|
Résumé |
I study the evolution of the event horizon in a “two-timescale” perturbative expansion around a stationary black hole. This leads to strong constraints on the “coarse-grained” horizon dynamics. At leading order, the horizon exhibits an “adiabatic rigidity”: the leading corrections to its angular velocity and inaffinity remain uniform on each horizon cut, while evolving on the slow timescale. We then provide a systematic procedure for transforming a perturbative bulk solution, given for example in Lorenz gauge, to an ingoing Newman--Unti gauge adapted to the horizon, allowing the perturbed horizon geometry to be extracted directly from the metric. Finally, we formulate “horizon conservation laws” associated with horizon symmetries, including energy, dynamical entropy, and angular momentum. We expand the charges through second order and their fluxes through third order in perturbation theory, providing a framework for future applications to horizon absorption and backreaction in extreme mass-ratio inspirals. |
