Deformed Schwarzschild horizons in second-order perturbation theory
- In recent years, gravitational-wave astronomy has motivated increasingly accurate perturbative studies of gravitational dynamics in compact binaries. This in turn has enabled more detailed analyses of the dynamical black holes in these systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)] recently computed the surface area of a Schwarzschild black hole's apparent horizon, perturbed by an orbiting body, to second order in the binary's mass ratio. In this paper, we take that as the starting point for a comprehensive study of a perturbed Schwarzschild black hole's apparent and event horizon at second perturbative order, deriving generic formulas for the first- and second-order corrections to the horizons' radial profiles, surface areas, Hawking masses, and intrinsic curvatures. We find that the two horizons are remarkably similar, and that any teleological behavior of the event horizon is suppressed in several ways. Critically, we establish that at all orders, the perturbed event horizon in a small-mass-ratio binary isIn recent years, gravitational-wave astronomy has motivated increasingly accurate perturbative studies of gravitational dynamics in compact binaries. This in turn has enabled more detailed analyses of the dynamical black holes in these systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)] recently computed the surface area of a Schwarzschild black hole's apparent horizon, perturbed by an orbiting body, to second order in the binary's mass ratio. In this paper, we take that as the starting point for a comprehensive study of a perturbed Schwarzschild black hole's apparent and event horizon at second perturbative order, deriving generic formulas for the first- and second-order corrections to the horizons' radial profiles, surface areas, Hawking masses, and intrinsic curvatures. We find that the two horizons are remarkably similar, and that any teleological behavior of the event horizon is suppressed in several ways. Critically, we establish that at all orders, the perturbed event horizon in a small-mass-ratio binary is effectively localized in time. Even more pointedly, the event horizon is identical to the apparent horizon at linear order regardless of the source of perturbation, implying that the seemingly teleological "tidal lead," previously observed in linearly perturbed event horizons, is not genuinely teleological in origin. The two horizons do generically differ at second order, but their Hawking masses remain identical, implying that the event horizon obeys the same energy-flux balance law as the apparent horizon. At least in the case of a binary system, the difference between their surface areas remains extremely small even in the late stages of inspiral. In the course of our analysis, we also numerically illustrate puzzling behavior in the black hole's motion around the binary's center of mass.…
Author details: | Riccardo BonettoORCiD, Adam PoundORCiD, Zeyd SamORCiD |
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DOI: | https://doi.org/10.1103/PhysRevD.105.024048 |
ISSN: | 2470-0010 |
ISSN: | 2470-0029 |
Title of parent work (English): | Physical review D, Particles, fields, gravitation, and cosmology |
Subtitle (English): | mass, geometry, and teleology |
Publisher: | American Physical Society |
Place of publishing: | College Park |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/01/20 |
Publication year: | 2022 |
Release date: | 2024/01/03 |
Volume: | 105 |
Issue: | 2 |
Article number: | 024048 |
Number of pages: | 42 |
Funding institution: | University of Trieste; Royal Society University Research Fellowship; [UF160110]; European Research Council under the European Union's Seventh; Framework Programme/ERC Grant [304978, FP7/2007-2013] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |