K-essence Emergent Spacetime as Generalized Vaidya Geometry

TL;DR

This paper explores how K-essence emergent gravity models relate to generalized Vaidya spacetimes, revealing conditions for consistent black hole solutions and discussing potential dynamical horizons within this framework.

Contribution

It establishes a formal link between K-essence emergent gravity and generalized Vaidya spacetimes, including conditions for black hole solutions and horizons.

Findings

Emergent metric resembles generalized Vaidya spacetime for null fluid collapse.

Null energy conditions impose restrictions on emergent metric functions.

Explicit black hole backgrounds compatible with the model are identified.

Abstract

We establish a formal connection between the {\bf K}-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the {\bf K}-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the {\bf K}-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor derived from the emergent Einstein equation, restrictions are obtained on the functions characterizing the emergent metric for consistent identification with generalized Vaidya spacetimes. We discuss the possibility of dynamical horizons in the {\bf K-}essence emergent Vaidya spacetime. Admissible explicit black hole background metrics are discussed as examples.