General Relativity & Quantum Cosmology

Current waveform models of binary black hole mergers incorporate a large amount of analytical information during the inspiral phase. In contrast, post-merger descriptions typically rely on phenomenological ansätze informed by numerical relativity, with the quasi-normal mode frequencies providing the only direct analytical input. In this seminar, I will first give a gentle introduction to black hole perturbation theory and the Green’s function approach, which is useful for describing the time-domain response of a black hole to a dynamical source, e.g., an infalling test particle. I will then present an analytical framework to study the dynamical excitation of quasi-normal modes during the plunge–merger–ringdown stages for generic orbits, including highly eccentric ones, and discuss its implications for ringdown modeling. I will conclude by presenting novel insights into the modelling of the prompt response, fundamental to correctly capture the signal emitted during the merger at the linear level. 

We study thermodynamics of spherically-symmetric spacetime with the aim of exploring spacetime entropy as an adiabatic invariant. We first describe the geometry and dynamics in terms of a local frame adapted to spherical foliations and find a geometro-hydrodynamic interpretation: the spacetime can be viewed as the worldvolume of a concentric stack of "gravitational bubbles", spherical collective modes with the Misner-Sharp energy density and a geometric pressure. We then introduce a notion of work and heat, and investigate the covariant phase space of a thermodynamic action corresponding to the adiabatic boundary condition. Identifying the phase space with the thermodynamic state space, these should provide the foundation for the spacetime thermodynamics. As an example, we apply this to the apparent horizon and employ Caratheodory’s idea, to derive the entropy of the dynamical horizon as an adiabatic-invariant Hamiltonian. This agrees with the Bekenstein-Hawking formula for the surface area of the apparent horizon, where a dynamical version of Hawking temperature appears. [arXiv: 2601.03077 + to appear]

Carrying the insights of conditional probability to the quantum realm is notoriously difficult due to the non-commutative nature of quantum observables. Nevertheless, conditional expectations on C* and von Neumann algebras have played a significant role in the development of quantum information theory, and especially the study of quantum error correction. In quantum gravity, it has been suggested that conditional expectations may be used to implement the holographic map algebraically, with quantum error correction underlying the emergence of spacetime through the generalized entropy formula. However, the requirements for exact error correction are almost certainly too strong for realistic theories of quantum gravity. In this talk, we provide an overview of the multifaceted nature of quantum conditional probability by exploring different non-commutative generalizations of conditional expectations which meet the demands of non-exact error correction. We then exemplify the utility of these tools through two examples. First, we demonstrate how operator valued weights can be used to classify the possible symmetries (including non-invertible symmetries) of a quantum system. Then, we introduce a generalization of Connes’ spatial theory leading to a fully non-commutative form of Bayes' law. This allows for an exact quantification of the information gap occurring in the data processing inequality for arbitrary quantum channels. When applied to algebraic inclusions, this further provides an approach to factorizing the entropy of states into a sum of terms including an emergent area operator that is fully non-commutative rather than central.