Black hole one-loop determinants in the large dimension limit

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 $\Delta$. We show that the behavior of the one-loop determinant at large $\Delta$ 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.

arXiv comment36 pages, 4 figures; v2: minor corrections, refs added, matches published version

References in corpus (36)

• Heat kernel expansion: user's manual
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• One-loop Partition Functions of 3D Gravity
• The large D limit of General Relativity
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Large D gravity and low D strings
• Black hole determinants and quasinormal modes
• Entropy Function and AdS(2)/CFT(1) Correspondence
• The Heat Kernel on AdS_3 and its Applications
• Effective theory of Black Holes in the 1/D expansion
• Decoupling and non-decoupling dynamics of large D black holes
• A One-loop Test of Quantum Black Holes in Anti de Sitter Space
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Instability of rotating black holes: large D analysis
• The Heat Kernel on $AdS$
• Tweaking one-loop determinants in AdS${}_3$
• The large D black hole Membrane Paradigm at first subleading order
• Currents and Radiation from the large $D$ Black Hole Membrane
• Rotating black holes and black bars at large D
• On Brane Instabilities in the Large $D$ Limit
• Charged rotating black holes in higher dimensions
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• The large D black hole dynamics in AdS/dS backgrounds
• The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space
• Stationary Solutions from the Large D Membrane Paradigm
• Divergences and Boundary Modes in N=8 Supergravity
• Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods
• One loop partition function from normal modes for $\mathcal{N}=1$ supergravity in AdS${}_3$
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• Connecting quasinormal modes and heat kernels in 1-loop determinants
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• Partition Functions with spin in AdS_2 via Quasinormal Mode Methods
• Computing black hole partition functions from quasinormal modes

Cited by in corpus (1)

• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT