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

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.

23 pages, 1 figure

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• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Unruh effect and its applications
• Theory of cosmological perturbations in an anisotropic universe
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• Predictions from an anisotropic inflationary era
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Entanglement of the Vacuum between Left, Right, Future, and Past: The Origin of Entanglement-Induced Quantum Radiation
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• A quantisation procedure in the presence of an initial Kasner singularity: primordial gravitational waves from triaxially anisotropic pre-inflation

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• Gravitational Waves Emitted by a Uniformly Accelerated Mass: The Role of Zero-Rindler-Energy Modes in the Classical and Quantum Descriptions
• Gravitational bremsstrahlung and the Fulling-Davies-Unruh thermal bath
• On the propagation of gravitational waves in matter-filled Bianchi I universe