boundary problem for the gravitational field.
I investigate rotating Bowen-York-type initial data for Einstein equations with a positive cosmological constant. They are obtained using the so-called conformal method. From the technical point of view, its most important part amounts to solving a corresponding Lichnerowicz equation. The first analysis of this equation was recently published by Bizoń, Pletka and Simon. Here I focus on additional branches of its solutions, bifurcating from the already known ones. I will briefly discuss the numerical method used to find such solutions, and also comment on the completeness of the obtained bifurcation diagram.
Starting from the cyclic models of the parallel universes with different evolution of the fundamental constants and the same geometry I will study the quantum mechanical entanglement problem of the classically separated universes. The basic approach will be based on the third-quantization formalism of quantum cosmology. Some interesting properties of quantum entanglement (entropy and temperature) at the points corresponding to classical singularities and maximum expansion will be discussed.
Ref: K. Marosek et al. MNRAS, 461, 2777 (2016); S.Robles-Perez et al. Phys. Rev. D. 95, 085505 (2017)
It is possible to include unobservable fields and particles in cosmological models (warm inflation of Berera and Moss) as well as contribution of quantum fluctuations (Starobinsky, Vilenkin) by adding a noise term to classical equations. Such a noise term breaks the energy-momentum conservation. I introduce a compensating term to the energy-momentum repairing the conservation laws. Solutions of the resulting stochastic Einstein equations will be discussed.
The parabolic-hyperbolic formulation of the initial data of the Einstein equations for multiple black holes systems has been proposed recently [1-3]. It provides an alternative to the traditional conformal method [4]. During the talk, a numerical implementation of the approach to the initial data problem of general relativity will be presented. It will involve black holes described by a metric of a Kerr-Schild form.
[1] I.Racz, Constraints as evolutionary systems, Class. Quant. Grav. 33, 015014 (2016).
[2] I.Racz, A simple method of constructing binary black hole initial data, arXiv:1605.01669 (2017).
[3] I.Racz, On the ADM charges of multiple black holes, arXiv:1608.02283 (2017).
[4] G.B.Cook, Initial data for numerical relativity, Living Rev. Rel. 3, 5 (2000).
Abstract: Already in the 30s, Schroedinger observed that all null Maxwell fields solve the equations for the electromagnetic field in any non-linear electrodynamics. More generally, we study properties of “universal” p-forms, i.e., electromagnetic fields that solve simultaneously any generalized electrodynamics (for which the field equations contain arbitrary powers and derivatives of the field strength). Some results including the coupling to Einstein's gravity are also discussed, and analogies with “universal spacetimes” (which solve simultaneously virtually any theory of gravity) mentioned.
Refs.: M. Ortaggio, V. Pravda, Electromagnetic fields with vanishing scalar invariants, Class.Quant.Grav. 33 (2016), 115010; S. Hervik, M. Ortaggio, V. Pravda, to appear
We present a modified method of investigation of particle content of a metric theory of gravitation whose Lagrangian explicitly depends on the Weyl tensor. Without any resort to observations we consider the problem from purely field–theoretical viewpoint. We apply the tenet of field theory that each classical field should correspond to a quantum particle with definite mass and spin and deterministic dynamics. These features may be established only for free fields (decoupled from spacetime curvature) and this is achieved by putting all coupling constants in the gravitational Lagrangian equal to zero. This method shows the Lagrangian should be free of the Weyl tensor since it generates a field in a gravitational multiplet which is dynamically undetermined and in consequence has no definite mass and spin.
We review some recent results concerning inflationary scenario in the framework of Starobinski-Palatini FLRW cosmology, which can be reduced to the two-dimensional singular (piecewise-smooth) dynamical system of Newtonian type. Therefore, it can be describe in geometric terms of the corresponding potential function. Analytical calculations are given for the case with dust matter and cosmological constant. We investigate the model in both Jordan and Einstein frames. We demonstrate that after transition to the Einstein frame we obtain both decaying Lambda and the form of a scalar field potential. In particular, we discuss slow-roll parameters, graceful exit and confront the model against observational data.
The lack of external and fixed time is encoded into the canonical formalism of general relativity by means of the Hamiltonian constraint. The lack of time does not imply the lack of evolution but rather brings to the fore the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. I will take this idea seriously and try to understand that what it may imply for quantum mechanics when the fixed external time is replaced by arbitrary internal clocks.