High and low dimensions in the black hole negative mode

Asnin, V.; Gorbonos, Dan; Hadar, S.; Kol, B.; Levi, M.; Miyamoto, U.

doi:10.1088/0264-9381/24/22/015

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High and low dimensions in the black hole negative mode

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Asnin, V., Gorbonos, D., Hadar, S., Kol, B., Levi, M., & Miyamoto, U. (2007). High and low dimensions in the black hole negative mode. Classical and Quantum Gravity, 24(22), 5527-5540. doi:10.1088/0264-9381/24/22/015.

Cite as: https://hdl.handle.net/21.11116/0000-0005-A4E8-C

Abstract

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black string instability. We analyze the eigenvalue as a function of spacetime dimension lambda = lambda(d) by constructing two perturbative expansions: one for large d and the other for small d - 3, and determining as many coefficients as we are able to compute analytically. By joining the two expansions, we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d = 4.