Abstract
We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an n + 3-dimensional Schwarzschild black hole background in the large dimension limit, due to the SO(n + 2)-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly we find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter ∆. We show that the behavior of the one-loop determinant at large ∆ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit.
Highlights
Theoretic approaches, and the quasinormal mode method
We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an n + 3-dimensional Schwarzschild black hole background in the large dimension limit, due to the SO(n + 2)-type tensor and vector fluctuations, using the quasinormal mode method
We show that the behavior of the one-loop determinant at large ∆ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit
Summary
We review the large dimension limit of a Schwarzschild black hole, as exhibited in [34] and [31]. [34] studied the linearized gravitational perturbations around the Schwarzschild black hole in the large dimension limit, and computed the quasinormal spectrum of its oscillations in analytic form in the 1/D expansion. They found two distinct sets of modes:. When finding the quasinormal modes, as done in [34], the key idea is to first solve the linearized field equation (2.6) perturbatively in the 1/n expansion in the near region, with ingoing boundary conditions imposed at the horizon. At large frequencies, another set of modes lives exclusively in the far region, at larger radius than the maximum of the potential. As we will see we need to extend the calculation of [34] to include a formal mass for the graviton
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