Related papers: Indirect (source-free) integration method. II. Sel…
With a view to developing a formalism that will be applicable at second perturbative order, we devise a new practical scheme for computing the gravitational self-force experienced by a point mass moving in a curved background spacetime. Our…
In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. An extension of an earlier…
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…
The mode-sum method provides a practical means for calculating the self force acting on a small particle orbiting a larger black hole. In this method, one first computes the spherical-harmonic $l$-mode contributions $F^{\mu}_l$ of the "full…
Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of the total area: A standard Metropolis simulation…
The self-force is the leading method in modelling waveforms for extreme mass ratio inspirals, a key target of ESA's future space-based gravitational wave detector LISA. In modelling these systems, one approximates the smaller body as a…
In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass $\mu$ orbiting a Schwarzschild black hole of mass $M$, where…
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…
We present a new, simple method for calculating the scalar, electromagnetic, and gravitational self forces acting on particles in orbit around a Kerr black hole. The standard ``mode-sum regularization'' approach for self-force calculations…
We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the…
The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…
In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass-ratio. That is, the local correction to equations of motion for a compact object orbiting…
Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that…
Accurately modeling astrophysical extreme-mass-ratio-insprials requires calculating the gravitational self-force for orbits in Kerr spacetime. The necessary calculation techniques are typically very complex and, consequently, toy…
A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum…
The problem of fixing measure in the path integral for the Regge-discretised gravity is considered from the viewpoint of it's "best approximation" to the already known formal continuum general relativity (GR) measure. A rigorous formulation…
A scalar charged particle moving in a curved background spacetime will emit a field affecting its own motion; the resolving of this resulting motion is often referred to as the self-force problem. This also serves as a toy model for the…
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…
To model the radiative evolution of extreme mass-ratio binary inspirals (a key target of the LISA mission), the community needs efficient methods for computation of the gravitational self-force (SF) on the Kerr spacetime. Here we further…
This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is…