**Description of research**

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.

Here's a description of recent research projects carried out with the
members of my research group.

### 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.