Black Holes in Higher Dimensional Gravity Theory with Quadratic in Curvature Corrections

Abstract

Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form ${\mathcal{C}}^2=C_{\alpha \beta \gamma \delta }{C}^{\alpha \beta \gamma \delta }$. The Gauss-Bonnet equation in four-dimensional (4D) spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar ${\mathcal{C}}^2$ correction. An important new feature of the spaces with dimension $D>4$ is that in the presence of the Weyl curvature-squared term a solution necessary differs from the corresponding `classical' vacuum Tangherlini metric. This difference is related to the presence of {\em secondary} or {\em induced} hair. We explore how the Tangherlini solution is modified by `quantum corrections', assuming that the gravitational radius $r_0$ is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ODE (master equation).

arXiv comment12 pages, 4 figures. A few references added, some details added to better illustrate the result. Version accepted in Physical Review D

References in corpus (19)

• Black Holes in Higher Dimensions
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Entropy of Lovelock Black Holes
• General Kerr-NUT-AdS Metrics in All Dimensions
• Effective Action of Vacuum: Semiclassical Approach
• Quantum Hair on Black Holes
• The Lovelock Black Holes
• Increase of Black Hole Entropy in Higher Curvature Gravity
• Conserved charges for gravity with locally AdS asymptotics
• Regular black holes in quadratic gravity
• How Many New Worlds Are Inside a Black Hole?
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions I -- Asymptotically Flat Black Holes --
• Universal regularization prescription for Lovelock AdS gravity
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Curvature invariants of static spherically symmetric geometries
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with $k=\pm 1$ --
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions II -- Asymptotically AdS Topological Black Holes --
• Extremal dyonic black holes in D=4 Gauss-Bonnet gravity
• Higher dimensional black holes with a generalized gravitational action

Cited by in corpus (22)

• Aspects of Quadratic Gravity
• Static Solutions for 4th order gravity
• On Newtonian singularities in higher derivative gravity models
• Constraints on Modified Gravity Models from White Dwarfs
• A Unified Approach to Variational Derivatives of Modified Gravitational Actions
• Multi-Scalar-Tensor Equivalents for Modified Gravitational Actions
• Silhouettes of invisible black holes
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• Features and stability analysis of non-Schwarzschild black hole in quadratic gravity
• Gravitational waves and stability of cosmological solutions in the theory with anomaly-induced corrections
• Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity
• Generation of Cosmological Flows in General Relativity (Features and Properties of Integrable Singularities)
• Dynamics of the Laplace-Runge-Lenz vector in the quantum-corrected Newton gravity
• Gravitational Lensing of a star by a rotating black hole
• Qualifying ringdown and shadow of black holes under general parametrized metrics with photon orbits
• Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form
• On effective models of regular black holes inspired by higher-derivative and nonlocal gravity
• On static and spherically symmetric solutions of Starobinsky model
• Emerging Newtonian potential in pure $R^2$ gravity on a de Sitter background
• The static charged black holes with Weyl corrections
• Black Hole Solutions in $R^2$ Gravity
• Visible shapes of black holes M87* and SgrA*