TY - JOUR

T1 - Gravitational waves in Kasner spacetimes and Rindler wedges in Regge-Wheeler gauge

T2 - Formulation of Unruh effect

AU - Sugiyama, Yuuki

AU - Yamamoto, Kazuhiro

AU - Kobayashi, Tsutomu

N1 - Funding Information:
We thank T. Inagaki, M. Taniguchi, Y. Matsuo, H. Sakamoto, H. Shimoji, D. Sakuma, K. Ueda, T. Tanaka, A. Higuchi, Y. Nambu, J. Soda, S. Kanno, A. Matsumura, and H. Suzuki for useful discussions related to the topic in the present paper. This work was partially supported by MEXT/JSPS KAKENHI Grant Numbers 17K05444 (K. Y.), 17H06359 (K. Y.), JP20H04745 (T. K.), and JP20K03936 (T. K.).
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/4/7

Y1 - 2021/4/7

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.103.083503

DO - 10.1103/PhysRevD.103.083503

M3 - Article

AN - SCOPUS:85104849621

VL - 103

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 8

M1 - 083503

ER -