Vaidya and generalized Vaidya solutions by gravitational decoupling

TL;DR

This paper introduces a gravitational decoupling method to derive new dynamical black hole solutions, including Vaidya and generalized Vaidya spacetimes, analyzing their horizons and singularities.

Contribution

It develops a novel application of gravitational decoupling to generate dynamical black hole solutions with variable mass functions.

Findings

Derived new dynamical black hole solutions using gravitational decoupling.

Analyzed apparent horizons and singularity locations for different mass functions.

Extended Vaidya solutions to include dependence on both space and time.

Abstract

In this paper we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution which can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and well-known when the mass function is the function only of space coordinate $r$. The second case is Vaidya spacetime case when the mass function depends on time $v$ . And the third case represents the generalization of these two cases: the mass function is the function of both $r$ and $v$. We also calculate the apparent horizon and singularity location for all three cases.