Effects of non-commutative geometry on black hole properties
A. A. Araújo Filho, J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio, Ali Övgün
Hide abstract | Show figures | Show BibTeX | Show discussion | View PDF | 2406.12015v1
In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.
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The generalized uncertainty principle within the ordinary framework of quantum mechanics
Y. V. Przhiyalkovskiy
Hide abstract | Show figures | Show BibTeX | Show discussion | View PDF | 2407.09123v1
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term results in a generalized uncertainty principle, which limits the minimum uncertainty in particle position to the Planck length. However, such a deformation of the commutator significantly changes the formalism, making it separate from the canonical formalism of quantum mechanics. In this study, it is shown that the deformed algebra of position and momentum operators can be incorporated into the framework of ordinary quantum mechanics.
