Causality, extremality, and all that

Abstract

It is well known that general relativity, when viewed from the perspective of quantum field theory, is a non-renormalisable theory --- this is central to the problem of quantum gravity. A less problematic perspective is to view general relativity from the perspective of effective field theory. As such, the Einstein-Hilbert action is considered just the lowest-order term in a derivative expansion, where higher-order terms are suppressed and agnostically parameterise the effects of an unknown UV completion. It was thought that all effective actions of this form are able to accurately capture the effect of UV physics at low energies, but certain observables within the low-energy theories can tip us off about possibly undesirable properties of UV completions. In this thesis, we are concerned with such qualitative features of low-energy gravitational effective field theories. In the first part, we will consider the restrictions that causality puts on the Wilson coefficients of an effective field theory. To that end, we first establish the use of an appropriate notion of causality and find consistency with gravitational positivity bounds. We then apply this so-called infrared causality to put constraints on the leading-order EFT of gravity on black hole and pp-wave backgrounds in five or higher dimensions. In the second part, we are concerned with qualitative features of extremal black holes, the kinematics of which are known to have interesting implications on quantum gravity. We first study deformations to the near-horizon region of known extremal black holes and use intuition from these to state a conjecture on Wilson coefficients in terms of the behaviour of the deformations near the horizon. Finally, we consider a prototypical scalar field toy example for restrictions on EFTs in the context of $\mathrm{AdS}_{2}$ holography.