Abstract
Critical gravity is a quadratic curvature gravity in four dimensions which is ghost-free around the AdS background. Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition. In addition, the solution shows that the Wald-Kodama dynamical entropy of a black hole is negative and can decrease. These properties expose the pathological aspects of critical gravity at the non-perturbative level.
Highlights
In addition to renormalizability, unitarity should be required for classical theories to be quantized in a perturbative manner
Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition
We have obtained Vaidya-type exact solutions in the most general quadratic curvature gravity in four dimensions in the presence of a null dust fluid and a Maxwell field. These solutions represent a dynamical black hole defined by a future outer trapping horizon and we have studied their physical properties in the case with the positive energy density of the null dust
Summary
We consider the most general quadratic curvature gravity in n(≥ 3) dimensions: I. where Im is the action for matter fields. Β, and γ are coupling constants to the quadratic terms and LGB is the Gauss-Bonnet term defined by LGB := R2 − 4Rμν Rμν + RμνρσRμνρσ. The energy-momentum tensor Tμν for matter comes from the matter action Im. Here Hμν is the quadratic curvature tensor defined by. The Gauss-Bonnet term is dynamical only for n ≥ 5 and Hμ(3ν) ≡ 0 holds for n ≤ 4
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