Selected Topics on General Relativity

Covered topics (time-ordered):

• Dynamics of compact binaries and gravitational-wave inspirals (V. Witzany)

Equations of motion in the post-Newtonian expansion. Equations of motion in the mass-ratio (post-geodesic) expansion. Phasing in gravitational-wave inspirals and the post-adiabatic iteration. Decay of an eccentric binary at leading PN order (Peters-Mathews formulas). Kerr geodesics and their integration. Adiabatic decay of “constants of motion” in Kerr (Mino formulas). The question of spins and non-integrability.

• Extensions of General Relativity in cosmology and astrophysics (I. Saltas)

I will start with a discussion of the hurdles of General Relativity (GR) to address the dark energy problem, and I will then introduce the basics of extending Einstein’s theory in cosmology. I will explain how the introduction of new degrees of freedom beyond GR can offer new perspectives for the dark energy problem, and will discuss their phenomenological implications for cosmology and astrophysics.

• Quantum phenomena in cosmological spacetimes (A. Conroy)

We investigate aspects of classical and quantum cosmology. In particular, we
(i) discuss the open topic of how to define temperature and surface gravity in dynamical spacetimes;
(ii) derive the mode decomposition and Wightman two-point function for FLRW spacetimes; and
(ii) investigate the thermal behaviour of an Unruh-DeWitt particle detector in asymptotically-de Sitter spacetimes.

• Gravitational action, boundary terms, and black hole thermodynamics (D. Kubizňák)

By demanding the gravitational action to yield a well posed variational problem, one needs to add the so called York-Gibbons-Hawking term. We shall derive this term and study some of its applications to black hole thermodynamics and beyond.