High and Low Dimensions in The Black Hole Negative Mode
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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 space-time dimension 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. Joining the two expansions we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d=4.
17 pages, 4 figures. v2: added reference. v3: published version
17 pages, 4 figures. v2: added reference. v3: published version