Light-cone gauge for black-hole perturbation theory

Brent Preston and Eric Poisson
Phys. Rev. D 74, 064010 – Published 8 September 2006

Abstract

The geometrical meaning of the Eddington-Finkelstein coordinates of Schwarzschild spacetime is well understood: (i) the advanced-time coordinate v is constant on incoming light cones that converge toward r=0, (ii) the angles θ and ϕ are constant on the null generators of each light cone, (iii) the radial coordinate r is an affine-parameter distance along each generator, and (iv) r is an areal radius, in the sense that 4πr2 is the area of each two-surface (v,r)=constant. The light-cone gauge of black-hole perturbation theory, which is formulated in this paper, places conditions on a perturbation of the Schwarzschild metric that ensure that properties (i)–(iii) of the coordinates are preserved in the perturbed spacetime. Property (iv) is lost, in general, but it is retained in exceptional situations that are identified in this paper. Unlike other popular choices of gauge, the light-cone gauge produces a perturbed metric that is expressed in a meaningful coordinate system; this is a considerable asset that greatly facilitates the task of extracting physical consequences. We illustrate the use of the light-cone gauge by calculating the metric of a black hole immersed in a uniform magnetic field. We construct a three-parameter family of solutions to the perturbative Einstein-Maxwell equations and argue that it is applicable to a broader range of physical situations than the exact, two-parameter Schwarzschild-Melvin family.

  • Received 21 June 2006

DOI:https://doi.org/10.1103/PhysRevD.74.064010

©2006 American Physical Society

Authors & Affiliations

Brent Preston and Eric Poisson

  • Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1

See Also

Light-cone coordinates based at a geodesic world line

Brent Preston and Eric Poisson
Phys. Rev. D 74, 064009 (2006)

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Vol. 74, Iss. 6 — 15 September 2006

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