Evolving black hole with scalar field accretion

We obtain approximate analytical solutions of the Einstein equations close to trapping horizon for a dynamical spherically symmetric black hole in presence minimally coupled self-interacting scalar field. This is made possible by new parametrization metric, which displacement from as well its expansion rate feature explicitly. Our results are valid neighbourhood and hold any field potential spacetime asymptotics. An exact equation accretion also obtained, generalizes standard Bondi formula. develop system approach study near-equilibrium holes; using this formalism, we focus on simple model show that dynamics characterised scaling relations among variables. Moreover, with purely ingoing energy-momentum flux never reach equilibrium.