Current seminars

Recently it was proposed that GME experiments may probe linearized gravity only as a quantum controlled field and not as a quantum field theory. I will argue that the concept of a relativistic quantum controlled field is fundamentally flawed because of causality violation. Quantum control is also implicit in a recent path-integral description of those experiments, which casts doubt on its validity beyond the Newtonian approximation.

The first half concerns Gregory—Laflamme (GL) instabilities which occur at the level of linearised gravity. Heuristic and numerical evidence suggests that GL instabilities plague black holes in dimensions greater than 4 which have an event horizon that has one direction that is large compared to all others. Sam will discuss a direct mathematical proof of the Gregory—Laflamme instability for the 5D Schwarzschild black string. The proof relies upon reducing the linearised vacuum Einstein equation to a Schrödinger equation to which direct variational methods can be applied.   The second half of the talk concerns the blue-shift instability in the interior of rotating Kerr black holes at the level of linearized gravity. This instability is intimately connected to Penrose’s strong cosmic censorship conjecture. In contrast to the GL instability, this instability is weak in the sense that the C^0 norms of metric perturbations do not grow. Jan will discuss a mathematical result on the blue-shift instability, illustrate the mechanism by a toy example, and, if time permits, discuss some elements of the proof.

The Standard Model (SM) is one of the greatest successes of modern theoretical physics. Despite this, mathematical references studying the full SM (rather than just its sectors in isolation) on curved spacetimes are somewhat scarce, even though it seems important to understand the theory at a classical level in a more geometric setting. In my talk, I will first briefly review the mathematical structure of the SM Lagrangian, the corresponding Euler-Lagrange equations, and some of their basic properties, particularly related to conformality. Then, I will present a global existence result for the SM equations on four-dimensional spacetimes of expanding type. The talk is focused on a geometrically intrinsic approach to the theory, and the main ingredient for the proof is a gauge-invariant energy estimate. This is joint work with Volker Branding.