Speaker
Description
We investigate the backreaction of a massive scalar configuration (“wig”) on a Schwarzschild black hole within a controlled perturbative framework. Working in ingoing Eddington–Finkelstein coordinates, we adopt the test-field approximation and solve the Einstein equations consistently to leading nontrivial order in the scalar stress-energy tensor. The scalar sector is treated using Detweiler’s approximation, which allows us to isolate and analytically characterize the fundamental s-wave mode governing the late-time dynamics.
Within this setup, we derive a closed-form expression for the dynamical mass function of the black hole, explicitly capturing the energy exchange between the geometry and the scalar field. At leading order in the test-field expansion, we also determine the evolution of the apparent horizon, providing an analytic description of its growth driven by scalar accretion. The resulting dynamics exhibits a nontrivial accretion law that departs from both quasi-stationary and instantaneous prescriptions commonly employed in the literature. In particular, the mass growth is intrinsically time-dependent and encodes memory effects associated with the scalar field profile, rather than being determined solely by local horizon quantities.
Finally, we establish analytic bounds relating the initial black hole mass and the scalar field mass, identifying the parametric regime in which our perturbative treatment remains valid and the backreaction remains controlled. Our results provide an analytically tractable model of backreaction beyond the standard adiabatic regime, clarifying the limitations of effective accretion laws and offering a benchmark for more complete numerical treatments of scalar-field–black-hole systems.