PHYSICS SEMINAR
Presented by the Physics Department & Astrophysics Research Cluster
THE STABILITY OF NON-GRAVITATING SCALAR FIELDS
Andres Zambrano
Physics Department
Bishop's University
Friday, May 21, 2010
1:00 pm
Nicolls 1
In scalar-tensor gravity, the Einstein-Hilbert action of General Relativity is modified by introducing a scalar field coupling explicitly to the Ricci curvature of spacetime. Exact solutions of the field equations of these theories which represent Minkowski spacetimes containing non-trivial Brans-Dicke-like scalar fields (non-gravitating or stealth scalar fields) are known. The stability of these solutions has not been addressed in the literature. Given that the scalar field is space-dependent, perturbations are necessarily inhomogeneous and one is faced with the well known problem of gauge dependence in General Relativity. We analyze the stability with respect to tensor perturbations (gravitational waves). This analysis uses the covariant and gauge-invariant first order perturbation formalism suitable for alternative theories of gravity developed by Hwang through the extension of the more well known formalism of Bardeen, Ellis, and Bruni for General Relativity.
In the theory associated to the "improved energy-momentum tensor" the solutions depend on three parameters: we find regions of the parameter space associated with stability and other regions associated with instability. In Brans-Dicke gravity (a different class of scalar-tensor theories), known non-gravitating solutions also contain three parameters: we discuss their stability with respect to homogeneous and inhomogeneous perturbations; also in this case we find regions of stability and regions of instability depending on certain parameters.
