First law of black hole mechanics as a condition for stationarity

Stephen McCormick
Phys. Rev. D 90, 104034 – Published 21 November 2014

Abstract

In earlier work, we provided a Hilbert manifold structure for the phase space for the Einstein-Yang-Mills equations, and used this to prove a condition for initial data to be stationary [, Adv. Theor. Math. Phys. 18, 799 (2014)]. Here we use the same phase space to consider the evolution of initial data exterior to some closed 2-surface boundary, and establish a condition for stationarity in this case. It is shown that the differential relationship given in the first law of black hole mechanics is exactly the condition required for the initial data to be stationary; this was first argued nonrigorously by Sudarsky and Wald [Phys. Rev. D 46, 1453 (1992)]. Furthermore, we give evidence to suggest that if this differential relationship holds then the boundary surface is the bifurcation surface of a bifurcate Killing horizon.

  • Received 11 August 2014

DOI:https://doi.org/10.1103/PhysRevD.90.104034

© 2014 American Physical Society

Authors & Affiliations

Stephen McCormick*

  • Department of Mathematics, School of Science and Technology, University of New England, Armidale, New South Wales 2351, Australia

  • *stephen.mccormick@une.edu.au

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Issue

Vol. 90, Iss. 10 — 15 November 2014

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