Uploaded July 2022 | Updated September 2026, 57 minutes ago
In an extreme-mass-ratio inspiral, the smaller-mass object is typically modelled as a point particle. While conceptually elegant, the main drawback of this approach is that the first-order-in-the-mass-ratio metric perturbation is singular at the particle. Current methods of dealing with this consist of splitting the full retarded field into a singular piece, encoding the local multipole moments of the particle, and a regular piece. This last piece is key in computing self-force corrections to geodesic motion in Kerr.
While it is not possible to obtain an exact expression of the singular piece, one can find a local one, in powers of the distance to the particle. The current methodology to do this invokes many subtle mathematical constructs. In addition to its technical complexity, it is challenging to obtain the local expression of the singular field beyond a few total orders.
In this presentation, I will show a novel, both simple and efficient, approach in computing this local expression. As a proof of principle, I will show that applying this method to a scalar charge in circular orbit around a Schwarzschild black hole, one can generate a 12th-order puncture. As a result, when used in a puncture scheme it will provide a smoother effective source, improving convergence of Fourier- and spherical-harmonic mode sums and particularly ameliorating the catastrophic mode-coupling problem that arises at second order.
Authors: Patrick Bourg, Adam Pound, Samuel Upton
Presenter: Patrick Bourg
In an extreme-mass-ratio inspiral, the smaller-mass object is typically modelled as a point particle. While conceptually elegant, the main drawback of this approach is that the first-order-in-the-mass-ratio metric perturbation is singular at the particle. Current methods of dealing with this consist of splitting the full retarded field into a singular piece, encoding the local multipole moments of the particle, and a regular piece. This last piece is key in computing self-force corrections to geodesic motion in Kerr.
While it is not possible to obtain an exact expression of the singular piece, one can find a local one, in powers of the distance to the particle. The current methodology to do this invokes many subtle mathematical constructs. In addition to its technical complexity, it is challenging to obtain the local expression of the singular field beyond a few total orders.
In this presentation, I will show a novel, both simple and efficient, approach in computing this local expression. As a proof of principle, I will show that applying this method to a scalar charge in circular orbit around a Schwarzschild black hole, one can generate a 12th-order puncture. As a result, when used in a puncture scheme it will provide a smoother effective source, improving convergence of Fourier- and spherical-harmonic mode sums and particularly ameliorating the catastrophic mode-coupling problem that arises at second order.
Authors: Patrick Bourg, Adam Pound, Samuel Upton
Presenter: Patrick Bourg
