Vaidya geometries and scalar fields with null gradients

Valerio Faraoni,Andrea Giusti,Bardia H Fahim

doi:10.1140/epjc/s10052-021-09040-9

Valerio Faraoni, Andrea Giusti + Show 1 more

Open Access

https://doi.org/10.1140/epjc/s10052-021-09040-9

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Abstract

Since, in Einstein gravity, a massless scalar field with lightlike gradient behaves as a null dust, one could expect that it can act as the matter source of Vaidya geometries. We show that this is impossible because the Klein–Gordon equation forces the null geodesic congruence tangent to the scalar field gradient to have zero expansion, contradicting a basic property of Vaidya solutions. By contrast, exact plane waves travelling at light speed and sourced by a scalar field acting as a null dust are possible.

Highlights

(where Rab is the Ricci tensor of the metric gab, R is its trace, and Tab is the matter energy-momentum tensor)1 are used to study gravitational collapse, the formation and evolution of event and apparent horizons, and as toy models of evaporating black holes
Since the components μ of a null vector can be reparametrized as μ → ̄μ = f μ can be without chosen changing its in which ρ is unnoirtmy ablyizcahtiooons,inagrefpr=ese√nρta,tibount the corresponding null geodesics followed by the null dust are not affinely parametrized [6]
A null dust is interpreted as a coherent zero rest mass field that propagates at light speed in the null direction a, in the geometric optics limit

Summary

Introduction

(where Rab is the Ricci tensor of the metric gab, R is its trace, and Tab is the matter energy-momentum tensor)1 are used to study gravitational collapse, the formation and evolution of event and apparent horizons, and as toy models of evaporating black holes. The source of a Vaidya geometry is a null dust, described by the stress-energy tensor In general, the covariant conservation equation ∇bTab = 0 for the stress-energy tensor (2) gives non-affinely parametrized geodesics.

Results

Conclusion