Static Gauss-Bonnet black holes at large D

• Published in: The journal of high energy physics Vol. 2017; no. 5; pp. 1 - 26
• Main Authors: Chen, Bin, Li, Peng-Cheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2017; Springer Nature B.V; SpringerOpen
• Subjects: Black Holes; Classical and Quantum Gravitation; Classical Theories of Gravity; Cosmological constant; Deformation effects; Elementary Particles; Gravitation; High energy physics; Mathematical analysis; Perturbation methods; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Stability; String Theory; Classical Theories of Gravity; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2017)025

A bstract We study the static black holes in the large D dimensions in the Gauss-Bonnet gravity with a cosmological constant, coupled to the Maxewell theory. After integrating the equation of motion with respect to the radial direction, we obtain the effective equations at large D to describe the nonlinear dynamical deformations of the black holes. From the perturbation analysis on the effective equations, we get the analytic expressions of the frequencies for the quasinormal modes of charge and scalar-type perturbations. We show that for a positive Gauss-Bonnet term, the black hole could become unstable only if the cosmological constant is positive, otherwise the black hole is always stable. However, for a negative Gauss-Bonnet term, we find that the black hole could always be unstable. The instability of the black hole depends not only on the cosmological constant and the charge, but also significantly on the Gauss-Bonnet term. Moreover, at the onset of instability there is a non-trivial static zero-mode perturbation, which suggests the existence of a new non-spherically symmetric solution branch. We construct the non-spherical symmetric static solutions of the large D effective equations explicitly.