Maximally Symmetric Spin-Two Bitensors on $S^3$ and $H^3$

Details Maximally Symmetric Spin-Two Bitensors on $S^3$ and $H^3$ Maximally Symmetric Spin-Two Bitensors on $S^3$ and $H^3$

1994-11-08

arxiv.org/abs/gr-qc/9411023v2

Phys.Rev. D51 (1995) 5491-5497

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, RevTeX, uuencoded compressed .tex file, minor typos corrected

Scientific paper

10.1103/PhysRevD.51.5491

The transverse traceless spin-two tensor harmonics on $S^3$ and $H^3$ may be denoted by $T^{(kl)}{}_{ab}$. The index $k$ labels the (degenerate) eigenvalues of the Laplacian $\square$ and $l$ the other indices. We compute the bitensor $\sum_l T^{(kl)}{}_{ab}(x) T^{(kl)}{}_{a'b'}(x')^*$ where $x,x'$ are distinct points on a 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 closed Friedman-Robertson-Walker cosmologies.

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