2006/06/21 by Brent Preston, Eric Poisson · 3 citations
Engineering · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black hole (networking) #Classical mechanics #Gauge theory #General relativity #Geophysics and Sensor Technology #Light cone #Mathematical physics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Ray #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.74.064010
published as Phys.Rev. D74 (2006) 064010 · 12 pages
arxiv created 2006/06/21 · openalex publication_date 2006/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathθ and \ensuremathφ 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\ensuremathπr2 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.