Boundary
conditions for Isolated Black Holes
Ayan Chatterjee*, Sahil
Devdutt
Department of
Physics and Astronomical Science, Central University of Himachal Pradesh,
Dharamshala-
176215, India.
ABSTRACT:
The laws of black hole mechanics which
describe the black hole in equilibrium are similar to the laws of
thermodynamics which describe thermodynamic system in equilibrium. This
suggests us to view equilibrium black hole as an isolated object. We discuss the
isolated horizon framework of [1,2] instead of event horizon. We briefly review
consequences of these boundary conditions on the local geometry of isolated
horizon and on the form of curvature. In addition to this, the framework can be
extended to describe the cosmological horizons.
1. INTRODUCTION:
In
equilibrium situations, laws of black hole mechanics are similar to the laws of
thermodynamics [2]. This motivates us to study the black hole in equilibrium as
an isolated system. An isolated black hole may be described by stationary
spacetimes which are solution of Einstein field equations. Other description of
isolated black hole depends on event horizon, specification of which requires
the precise knowledge of full space-time. However, it is desirable to describe
the isolated black hole in terms of intrinsic geometry of the horizon without
making any reference to the full space-time. In addition to this, one can also
assign the entropy and temperature to the cosmological horizons of de-sitter
space-time [3], which enclose no singularities inside them and hence they are
not black hole event horizons. So we need to replace the notion of event
horizon by quasi local notion of isolated horizon.
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