Double-null coordinates for the Vaidya metric

Details Double-null coordinates for the Vaidya metric Double-null coordinates for the Vaidya metric

Nov 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..34.2978w&link_type=abstract

Physical Review D (Particles and Fields), Volume 34, Issue 10, 15 November 1986, pp.2978-2984

Physics

37

Fundamental Problems And General Formalism, Late Stages Of Stellar Evolution

Scientific paper

Einstein's equations with spherical symmetry are formulated in double-null coordinates, and the high-frequency approximation to a unidirectional radial flow of unpolarized radiation (the Vaidya metric) is studied in detail. For this case the Einstein equations reduce to a single first-order nonlinear partial differential equation. Integration of this equation introduces an arbitrary function (of one null variable) which must be chosen so as to regularize the metric across horizons. Although the problem is, in general, not analytically solvable, we are able to extend the class of known analytic solutions from the constant-mass case (Kruskal-Szekeres metric) to linear and exponential mass functions. In the linear case we give the first explicit regular covering of a spacetime with a naked shell-focusing singularity.

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