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Spin-Coefficient Form of the New Laws of Black-Hole Dynamics

Sean A. Hayward
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Abstract

General laws of black-hole dynamics, some of which are analogous to the laws of thermodynamics, have recently been found for a general definition of black hole in terms of a future outer trapping horizon, a hypersurface foliated by marginal surfaces of a certain type. This theory is translated here into spin-coefficient language. Second law: the area form of a future outer trapping horizon is generically increasing, otherwise constant. First law: the rate of change of the area form is given by an energy flux and the trapping gravity. Zeroth law: the total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant. Topology law: a compact future outer marginal surface has spherical topology. Signature law: an outer trapping horizon is generically spatial, otherwise null. Trapping law: spatial surfaces sufficiently close to a compact future outer marginal surface are trapped if they lie inside the trapping horizon. Confinement law: if the interior and exterior of a future outer trapping horizon are disjoint, an observer inside the horizon cannot get outside.

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Sean A. Hayward. 1994-06-21. Spin-Coefficient Form of the New Laws of Black-Hole Dynamics. https://doi.org/10.1088/0264-9381%2F11%2F12%2F016

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