Frequency-domain approach to self-force in hyperbolic scattering

Abstract

Gravitational self-force is a well-established method for modelling the dynamics of binary systems in general relativity when one object is significantly less massive than the other. Existing study has focused primarily on the dynamics of bound systems, driven by a desire to model astrophysically relevant extreme mass ratio inspirals. In recent years, however, it has come to be understood that self-force can play a vital role in an ongoing cross-disciplinary effort to study black hole scattering, enabling explorations of the interface between different modelling approaches and advancing the post-Minkowskian and effective-one-body approaches to general relativistic 2-body motion.

In this thesis we investigate a method for calculating the self-force along hyperbolic orbits. Whilst some progress has previously been made towards this aim by working in the time-domain, our purpose will be the development of a frequency-domain approach. Frequency domain self-force methods are common for bound systems, where they provide superior performance compared to time-domain codes, but there are several challenges when moving to unbound systems. To investigate and overcome these, we will use a scalar-field toy model, which captures all of the essential challenges but is simpler to implement, and restrict ourselves to the case of a non-rotating, Schwarzschild black hole. Problems will be encountered with the standard method of extended homogeneous solutions, which cannot be fully applied to the unbound problem, and which suffers growing errors at early and late times. We will also face and overcome difficulties numerically evaluating oscillatory integrals which stretch to radial infinity. We develop solutions to each of these issues in turn, and present example results from our numerical implementation. We then illustrate how strong-field self-force scatter results can be used to resum weak-field post-Minkowskian results, extending the latter's domain of validity. We find that our frequency-domain approach is critical for high-precision strong-field calculations at high velocities. Initial work on an analytical calculation to obtain the self-force at early and late times is also presented. To conclude, we discuss the future development of the techniques developed herein, and the outlook for the self-force scatter programme at large.

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Identifiers

ORCID for Christopher Luke Whittall: orcid.org/0000-0003-2152-6004

ORCID for Leor Barack: orcid.org/0000-0003-4742-9413

ORCID for Adam Pound: orcid.org/0000-0001-9446-0638

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