Research Interests | External Research Grants | Internal Research Grants
My work is supported by the National Science and Engineering Research Council of Canada (NSERC) and Bishop's University.
RESEARCH INTERESTS
I am a theoretical physicist with research interests in gravitational physics, quantum field theory under external conditions and the rich interplay between the two.
Below is a list and description of my more recent projects.
Magnetic monopole in AdS space: symmetry breaking via gravitation
In this work, we obtain a magnetic monopole where the spontaneous symmetry breaking occurs via gravitation. In this scenario, the vacuum expectation value of the scalar field is related to the constant Ricci curvature of AdS space. At large distances, the spacetime is Schwarzschild-AdS with the magnetic monopole acting as the source.The original action is conformally invariant and contains a higher-derivative gravity term instead of the Einstein-Hilbert term. However, after symmetry breaking, the low energy effective action is governed by Einstein gravity (General Relativity) and this is why outside the core region the metric is Schwarzschild. Numerical computations show that the spacetime is non-singular in the core region. This is due to a departure from the Schwarzschild metric at short distances where higher-derivative contributions become more significant.
Quantum corrections to the gravitationally coupled magnetic monopole
During the spontaneous symmetry breaking of the gauge group, the conformal symmetry of the vacuum for the gravitationally coupled magnetic monopole gets partly broken from the 15 parameter conformal group SO(2,4) to a 14 parameter subgroup. The residual conformal symmetry needs to be broken and this is achieved by including quantum matter corrections. The anomalous trace for the monopole action contains the usual higher-derivative geometrical terms but also non-geometrical terms because of the presence of a non-zero commutator curvature. The parameters related to Einstein gravity in the effective action can be expressed in terms of the renormalized constants of the theory and Planck's constant, a novel and interesting result.
Black hole thermodynamics and gravitational collapse of a 5D instanton
The 4D instanton is stable under gravity: it does not undergo gravitational collapse. This is no longer the case in 5D where instantons can collapse to a black hole. 5D gravity systems have attracted attention because of the AdS/CFT correspondence and brane-world scenarios. My M.Sc. student and I are investigating numerically the spherical gravitational collapse of a 5D instanton to a black hole and tracking the "free energy" during the collapse. We are presently exploring how different non-static initial conditions affect the spacetime and the thermodynamics at late stages.
Gravitational lensing
Early on in my career I worked on gravitational lensing problems and obtained a seminal result for the deflection of light in Weyl gravity. We showed that the deflection was negative (repulsive) on galactic scales, a problem for the viability of the theory if the conformal symmetry was left unbroken. I have continued to work from time to time on lensing problems and a few years ago, with my student Jeremy Godin, we obtained the deflection of light in the Kerr metric up to second order. This result was interesting because the second order correction to Schwarzschild is actually greater in magnitude than the first order correction due to rotation for any realistic astrophysical object.
Quantum field theory under the influence of external conditions
I have interests in statistical or quantum field theory under external conditions such as the curvature of spacetime or the boundary conditions imposed by materials such as perfect conductors. External conditions distort vacuum field fluctuations leading to a measurable effect called the Casimir effect. A new generation of highly precise Casimir experiments has turned this into an exciting field and forced theorists to develop elaborate mathematical techniques to carry out complex calculations. I have made some important contributions in this area. In 2006, I developed a novel multidimensional cut-off technique and obtained explicit Casimir formulas for Dirichlet and Neumann boundary conditions for geometries with arbitrary sides. Using the results of this work, I became the first to solve exactly the full 3+1 dimensional Dirichlet Casimir piston, a scenario introduced in 2004 but solved only in 2+1 dimensions. With my previous honors student Ilana MacDonald we showed explicitly that in the piston scenario non-renormalizable hypersurface terms cancel in any dimension.
Recently, with my collaborator, Valery Marachevsky of the Laboratoire Kastler Brossel, CNRS Paris, we recently published an important paper that shows that a perfect conductor will have continuum modes (be partly transparent) in a compactified M4 x S1 spacetime.
EXTERNAL RESEARCH GRANTS
2013 - 2018 |
Five year NSERC Discovery GrantA new dynamical approach to black hole thermodynamics. |
2008 - 2013 |
Five year NSERC Discovery GrantConformal anomaly in the gravitationally coupled magnetic monopole and vacua effects under external conditions. |
2005 - 2008 |
Three year NSERC Discovery grantMassless Solitons via Gravitation: Kinks, Vortices, and Monopoles in Curved Spacetime. |
INTERNAL RESEARCH GRANTS
2014 - 2015  |
Bishop’s Senate Research GrantThe hierarchy problem, scale invariance and radiatively induced symmetry breaking. |
2011 - 2012 |
Bishop’s Senate Research GrantThe classical statistical mechanics of black hole entropy. |
2008 - 2009 |
Bishop’s Senate Research GrantEntropy formation during gravitational collapse |
2007 |
Bishop’s Merit Bonus for excellence in research |
2004 - 2005 |
Bishop’s Senate Research GrantMassless Kinks in an Evolving Spacetime. |