Birkhoff's Theorem in Higher Derivative Theories of Gravity II: Asymptotically Lifshitz Black Holes

Abstract

As a continuation of a previous work, here we examine the admittance of Birkhoff's theorem in a class of higher derivative theories of gravity. This class is contained in a larger class of theories which are characterized by the property that the trace of the field equations are of second order in the metric. The action representing these theories are given by a sum of higher curvature terms. Moreover the terms of a fixed order k in the curvature are constructed by taking a complete contraction of k conformal tensors. The general spherically (hyperbolic or plane) symmetric solution is then given by a static asymptotically Lifshitz black hole with the dynamical exponent equal to the spacetime dimensions. However, theories which are homogeneous in the curvature (i.e., of fixed order k) possess additional symmetry which manifests as an arbitrary conformal factor in the general solution. So, these theories are analyzed separately and have been further divided into two classes depending on the order and the spacetime dimensions.

10 pages, no figures. v2: minor corrections. Rejected by CQG. v3: Final version, to appear in PRD with the title "Birkhoff's Theorem in Higher Derivative Theories of Gravity II"

References in corpus (4)

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• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
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• The tetralogy of Birkhoff theorems
• Holographic Studies of The Generic Massless Cubic Gravities
• Holographic entanglement entropy for perturbative higher-curvature gravities
• Cardy formula for charged black holes with anisotropic scaling
• Charged Black Holes in Colored Lifshitz Spacetimes
• Conformal Tensors via Lovelock Gravity
• Is Birkhoff's Theorem Valid in Einstein-Aether Theory?
• Seeded vacuum decay with Gauss-Bonnet
• Existence of Vacuum Wormholes in Einsteinian Cubic Gravity
• Gravitational Wormholes
• Null-null components of the generalized Einstein tensor for Lovelock models
• Exact Solutions in Weyl-Cubed Gravity