Isolated horizon

It was customary to represent black hole horizons via stationary solutions of field equations, i.e., solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole. While this simple idealization was natural as a starting point, it is overly restrictive. Physically, it should be sufficient to impose boundary conditions at the horizon which ensure only that the black hole itself is isolated. That is, it should suffice to demand only that the intrinsic geometry of the horizon be time independent, whereas the geometry outside may be dynamical and admit gravitational and other radiation.

An advantage of isolated horizons over event horizons is that while one needs the entire spacetime history to locate an event horizon, isolated horizons are defined using local spacetime structures only. The laws of black hole mechanics, initially proved for event horizons, are generalized to isolated horizons.

An isolated horizon ${\displaystyle (\Delta \,,[\ell ])}$ refers to the quasilocal definition of a black hole which is in equilibrium with its exterior, and both the intrinsic and extrinsic structures of an isolated horizon (IH) are preserved by the null equivalence class ${\displaystyle [\ell ]}$. The concept of IHs is developed based on the ideas of non-expanding horizons (NEHs) and weakly isolated horizons (WIHs): A NEH is a null surface whose intrinsic structure is preserved and constitutes the geometric prototype of WIHs and IHs, while a WIH is a NEH with a well-defined surface gravity and based on which the black-hole mechanics can be quasilocally generalized.

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