Speaker
Prof.
Gopinath Kamath
(Indian Institute of Technology Tirupati,Tirupati 517506,India)
Description
The spherically symmetric Schwarzschild solution is a staple of textbooks on general
relativity; not so perhaps, the static but cylindrically symmetric ones, though they were obtained almost contemporaneously by H. Weyl, Ann.Phys.Lpz.**54**,117(1917) and T. Levi-Civita, Atti Acc.Lincei Rend. **28** ,101(1919). A renewed interest in this subject recently in C.S. Trendafilova and S.A.Fulling , Eur.J.Phys. **32**,1663(2011) – to which the reader is referred to for more references, motivates this work; to elaborate, we rework the Antonsen-Bormann idea – F.Antonsen and K.Bormann,arXiv:hep-th/9608141v1 – that was originally intended to compute the heat kernel in curved space, to determine – following D.McKeon and T.Sherry, Phys.Rev.D **35**,3584(1987) – the zeta-function associated with the Lagrangian density for a massive real scalar field theory in 3 + 1 dimensional
stationary curved space, the metric for which is cylindrically symmetric. As a calculation, it pays to use a metric characterised by the parameters j, k with j = - 4 and k = - 4, j,k being integer solutions to the equation 2(j + k)= - jk . Importantly, this enables – unlike the obvious choice j = 2, k = - 1, an easy evaluation of the momentum integrals implied in the Schwinger expansion for the zeta-function. Happily, the work reported here is easy to go through – relative to that presented by the author at ICHEP2014 with the Schwarzschild metric, and this contrast will be taken up in some
detail.
Author
Prof.
Gopinath Kamath
(Indian Institute of Technology Tirupati,Tirupati 517506,India)
