WHAT IS A REDUCED BOUNDARY IN GENERAL RELATIVITY?

by Dr Emanuele Battista (KIT, Karlsruhe, TTP)

Friday 9 Apr 2021, 14:30 → 15:30 Europe/Rome

https://infn-it.zoom.us/j/81784364024?pwd=Q2pZaEhpT2h4U0lQejQxRFJlNEdFdz09 (Zoom)

Geometric measure theory can be viewed as differential geometry,
generalized through measure theory to deal with maps and surfaces that are
not necessarily smooth, and applied to the calculus of variations. Within this
branch of mathematics, the notion of reduced boundary of a finite-perimeter
set (also known as Caccioppoli set) fulfills a central role.
In this talk, I will consider the measure-theoretic concepts of finite-perimeter
sets and their reduced boundary in the context of general relativity in the
case of Euclidean Schwarzschild geometry. Furthermore, I will show how this
framework can be employed to calculate the intrinsic quantum mechanical
entropy of a black hole.
The research program described in this seminar prepares the ground for a
measure-theoretic approach to several topics in gravitational physics.
Moreover, it can have important implications for a functional integral
approach to Euclidean quantum gravity, where finite-perimeter sets having a
non-empty reduced boundary represent good candidates for the evaluation
of the underlying in-out amplitude.

Link Zoom

ID riunione: 817 8436 4024
Passcode: 555612