Scattering on compact body spacetimes

In this thesis we study the propagation of scalar and gravitational waves on compact body spacetimes. In particular, we consider spacetimes that model neutron stars, black holes, and other speculative exotic compact objects such as black holes with near horizon modifications. We focus on the behaviour of time-independent perturbations, and the scattering of plane waves.

First, we consider scattering by a generic compact body. We recap the scattering theory for scalar and gravitational waves, using a metric perturbation formalism for the latter. We derive the scattering and absorption cross sections using the partial-wave approach, and discuss some approximations.
The theory of this chapter is applied to specific examples in the remainder of the thesis.

The next chapter is an investigation of scalar plane wave scattering by a constant density star. We compute the scattering cross section numerically, and discuss a semiclassical, high-frequency analysis, as well as a geometric optics approach. The semiclassical results are compared to the numerics, and used to gain some physical insight into the scattering cross section interference pattern.

We then generalise to stellar models with a polytropic equation of state, and gravitational plane wave scattering. This entails solving the metric perturbation problem for the interior of a star, which we accomplish numerically. We also consider the near field scattering profile for a scalar wave, and the correspondence to ray scattering and the formation of a downstream cusp caustic.

The following chapter concerns the scalar wave absorption spectrum of exotic compact objects, modelled as black holes with a partially reflective surface just above the event horizon. We discuss the systems natural modes of vibration, and derive low and high-frequency approximations for the absorption spectra.

Finally, we apply complex angular momentum (CAM) techniques to the perturbed constant density stellar model. We compute Regge poles (CAM resonance modes) by numerically solving a four-term recurrence relation. The utility of the CAM method is demonstrated by reproducing the scattering cross sections calculated earlier using partial waves.