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 λ = λ(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.
Original language | English |
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Pages (from-to) | 5527-5540 |
Number of pages | 14 |
Journal | Classical and Quantum Gravity |
Volume | 24 |
Issue number | 22 |
DOIs | |
State | Published - 2007 |