Birkhoff's Theorem in Higher Derivative Theories of Gravity

Abstract

In this paper we present a class of higher derivative theories of gravity which admit Birkhoff's theorem. In particular, we explicitly show that in this class of theories, although generically the field equations are of fourth order, under spherical (plane or hyperbolic) symmetry, all the field equations reduce to second order and have exactly the same or similar structure to those of Lovelock theories, depending on the spacetime dimensions and the order of the Lagrangian.

7 pages, no figures. v1: This version received an Honorable Mention from the Gravity Research Foundation - 2011 Awards for Essays on Gravitation. v2: Expanded version. To appear in CQG

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• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions

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