M Vasu’s research while affiliated with Yale University and other places

We perform a linear perturbation study of two instances of Bianchi III manifolds: dust and radiation. We take the metric approach and perturb the metric component by component. Once we construct gauge-invariant variables we work without fixing the gauge and use the perturbations as ingredients of the gauge-invariant equations that result when the field equations are enforced to first order. Exact solutions to gauge-invariant equations are extracted explicitly. When possible, we rewrite our solutions as wave equations, giving the evidence of gravitational radiation and sound waves. In total, we list four gravitational wave equations, three sound wave equations and one equation coupling a gravitational wave to a sound wave. These resonances are not at all independent and we point out some identities. Some late-time behaviour is discussed. The approach is wholly general; the resulting equations are physically relevant and informative.