1201.5601 (Julio Oliva et al.)

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

Julio Oliva, Sourya Ray

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.

View original: http://arxiv.org/abs/1201.5601