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A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces…
This is a review of current theory of black-hole dynamics, concentrating on the framework in terms of trapping horizons. Summaries are given of the history, the classical theory of black holes, the defining ideas of dynamical black holes,…
An essentially complete new paradigm for dynamical black holes in terms of trapping horizons is presented, including dynamical versions of the physical quantities and laws which were considered important in the classical paradigm for black…
We explore various aspects of dynamical black holes defined by a future outer trapping horizon in $n(\ge 5)$-dimensional Einstein-Gauss-Bonnet gravity. In the present paper, we assume that the spacetime has symmetries corresponding to the…
A property well known as the first law of black hole is a relation among infinitesimal variations of parameters of stationary black holes. We consider a dynamical version of the first law, which may be called the first law of black hole…
The close similarities of the three laws of black hole mechanics, discovered by Bardeen, Carter and Hawking, with the laws of thermodynamics led to the identification of a multiple of the area of the event horizon with entropy. However,…
We consider two proposals for defining black hole entropy in spherical symmetry, where the horizon is defined locally as a trapping horizon. The first case, boundary terms in a dual-null form of the reduced action in two dimensions, gives a…
For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The…
Trapped regions bounded by horizons are the defining features of black holes. However, formation of a singularity-free apparent horizon in finite time of a distant observer is consistent only with special states of geometry and matter in…
In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those…
The third law of black hole dynamics states that it is impossible, through any classical perturbation of a stationary configuration, to reduce the surface gravity of a black hole to zero. In this work, we examine the validity of this law…
A unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity. This equation expresses the gradient of the active gravitational energy E according to the Einstein equation,…
A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A space-time representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such…
Singularity-free regular black holes are a popular alternative to the singular mathematical black holes predicted by general relativity. Here, we derive a generic condition that spherically symmetric dynamical regular black holes must…
The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the…
The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian can be defined. The first law is established for stationary spacetimes, and the second law…
A generic formula for the entropy of three-dimensional black holes endowed with a spin-3 field is found, which depends on the horizon area A and its spin-3 analogue, given by the reparametrization invariant integral of the induced spin-3…
Black holes can be practically located (e.g. in numerical simulations) by trapping horizons, hypersurfaces foliated by marginal surfaces, and one desires physically sound measures of their mass and angular momentum. A generically unique…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
In a recent paper (gr-qc/0509107) the author and Rick Schoen obtained a generalization to higher dimensions of a classical result of Hawking concerning the topology of black holes. It was proved that, apart from certain exceptional…