Notes on the Area Theorem

Abstract

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes $positive$ energy matter, ``independent of the details of the gravity action''. I use this process to study the dynamics of the ``inner'' as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon ``can decrease'', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon ``never decrease'' such as the usual area theorem still works in our examples, though this is quite non-trivial in general. There exist the instability of the inner horizons and the connected effects of ``mass inflation'' but, according to more detailed analysis, it seems that the instability is not important in my analysis. I also find a ``generalized'' area theorem by combining those of the outer and inner horizons.

Minor changes in the section organization; Added footnotes and references; Accepted in Class. Quant. Grav

References in corpus (32)

• The World as a Hologram
• The Black Hole in Three Dimensional Space Time
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• General Laws of Black-Hole Dynamics
• On Black Hole Entropy
• The (2+1)-Dimensional Black Hole
• Holographic Gravitational Anomalies
• Black holes and asymptotics of 2+1 gravity coupled to a scalar field
• Increase of Black Hole Entropy in Higher Curvature Gravity
• The black holes of topologically massive gravity
• Holography with Gravitational Chern-Simons Term
• Constant Curvature Black Holes
• Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity
• Anti-de Sitter space and black holes
• BTZ Black Hole with Chern-Simons and Higher Derivative Terms
• The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method
• Miens of The Three Dimensional Black Hole
• Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion
• Modifications of the BTZ black hole by a dilaton/scalar
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity
• Near-Horizon Conformal Symmetry and Black Hole Entropy in Any Dimension
• Conserved Charges of Higher D Kerr-AdS Spacetimes
• Birkhoff's Theorem for Three-Dimensional AdS Gravity
• A finite action for three dimensional gravity with a minimally coupled scalar field
• Black Holes in Three Dimensional Topological Gravity
• Non-linear instability of Kerr-type Cauchy horizons
• Thermodynamics of Exotic Black Holes, Negative Temperature, and Bekenstein-Hawking Entropy
• Interior Structure of a Charged Spinning Black Hole in $(2+1)$-Dimensions
• Fate of Three-Dimensional Black Holes Coupled to a Scalar Field and the Bekenstein-Hawking Entropy
• Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges

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