Advanced numerical methods for gravitational self-force calculations

Lead Research Organisation: University of Southampton
Department Name: School of Mathematics

Abstract

Gravitational self-force theory is a perturbative approach to the two-body problem in General Relativity, with important applications in gravitational-wave astronomy. The project will explore a new, computationally efficient approach to self-force calculations in Kerr spacetime, based on a time-domain numerical evolution of certain curvature scalars. The project will have a theoretical component---the formulation of metric reconstruction in nonvacuum spacetimes---as well as a numerical-analysis component---the development of a novel, pseudo-spectral method for time-domain integration of the gravitational field equations.

Publications

10 25 50
 
Description The most significant finding is a new method used in black hole perturbation theory. This new method circumvents a problem with a previous method that caused the data to be dominated by a numerical instability. The new method has been shown to work and applied to the case of hyperbolic orbits where a small black hole does a flyby around a supermassive black hole, the first known calculation of its kind.
Exploitation Route What we have found here is the first step in performing self-force calculations for hyperbolic orbits. Once this has been calculated, it can be used to compare with other hyperbolic methods and also be used to add data into other methods in black hole modelling.
Sectors Other
 
Title Time-Domain Hyperbolic Regge-Wheeler Code 
Description The time-domain hyperbolic Regge-Wheeler code is a code that calculates fields within black hole perturbation theory. Given the orbital parameters of a hyperbolic orbit it can calculate the Regge-Wheeler field and Hertz potential associated with that orbit using a finite-difference scheme applied on a characteristic null grid. Details of the code and sample results are due to be released in a forthcoming publication. 
Type Of Material Computer model/algorithm 
Year Produced 2021 
Provided To Others? No  
Impact This is the first known calculation of black hole perturbation theory fields to first order in the mass ratio which has been applied to hyperbolic orbits. This code also circumvents an instability present when calculating the Hertz potential in the usual way, via the Teukolsky equation.