Geometry of Vaidya spacetimes

Abstract

We investigate the geometrical structure of Vaidya's spacetime in the case of a white hole with decreasing mass, stabilising to a black hole in finite or infinite time or evaporating completely. Our approach relies on a detailed analysis of the ordinary differential equation describing the incoming principal null geodesics, among which are the generators of the past horizon. We devote special attention to the case of a complete evaporation in infinite time and establish the existence of an asymptotic light-like singularity of the conformal curvature, touching both the past space-like singularity and future time-like infinity. This singularity is present independently of the decay rate of the mass. We derive an explicit formula that relates directly the strength of this null singularity to the asymptotic behaviour of the mass function.

arXiv comment19 pages, 4 figures

References in corpus (5)

• Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• On the proximity of black hole horizons: lessons from Vaidya
• Tensor calculus with open-source software: the SageManifolds project
• On maximal analytical extension of the Vaidya metric

Cited by in corpus (5)

• A Vaidya-type spacetime with no singularities
• Geodesic structure of generalized Vaidya spacetime through the K-essence
• Kerr-Vaidya type radiating black holes in semi-classical gravity with conformal anomaly
• Shadow of higher dimensional collapsing dark star and blackhole
• Generalized Eddington--Finkelstein Coordinates and Exact Vaidya-Type Solutions in Weyl Conformal Gravity