# Isolated and Dynamical Horizons and Their Applications

**Abhay Ashtekar
**

Institute for Gravitational Physics and Geometry

Pennsylvania State University

University Park, PA 16801, U.S.A.

and

Kavli Institute of Theoretical Physics

University of California

Santa Barbara, CA 93106-4030, U.S.A.

and

Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut

Am Mühlenberg 1, 14476 Golm, Germany

and

Erwin-Schrödinger-Institut

Boltzmanngasse 9, 1090 Vienna, Austria

http://cgpg.gravity.psu.edu/people/Ashtekar/

**Badri Krishnan
**

Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut

Am Mühlenberg 1, 14476 Golm, Germany

and

Erwin-Schrödinger-Institut

Boltzmanngasse 9, 1090 Vienna, Austria

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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.