# Time-domain metric reconstruction for self-force applications

## TL;DR

This paper introduces a new, computationally efficient time-domain method for calculating the gravitational self-force in Kerr spacetime, enabling more flexible and stable orbit evolution simulations.

## Contribution

The paper presents a novel time-domain metric reconstruction approach from curvature scalars for GSF calculations, improving efficiency and stability over existing methods.

## Key findings

- Method successfully applied to circular orbits in Schwarzschild geometry.
- Reduces computational cost compared to traditional time-domain approaches.
- Allows for flexible orbit types and self-consistent orbit evolution.

## Abstract

We present a new method for calculation of the gravitational self-force (GSF) in Kerr geometry, based on a time-domain reconstruction of the metric perturbation from curvature scalars. In this approach, the GSF is computed directly from a certain scalar-like self-potential that satisfies the time-domain Teukolsky equation on the Kerr background. The approach is computationally much cheaper than existing time-domain methods, which rely on a direct integration of the linearized Einstein's equations and are impaired by mode instabilities. At the same time, it retains the utility and flexibility of a time-domain treatment, allowing calculations for any type of orbit (including highly eccentric or unbound ones) and the possibility of self-consistently evolving the orbit under the effect of the GSF. Here we formulate our method, and present a first numerical application, for circular geodesic orbits in Schwarzschild geometry. We discuss further applications.