Maximally symmetric spin-two bitensors on S3 and H3

Allen, Bruce

doi:10.1103/PhysRevD.51.5491

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Maximally symmetric spin-two bitensors on S3 and H3

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Allen, Bruce
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Citation

Allen, B. (1995). Maximally symmetric spin-two bitensors on S3 and H3. Physical Review D, 51(10), 5491-5497. doi:10.1103/PhysRevD.51.5491.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5BD4-7

Abstract

The transverse traceless spin-two tensor harmonics on S3 and H3 may be denoted by Tab(kl). The index k labels the (degenerate) eigenvalues of the Laplacian √ and l the other indices. We compute the bitensor ∑tTab(kl)(x)Ta′b′(kl)(x′)* where x,x′ are distinct points on a three-dimensional sphere or hyperboloid of unit radius. These quantities may be used to find the correlation function of a stochastic background of gravitational waves in spatially open or close Friedmann-Robertson-Walker cosmologies.