Linear Response to Black Hole Deformations
Abstract
Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue ℰ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, ℰ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on ℰ, which in turn grant insights into the effective physics in the vicinity of the black hole.
Related
- Curvature scaling and linear area response in charged black-hole interiors
- Adiabatic Deformations of Black Hole Moduli: II. The Magnetic GHS Family
- Adiabatic Deformations of Black Hole Moduli: I. Canonical Slices and Fredholm Solvability
- Second-order scattering response of a Schwarzschild black hole
- Topological changes and response singularities in black hole thermodynamic branch structure
BibTeX
@misc{hohenegger2026linear,
title = {{Linear Response to Black Hole Deformations}},
author = {Stefan Hohenegger},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18521},
eprint = {2610.18521},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05842361v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear Response to Black Hole Deformations
AU - Stefan Hohenegger
PY - 2026
DA - 2026/10/13
PB - HAL
DO - 10.48550/arxiv.2610.18521
UR - https://hal.science/hal-05842361v1
AB - Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue ℰ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, ℰ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on ℰ, which in turn grant insights into the effective physics in the vicinity of the black hole.
ER -