On the Limitations of a Generalized Vaidya Metric

2025/11/12 by Chakrabarti, Soumya, Dadhich, Naresh, Singha, Chiranjeeb
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2511.09011

Abstract

We prove that there can not be a smooth matching of the Generalized Vaidya metric with an exterior Schwarzschild/Vaidya patch across a finite boundary hypersurface unless the mass function is a function of the null coordinate alone. By explicitly deriving the extrinsic curvature components, we show that for ∂ m / ∂ r ≠ 0 one has a discontinuity in the curvature and induces a surface stress-energy tensor, corresponding to a thin shell of matter. This discontinuity also appears in the geometric invariant K = K_abK^ab and in the Kodama current, indicating a mismatch in quasi-local energy flux across the boundary. The analysis of timelike geodesics leads to the same condition, reinforcing that the generalized Vaidya geometry with ∂ m / ∂ r ≠ 0 cannot represent a consistent stellar interior bounded by a regular surface. We therefore note that the generalized Vaidya spacetime should be interpreted as an unbounded geometry with intrinsic heat flux rather than a viable bounded source.

Citations

• Gravitational Collapse of Bose-Einstein condensate dark matter in Generalized Vaidya spacetime
• Dynamical Black Holes: Apparent Horizon Versus Energy Conditions
• The generalized Vaidya spacetime with polytropic equation of state

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