### 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.

### Primary author

Prof.
Gopinath Kamath
(Indian Institute of Technology Tirupati,Tirupati 517506,India)