Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow

Abstract

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem to may be extended to give a negative lower bound for the mass of asymptotically Anti-de-Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form ${\Sigma }_g\times \mathbb{R}$, in terms of the cosmological constant. We also show how the method gives a lower bound for for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, $|Z(Q,P)|$ of the double extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function $|Z(Q,P)|$. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function $|Z(Q,P)|$. There are hints that higher dimensional generalizations may involve the Yamabe conjectures.

13pp. latex

References in corpus (7)

• Black Holes and Critical Points in Moduli Space
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Topological Censorship and Higher Genus Black Holes
• Black Holes of Negative Mass
• Collapsing Shells and the Isoperimetric Inequality for Black Holes
• Scalar charges and the first law of black hole thermodynamics
• Upper bound for entropy in asymptotically de Sitter space-time

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