Light-cone gauge for black-hole perturbation theory
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada)
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 {theta} and {phi} 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 4{pi}r{sup 2} 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.
- OSTI ID:
- 20871212
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 74, Issue 6; Other Information: DOI: 10.1103/PhysRevD.74.064010; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Light-cone coordinates based at a geodesic world line
Nonrotating black hole in a post-Newtonian tidal environment