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We compute the linear metric perturbation to a Schwarzschild black hole generated by a spinning compact object, specialising to circular equatorial orbits with an (anti-)aligned spin vector. We derive a two-timescale expansion of the field…

General Relativity and Quantum Cosmology · Physics 2022-05-04 Josh Mathews , Adam Pound , Barry Wardell

Extreme mass-ratio inspirals (EMRIs), consisting of a stellar-mass black hole orbiting a supermassive black hole, are among the primary targets for future space-based gravitational wave detectors. By analyzing the emitted gravitational wave…

General Relativity and Quantum Cosmology · Physics 2025-06-24 Li Huang

We present a practical method for calculating the local gravitational self-force (often called ``radiation-reaction force'') for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of {\it…

General Relativity and Quantum Cosmology · Physics 2009-10-09 Leor Barack , Yasushi Mino , Hiroyuki Nakano , Amos Ori , Misao Sasaki

The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M G/c^2$. If the particle is endowed with mass $\mu(\ll M)$, it experiences a gravitational…

General Relativity and Quantum Cosmology · Physics 2009-06-30 Leor Barack , Norichika Sago

The field of gravitational waves is rapidly progressing due to the noticeable advancements in the sensitivity of gravitational-wave detectors that has enabled the detection prospects of binary black hole mergers. Extreme mass ratio inspiral…

General Relativity and Quantum Cosmology · Physics 2026-03-05 Mostafizur Rahman , Shailesh Kumar , Arpan Bhattacharyya

This paper presents the first calculation of the gravitational self-force on a small compact object on an eccentric equatorial orbit around a Kerr black hole to first order in the mass-ratio. That is the pointwise correction to the object's…

General Relativity and Quantum Cosmology · Physics 2016-08-24 Maarten van de Meent

We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with mass $m$ orbiting in the background spacetime induced by a heavy gravitational source with mass $M$. Observables are organized as an…

High Energy Physics - Theory · Physics 2024-04-02 Dimitrios Kosmopoulos , Mikhail P. Solon

Understanding the orbits of spinning bodies in curved spacetime is important for modeling binary black hole systems with small mass ratios. At zeroth order in mass ratio, the smaller body moves on a geodesic. Post-geodesic effects are…

General Relativity and Quantum Cosmology · Physics 2025-09-05 Lisa V. Drummond , Philip Lynch , Alexandra G. Hanselman , Devin R. Becker , Scott A. Hughes

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations…

General Relativity and Quantum Cosmology · Physics 2011-05-05 Sofiane Aoudia , Alessandro D. A. M. Spallicci

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It…

General Relativity and Quantum Cosmology · Physics 2016-03-22 P. Ritter , S. Aoudia , A. Spallicci , S. Cordier

Considering the self force and radiation due to a small body in orbit (especially aperiodic) around a black hole, this paper defines a decomposition of the source into a sum over the shape preserving periodic motions of extended objects…

General Relativity and Quantum Cosmology · Physics 2013-08-02 Barak Kol

Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is…

General Relativity and Quantum Cosmology · Physics 2024-01-26 Adam Pound , Barry Wardell

Here, we explore the effect of the cloud of strings (CoS) on the gravitational waveforms of extreme mass ratio inspirals (EMRIs). The EMRI system consists of a supermassive black hole (BH) and a compact stellar mass object moving around it.…

General Relativity and Quantum Cosmology · Physics 2025-12-16 Mirzabek Alloqulov , Ahmadjon Abdujabbarov , Bobomurat Ahmedov , Chengxun Yuan

We present an improved numerical kludge waveform model for circular, equatorial EMRIs. The model is based on true Kerr geodesics, augmented by radiative self-force corrections derived from perturbative calculations, and in this paper for…

General Relativity and Quantum Cosmology · Physics 2011-09-22 E. A. Huerta , Jonathan R. Gair

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian…

General Relativity and Quantum Cosmology · Physics 2023-02-15 Francisco M. Blanco , Éanna É. Flanagan

We discuss the energy loss due to gravitational radiation of binaries composed of exotic objects whose horizon boundary conditions are replaced with reflective ones. Our focus is on the extreme mass-ratio inspirals, in which the central…

General Relativity and Quantum Cosmology · Physics 2021-09-06 Norichika Sago , Takahiro Tanaka

We develop the first model for extreme mass-ratio inspirals (EMRIs) into a rotating massive black hole driven by the gravitational self-force. Our model is based on an action angle formulation of the method of osculating geodesics for…

General Relativity and Quantum Cosmology · Physics 2022-08-04 Philip Lynch , Maarten van de Meent , Niels Warburton

[Abridged] This review surveys the theory of gravitational self-force in curved spacetime and its application to the gravitational two-body problem in the extreme-mass-ratio regime. We first lay the relevant formal foundation, describing…

General Relativity and Quantum Cosmology · Physics 2018-12-26 Leor Barack , Adam Pound

We study eccentric orbits of the Schwarzschild spacetime for extreme mass ratio system (EMRI) in modified gravity theories with additional scalar fields. Due to the additional energy and angular momentum carried away by the scalar field,…

General Relativity and Quantum Cosmology · Physics 2023-07-05 Chao Zhang , Yungui Gong , Dicong Liang , Bin Wang

A small mass \mu in orbit about a much more massive black hole M moves along a world line that deviates from a geodesic of the black hole geometry by O(\mu/M). This deviation is said to be caused by the gravitational self-force of the…

General Relativity and Quantum Cosmology · Physics 2010-05-12 Steven Detweiler