The research activities of the Guelph Gravitation Group have recently been divided into two broad streams. The first stream is concerned with the physics of black holes and neutron stars in tidal environments. The second is concerned with the gravitational self-force.
Compact bodies in tidal environments. What happens to a black hole or a neutron star when it is not isolated, but placed in the presence of other bodies which exert tidal forces on it? To answer this question requires a description of the tidal environment, a computation of the gravitational perturbation created by the external bodies, and the extraction of physical, measurable consequences. Among the most exciting of those is the effect of the tidal coupling on the phasing of gravitational waves; a measurement of this effect will allow a black hole or a neutron star to be observationally distinguished from other types of compact bodies.
Gravitational self-force. The term "gravitational self-force" refers to the motion of a small-mass body around a much larger body, in a treatment that goes beyond the test-mass description. In this treatment, the small mass creates a (small but significant) perturbation in the gravitational field of the large body. The perturbation affects the motion of the small body --- the motion is no longer geodesic, but accelerated, and the body is said to move in response to its own gravitational self-force. The perturbation also propagates outward in the form of gravitational waves. What is the nature of the self-forced motion, and what information concerning the strong-field dynamics can be extracted from the gravitational waves? These are the questions that my research group and I have been exploring.
A description of recent research projects carried out with the members of my research group follows below.
Self-force and fluid resonances
The gravitational self-force acting on a particle orbiting a massive central body has thus far been computed for vacuum spacetimes involving a black hole. In this work, post-doctoral fellows Soichiro Isoyama, Raissa Mendes, and I continue an ongoing effort to study the self-force in nonvacuum situations. We replace the black hole by a material body consisting of a perfect fluid, and determine the impact of the fluid's dynamics on the self-force and resulting orbital evolution. We show that as the particle inspirals toward the fluid body, its gravitational perturbations trigger a number of normal modes of the fluid-gravity system, which produce resonant features in the conservative and dissipative components of the self-force. As a proof-of-principle, we demonstrate this phenomenon in a simplified framework in which gravity is mediated by a scalar potential satisfying a wave equation in Minkowski spacetime.
Tidal deformation of a slowly rotating compact body
Graduate student Philippe Landry and I are investigating the tidal deformation of compact bodies in general relativity, allowing the body to rotate. We keep the tidal environment generic, and account for the coupling betwen the tidal and rotational perturbations. The body's response to the external field is measured in part by the familiar gravitational Love numbers, but we find that the coupling between the body's rotation and the tidal environment requires the introduction of an additional set of Love numbers. In a recent development, we discovered that the tidal response of the body is time-dependent even when the tidal field is stationary.
Relativistic theory of surficial Love numbers
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated several years ago by Damour and Nagar. Graduate student Philippe Landry and I revisited this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refined the definition of surficial Love numbers proposed by Damour and Nagar, and formulated it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we developed a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derived a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and showed that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplified the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
Self-force in nonvacuum spacetimes
The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. Former graduate student Peter Zimmerman and I provided a foundation for such extensions, and carried out a concrete formulation of the gravitational self-force in two specific cases. In the first we considered a particle with scalar charge moving in a background spacetime that contains a background scalar field. In the second we considered a particle with electric charge moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields.
Self-force around a five-dimensional black hole
Former undergraduate student Matt Beach, my colleague Bernie Nickel, and I computed the electromagnetic self-force acting on a charged particle held in place outside a five-dimensional black hole. The self-force is repulsive at large distances, and its behaviour is related to a model according to which the force results from a gravitational interaction between the black hole and the distribution of electrostatic field energy attached to the particle. The model, however, is shown to become inadequate at small distances from the black hole, where the self-force changes sign and becomes attractive.
Self-force as a cosmic censor
Former graduate student Peter Zimmerman, postdoctoral fellow Ian Vega, PhD student Roland Hass, and I examined Hubeny's scenario according to which a charged black hole can absorb a particle and be driven toward a final state in which its charge exceeds the mass, signalling the destruction of the black hole. Our analysis incorporates the particle's electromagnetic self-force and the energy radiated to infinity in the form of electromagnetic waves. With these essential ingredients, our sampling of the parameter space reveals no instances of an overcharged final state, and we conjecture that the self-force acts as a cosmic censor, preventing the destruction of a black hole by the absorption of a charged particle. We argue, on the basis of the third law of black-hole mechanics, that this conclusion is robust and should apply to attempts to overspin a Kerr black hole.
Self-force in Schwarschild-de Sitter spacetime
Former graduate student Joseph Kuchar, postdoctoral fellow Ian Vaga, and I computed the self-force acting on an electric charge at rest in Schwarzschild-de Sitter spacetime, allowing the cosmological constant to be either positive or negative. In the case of a positive cosmological constant, we showed that the self-force is always positive, representing a repulsion from the black hole, and monotonically decreasing with increasing distance from the black hole. The spectrum of results is richer in the case of a negative cosmological constant. Here the self-force is not always positive and not always monotonically decreasing. The self-force also approaches a constant asymptotic value when the charge is moved to large cosmological distances; this feature can be explained in terms of an interaction between the charge and the conformal boundary at infinity, which acts as a grounded conductor.