“Self-Force in Non- Vacuum SPACE TIMES: Theory and Applications”
By: Peter Zimmerman
Advisor: Eric Poisson
In the past, the formulation of the gravitational self-force problem has been restricted to background space-time’s which are devoid of additional matter fields. The solutions describing these geometries obey the vacuum Einstein field equations and the motion of test-particles is geodesic. While the vacuum formulation may be adequate for characterizing extreme mass ratio in spirals around black holes, which form the most promising candidates for the proposed space-based gravitational wave detector (e)LISA, many phenomena require contending with extra fields. For example, one may wish to consider the motion of a small charged body through the magnetosphere of a larger object as it in spirals, which would require modelling the combined effects of the electromagnetic and gravitational perturbations created by the small body. The non-vacuum gravitational self-force will also play an important role in describing the motion of small bodies in alternative theories of gravity, where the gravitational field is mediated by both the space time metric and additional fields. An important prediction of one such theory, scalar-tensor theory, is the existence of floating orbits around rotating black holes, where the in spiral is halted due to a combination of super radiance and the presence of a potential barrier preventing the scalar radiation from escaping. The self-force will also be instrumental for understanding how floating orbits arise dynamically and addressing their stability. Moreover, the non-vacuum self-force is needed to test whether a Reissner-Nordro ̈m black hole can be driven to an overcharged state by bombarding it with a charged particle.
In this thesis, we provide a foundational framework for tackling these problems through a sequence of formal derivations of the first-order self-force in non-vacuum space times containing additional matter fields with integer little group representations. Specifically, we present two derivations: one based on regular solutions to the linearized field equations, and the other following from effective field theory principles.
Both derivations utilize a novel “meta-index” notation to collect the fields into a single “super-field” which streamlines the analysis. The formalism is then applied to the scalarvac and electovac space times as concrete scenarios. The non-vacuum self- force equations of motion are characterized by the presence of new local couplings involving derivatives of the background matter potentials, and non-local terms which involve “non-diagonal” Green functions that govern retarded correlations between the metric and the perturbed matter fields. In the scalarvac space-time we also derive the evolution equation for the particle’s effective mas under the influence of its self- field. Lastly, we derive the first-order self-force in scalar-tensor theory of gravity and mention the prospect of constraining the theory using the result. We also find that both the mass and effective charge of the particle in scalar-tensor theory evolve due to the self-field, indicating that scalarization phenomena are exhibited in the EMRI problem.
Dr. Xiaorong Qin, Chair,
Dr. Eric Poisson, Advisory Committee Member
Dr. Luis Lehner, Advisory Committee Member
Dr. Alex Gezerlis, Additional Member
Dr. Chad Galley , External Examiner. (California Institute of Technology, Pasedena , California)
M.Sc - University of Guelph
B.Sc - Syracuse University
Zimmerman P., Submitted (2015) Gravitational self-force in non-vacuum spacetimes: an effective field theory derivation.
Zimmerman P., Poisson E., Submitted (2014) Gravitational self-force in nonvacuum spacetimes. Zimmerman P., Vega, I., Poisson E., Haas R., (2013) Self-force as a cosmic censor. Phys.Rev D87.
Zimmerman P., Brown D., (2010) The Effect of Eccentricity on Searches for Gravitational-Waves from Coalescing Compact Binaries in Ground- based Detectors. Phys.Rev D81.