## Geometry Seminar - Abstracts

### Talk

Monday 8 April 2019, 16:00-17:00 in HG03.085

**Annegret Burtscher** (RU)

*The second Bianchi identity for singular spacetimes*

### Abstract

The second Bianchi identity is a well-known and fundamental
differential identity of the Riemann curvature tensor, which holds on any
smooth (semi-)Riemannian manifold. In general relativity, due to the relation
of the Riemann curvature tensor and the energy-momentum tensor via the
Einstein equations, the energy-momentum tensor must also satisfy the
contracted second Bianchi identity. This identity then naturally implies
energy and momentum conservation for matter fields. What happens in situations
where curvature singularities associated to timelike singularities occur and
the classical Bianchi identity no longer makes sense? In this talk we
establish a distributional version of the contracted Bianchi identity, and
investigate for which matter fields this identity holds. Surprisingly, the
well-known Reissner-Weyl-Nordström spacetime of a single point charge does not
belong to this class, but other electromagnetic theories and certain perfect
fluids with one-dimensional timelike singularities satisfy the second Bianchi
identity weakly. This is joint work with Michael Kiessling and Shadi
Tahvildar-Zadeh (both Rutgers University).

(

Back to geometry seminar schedule)