Deformed Schwarzschild horizons in second-order perturbation theory:Mass, geometry, and teleology

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 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 behaviour in the black hole's motion around the binary's center of mass.Comment: 39 pages, 4 figures. v2 modifies the title, abstract, and Conclusion to better highlight the content. v3 corrects minor typo

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from communit

Geometrical and Perturbative study of Tidally Deformed Schwarzschild Spacetime

Vi undersöker tidvattendeformationen av ett icke-roterande, så kallade Schwarzschild, svarta hål. Vi formulerar geometrin i form av inre och yttre geometriska kvantitet på händelsehorisonten, som beskrivs av en hyperyta inbäddad i rumtiden, och vi gör det genom att formulera Gauss-Codazzi teorin om nollhyperytor som sträcker det standard resultat för rumslika och tidslika fallen. Denna formalism tillämpas sedan på en lösning av Einstein-fältekvationerna i vaccum, för att beskriva tidvattensförvrängningar till svarthålshorisonten på grund av en liten kretsande objekt. De tekniker som vi använder är giltiga för små objekt som rör sig snabbt i omloppsbanor, i det svarta hålets starka gravitationsfält. Denna analys bygger på en perturbativ strategi för två kroppar med ett mycket stort massförhållande - det vill säga, det små objektet är mycket mindre än den andra. Vi genomför studien i frekvensdomänen för störningsteori för svart hål, för en liten kropp som går i en cirkulär bana. Resultaten visualiseras genom att bädda in den förvrängda horisonten i det euklidiska rymden, vilket visar hur horisonten deformeras från en inbäddad sfär till en ellipsoid när den lilla kroppen är nära det svarta hålet, och när orbitalavskiljningen ökar, vilket i båda fallen visar vinkelförskjutning mellan horisontbukten och kroppen som producerar den. För båda orbitalskillnader som beaktas tillhandahåller vi ögonblicksbilder av tidvattenförvrängningen när den mindre kroppen kretsar runt det svarta hålet

Geometrical and Perturbative study of Tidally Deformed Schwarzschild Spacetime

Vi undersöker tidvattendeformationen av ett icke-roterande, så kallade Schwarzschild, svarta hål. Vi formulerar geometrin i form av inre och yttre geometriska kvantitet på händelsehorisonten, som beskrivs av en hyperyta inbäddad i rumtiden, och vi gör det genom att formulera Gauss-Codazzi teorin om nollhyperytor som sträcker det standard resultat för rumslika och tidslika fallen. Denna formalism tillämpas sedan på en lösning av Einstein-fältekvationerna i vaccum, för att beskriva tidvattensförvrängningar till svarthålshorisonten på grund av en liten kretsande objekt. De tekniker som vi använder är giltiga för små objekt som rör sig snabbt i omloppsbanor, i det svarta hålets starka gravitationsfält. Denna analys bygger på en perturbativ strategi för två kroppar med ett mycket stort massförhållande - det vill säga, det små objektet är mycket mindre än den andra. Vi genomför studien i frekvensdomänen för störningsteori för svart hål, för en liten kropp som går i en cirkulär bana. Resultaten visualiseras genom att bädda in den förvrängda horisonten i det euklidiska rymden, vilket visar hur horisonten deformeras från en inbäddad sfär till en ellipsoid när den lilla kroppen är nära det svarta hålet, och när orbitalavskiljningen ökar, vilket i båda fallen visar vinkelförskjutning mellan horisontbukten och kroppen som producerar den. För båda orbitalskillnader som beaktas tillhandahåller vi ögonblicksbilder av tidvattenförvrängningen när den mindre kroppen kretsar runt det svarta hålet

Deformed Schwarzschild horizons in second-order perturbation theory: mass, geometry, and teleology

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 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 behaviour in the black hole’s motion around the binary’s center of mass

Waveform Modelling for the Laser Interferometer Space Antenna

International audienceLISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome

Waveform Modelling for the Laser Interferometer Space Antenna

International audienceLISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome

Waveform Modelling for the Laser Interferometer Space Antenna

International audienceLISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome