High and Low Dimensions in The Black Hole Negative Mode

Details High and Low Dimensions in The Black Hole Negative Mode High and Low Dimensions in The Black Hole Negative Mode

2007-06-12

arxiv.org/abs/0706.1555v3

Class.Quant.Grav.24:5527-5540,2007

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 4 figures. v2: added reference. v3: published version

Scientific paper

10.1088/0264-9381/24/22/015

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.

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