Abstract
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.
Highlights
On author request a Living Reviews article can be amended to include errata and small additions to ensure that the most accurate and up-to-date information possible is provided
Applications of the quasi-local framework can be summarized as follows: Black hole mechanics Isolated horizons extract from the notion of Killing horizons, just those conditions which ensure that the horizon geometry is time independent; there may be matter and radiation even nearby [68]
(With these conventions, de Sitter space-time has positive cosmological constant Λ.) We assume that Tab satisfies the dominant energy condition Cauchy surfaces will be denoted by M, isolated horizons by ∆, and dynamical horizons by H
Summary
Research inspired by black holes has dominated several areas of gravitational physics since the early seventies. In contrast to apparent horizons, they are not tied to the choice of a partial Cauchy slice This framework provides a new perspective encompassing all areas in which black holes feature: quantum gravity, mathematical physics, numerical relativity, and gravitational wave phenomenology. It brings out the underlying unity of the subject. Applications of the quasi-local framework can be summarized as follows: Black hole mechanics Isolated horizons extract from the notion of Killing horizons, just those conditions which ensure that the horizon geometry is time independent; there may be matter and radiation even nearby [68]. (With these conventions, de Sitter space-time has positive cosmological constant Λ.) We assume that Tab satisfies the dominant energy condition (as the reader can tell, several of the results will hold under weaker restrictions.) Cauchy (and partial Cauchy) surfaces will be denoted by M , isolated horizons by ∆, and dynamical horizons by H
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