Triangle Seminars

Abstract:
Energy conditions were originally formulated as pointwise bounds on contractions of the stress–energy tensor and have played a central role as assumptions in many foundational results of classical general relativity, most notably the singularity theorems. However, these conditions are generically violated by quantum fields, which admit states with locally negative energy density. Such violations are nevertheless constrained: quantum energy inequalities impose bounds on the magnitude and duration of negative energy.

In this course, I will first introduce the classical energy conditions and review their physical motivation and known violations. Then I will provide a brief introduction to quantum field theory on curved spacetimes and demonstrate how quantum energy inequalities can be derived. Finally, I will discuss in detail the average null energy condition and the limitations it imposes to causality violating spacetimes.

Course plan:
Lecture 1: Classical energy conditions and their violations
Lecture 2: Quantum field theory on curved spacetimes
Lecture 3: A derivation of a quantum energy inequality
Lecture 4: The average null energy condition​

Abstract:
The past decade has completely transformed our understanding of what happens after black holes collide. What we once thought could be well-described by simple ringdowns—neat linear combinations of damped sinusoids (quasi-normal modes)—have turned out to be far richer and messier. Today we recognize ringdowns as an intricate tapestry woven from these quasinormal modes, nonlinear effects, tails, and secular phenomena like gravitational memory. In this talk, I’ll dive into the nonlinear aspects: where the theory stands today and some exciting recent observational claims that we might already be seeing these effects in GW250114. In the second half, I’ll switch gears to the early inspiral phase and tackle a practical question. Post-Newtonian theory is an asymptotic series, so at some point adding higher orders will yield less accurate results. Have we already reached this? By comparing PN to NR, we argue that we can still gain significant improvements by going to higher PN order, but that soon NR and PN will be equally accurate in the early inspiral.

Abstract:
The detection of gravitational waves (GW) after several decades from their formulation opened a new window to observe the universe. The new generation of GW detectors is expected to span a large parameter space, requiring theoretical physicist to develop different approaches to face the two-body problem in General Relativity, each of them based on some perturbative expansion, e.g. Post Newtonian, Post Minkowskian (PM), Self Force. Among these, Effective Field Theories and quantum amplitudes are used together to extract scattering observables which also have a meaningful classical limit, both in the PM and Self Force frameworks.

We analyse the high energy (Regge) regime of spinless two body scattering within this approach, by the prospect of isolating universal effects and to give insights on the resummation of the PM observables at higher orders, made possible by the simplicity of the calculations in the Regge limit. A sequence of classical Feynman diagrams is recognised to contribute to the leading power and leading log(s/t) in the high energy expansion. We compute them up to four loops (5PM) and use analyticity properties of the S-Matrix to maximise the information that we can extract at any PM order.

Abstract:
I will discuss thermal correlators in holographic CFTs. Using the operator product expansion, one can isolate a sector of the correlator which exhibits singularities. Some of these singularities are associated with the singularities of dual asymptotically AdS black holes, providing a useful window into the black hole interior.

Abstract:
Consistency on manifolds other than flat space is known to constrain CFT data, as exemplified by Cardy’s celebrated formula for the asymptotic density of states. I will discuss some recent results coming from studying CFTs on thermal geometries in higher dimensions. In particular, I will show how multi-stress-tensor CFT data, known form the bulk, together with the KMS invariance of the thermal two-point function can be used to compute the latter in holographic theories. Time permitting, I will also discuss new asymptotic formulas for heavy-heavy-light OPE coefficients in generic three-dimensional CFTs.

Abstract:
One of key theoretical inputs for gravitational wave detection is an analytic description of binary dynamics, which provides the foundation for constructing waveform models used to generate waveform templates for detection. The conventional approach to binary dynamics is to construct the effective two-body Hamiltonian, which provides the equations of motion of the binary source. Motivated by the eikonal approximation of 2-to-2 scattering amplitudes in particle physics, we propose to approach the binary dynamics using the Magnusian (eikonal generator), which can be considered as integrated equations of motion. How the new approach relates to post-Minkowskian gravity, and the potential benefits that the new approach may provide, will be discussed.