Seminars of fiscal year 2025

Gravity beyond a single metric: Ghost-free interactions of spin-2 fields.

The fundamental interactions of nature are formulated in terms of fields classified by mass and spin. Two of the most successful theories, General Relativity (GR) and the Standard Model (SM), can be derived from fields of fixed mass and spin by imposing theoretical consistency conditions. The SM contains well-understood interactions for fields with spin s<2, whereas local interacting theories with s>2 face fundamental obstacles, placing s=2 in a special position. Spin-2 fields are intrinsically linked to gravity, yet theories of interacting spin-2 fields remain comparatively unexplored. Lovelock’s theorem essentially establishes GR as the unique theory for a single massless spin-2 field, so it is natural to ask whether GR is part of a larger structure, as electromagnetism was later understood to sit within electroweak theory. This may be relevant to open questions in gravitational physics, such as dark matter, dark energy, the Hubble tension, and, ultimately, quantum gravity. However, theories of interacting spin-2 fields are notoriously plagued by ghosts—pathological fields with negative kinetic energy—and requiring their absence severely restricts the allowed interactions. In this talk, I will discuss multi-gravity theories, containing multiple interacting spin-2 fields, focusing on their theoretical consistency via the absence of ghosts.

Unified On-Shell Framework for Black-Hole Mergers and Hawking Radiation

Over the past seven years, the amplitudes community has shown that black-hole interactions can be described — to all orders in the post-Minkowskian expansion — purely in terms of on-shell amplitudes, without ever invoking a Lagrangian or equations of motion. This approach — based on the most advanced amplitude techniques used for precision physics at the LHC — has already led to state-of-the-art calculations in General Relativity and to the growth of a vibrant research community.

However, despite this progress, very little is known about whether this framework can be made systematic enough to address more complex aspects of black-hole physics — such as binary mergers or the Hawking radiation they emit — both of which are inherently nonperturbative phenomena.

In this talk, I will argue that these two phenomena can be treated within a unified framework based on a universal, mass-changing three-point amplitude. Using massive spinor-helicity and on-shell methods, I will show that the amplitude describing both cases is unique, with only a coupling constant left undetermined. This coupling can be fixed by matching to physical and gauge-invariant quantities. Once the matching conditions are specified, this building block can be iterated, as in any other perturbative on-shell approach to quantum field theory (QFT), to compute higher order processes.

As an application, I will show how to derive conservation laws and memory waveforms in black-hole mergers. Using the same tools, I will then explain how to compute mass-changing effects in binary dynamics arising from the presence of event horizons, including those associated with Hawking radiation. To the best of our knowledge, this provides the first example of a universal simplicity shared by black-hole mergers and Hawking radiation — a connection that becomes evident when viewed through on-shell methods.