Dynamical black holes and accretion-induced backreaction

TL;DR

This paper studies the evolution of black hole horizons under accretion effects, using perturbative methods to analyze horizon shifts and the influence of stress-energy components on horizon geometry.

Contribution

It introduces a systematic perturbative framework for analyzing accretion backreaction on black hole horizons in spherically symmetric spacetimes.

Findings

Accretion causes measurable shifts in horizon positions.

Momentum influx and energy density have distinct effects on extremal horizons.

First-order corrections reveal significant horizon displacements due to stress-energy components.

Abstract

We investigate the evolution of future trapping horizons through the dynamics of the Misner-Sharp mass using ingoing Eddington-Finkelstein coordinates. Our analysis shows that an integral formulation of Hayward's first law governs much of the evolution of general spherically symmetric spacetimes. To account for the accretion backreaction, we consider a near-horizon approximation, yielding first-order corrections of a Vaidya-dark energy form. We further propose a systematic perturbative scheme to study these effects for an arbitrary background. As an application, we analyze an accreting Reissner-Nordstr\"om black hole and demonstrate the horizon shifts that are produced. Finally, we compute accretion-induced corrections to an extremal configuration. It is shown that momentum influx and energy density produce distinct effects: the former forces the splitting of the extremal horizon, while the latter induces significant displacements in its position, computed up to first-order perturbative corrections. These results highlight how different components of the stress-energy tensor significantly affect horizon geometry, with potential implications for broader areas of research, including black-hole thermodynamics.