Speaker : A. Shah

Title : Gauge invariant perturbations of Petrov type D spacetimes - II

Abstract : In this section of the two-part talk, we discuss and present the gauge-invariant quantities that are expressed in terms of GHP operators, presenting their tetrad-invariance inherently. We begin with the two odd parity invariants, one by Moncrief and the other by Regge-Wheeler ; we also present the 2nd order (in radial and time derivative) PDE it satisfies, showing how easy it is to "separate" the equations into radial and angular parts (in the GHP form itself). Then we move on to the tougher even-parity invariant, the one by Zerilli, and also present the differential equation it satisfies. We then present a new even-parity invariant we recently found, along with the separable 2nd order equation it satsfies. Later on we also show another odd- and even-parity invariants, and relations between them. For completeness, we also present the invariants, Ψ0 and Ψ4, along with the equations they satisfy.