Gravitational waves in Kasner spacetimes and Rindler wedges in Regge-Wheeler gauge: Formulation of Unruh effect

Yuuki Sugiyama, Kazuhiro Yamamoto, Tsutomu Kobayashi

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1 Citation (Scopus)

Abstract

We derive the solutions of gravitational waves in the future (F) expanding and past (P) shrinking Kasner spacetimes, as well as in the left (L) and right (R) Rindler wedges in the Regge-Wheeler gauge. The solutions for all metric components are obtained in an analytic form in each region. We identify the master variables, which are equivalent to massless scalar fields, to describe the gravitational degrees of freedom for the odd-parity and even-parity modes under the transformation in the two-dimensional plane-symmetric space. Then, the master variables are quantized, and we develop the quantum field theory of the gravitational waves in the F, P, L, and R regions. We demonstrate that the mode functions of the quantized gravitational waves in the left and right Rindler wedges are obtained by an analytic continuation of the left-moving and right-moving wave modes in Kasner spacetime. On the basis of these analyses, we discuss the Unruh effect of the quantized gravitational waves for an observer in a uniformly accelerated motion in Minkowski spacetime in an explicit manner for the first time.

Original languageEnglish
Article number083503
JournalPhysical Review D
Volume103
Issue number8
DOIs
Publication statusPublished - Apr 7 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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