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

TL;DR

This paper analytically derives and quantizes gravitational wave solutions in Kasner and Rindler spacetimes, exploring their relation and the Unruh effect for accelerated observers.

Contribution

It provides explicit analytic solutions for gravitational waves in Kasner and Rindler regions and develops their quantum field theory, linking mode functions via analytic continuation.

Findings

Mode functions in Rindler wedges are analytic continuations of Kasner modes.

Quantized gravitational waves exhibit the Unruh effect for accelerated observers.

Master variables behave as massless scalar fields, simplifying analysis.

Abstract

We derive the solutions of gravitational waves in the future (F) expanding and the past (P) shrinking Kanser 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 quantized gravitational waves for an observer in a uniformly accelerated motion in Minkowski spacetime.