Ateneo physics alumnus Dr. Ian Vega gives a plenary talk at a Gravitation Conference in PIRSA: 3+1 approach to self-force computations for orbits around supermassive black holes

3+1 approach to self-force computations

by Dr. Francis Ian Vega III

A plenary talk at “Theory Meets Data Analysis at Comparable and Extreme Mass Ratios” Conference held at the Perimeter Institute for Theoretical Physics last 20-26 June 2010. Dr. Ian Vega finished his B.S. Physics in Ateneo de Manila University (2001) and his Ph.D. in Physics in University of Florida (2009). He is now a Postdoctoral fellow at the University of Guelph, Canada.

The plenary talk Dr. Vega was invited to give was about a new approach in self-force calculations that was pioneered by his adviser and himself. This novel approach was the topic of his dissertation. The talk he gave was a both an introduction to the subject, and a review of published work and open problems.

The abstract of Dr.Vega’s dissertation is below:

The dynamics of point particles around black holes

Abstract. A point particle moving in a curved spacetime gives rise to fields that in turn affect its motion. One conveniently thinks of this interplay as the response of the particle to its self-force. To date, models of point particle motion in the vicinity of black holes have ignored parts of this self-force because it is such a challenge to calculate. This work is part of a larger effort to develop systematic tools for the efficient calculation of such self-forces. This development is made with the aim of accurately simulating the inspiraling motion of compact objects onto supermassive black holes (also known as extreme-mass-ratio binary inspirals, or EMRIs), and of obtaining good predictions of the gravitational waves they emit. EMRIs are the main targets for the proposed space-based gravitational wave detector, the Laser Interferometer Space Antenna (LISA). For the mission to succeed, accurate templates of the gravitational waves it will pick up are necessary. This work is an attempt to address this need.

The main contribution of this dissertation is the design and testing of a novel method for simultaneously calculating self-forces and radiation fluxes due point particle sources using (3+1) codes. Concrete calculations of self-forces for particles in strong-field gravity have only previously been done through mode sum approaches, which, while having been critical to the development of the subject, appears inconvenient for the eventual goal of using a calculated self-force to update particle trajectories. The new method avoids a mode decomposition entirely, and instead properly replaces the distributional source of the curved spacetime wave equation by an effective regular source. The resulting regular solution of the wave equation, under appropriate boundary conditions, results in the physical retarded field when evaluated in the wavezone, while its gradient at the location of the particle gives the full self-force.

This prescription is founded on the possibility of properly smearing out or regularizing delta function sources using an elegant decomposition of point source retarded fields, introduced by Detweiler and Whiting. Concrete implementations of the method are presented here, focusing exclusively on the ideal test case of a scalar point charge in a circular orbit around a Schwarzschild black hole. For a quick proof-of-principle, the method is first implemented in time-domain, using a 4th-order (1+1) algorithm for evolving the wave equation. This was used to calculate the self-force and the retarded field in the wave zone. To assess the quality of the numerical results, they were compared with the results of highly accurate frequency-domain calculations found in the literature. Encouraging agreement to within [less or equivalent to] 1% is achieved.

This work also presents the first successful self-force calculations performed with (3+1) codes. For this task, two independent (3+1) codes (finite difference and pseudospectral) developed originally for full-fledged numerical relativity applications were adapted to implement our new technique. Again, good agreement of [less or equivalent to] 1% error in the self-force and fluxes is achieved.

These results open the door towards employing the well-developed machinery of numerical relativity in tackling the extreme-mass-ratio regime of black hole binaries, and consequently pave the way towards long sought self-force waveforms for EMRIs.


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