### Conveners

#### Topological Methods, Global Existence Problems, and Spacetime Singularities: Block 1

- Spiros Cotsakis (Univ. Aegean, Greece; IGC, RUDN Univ., Moscow, Russia)

### Description

This is session is about global causal structure problems, topological methods for spacetime structure and evolution, global existence and stability problems, nature and classification of singularities, general theory of black holes, character of singularities in geometric extensions of GR and string theories.

We consider the problem of asymptotic synchronization of different spatial points coupled to each other in inhomogeneous spacetime and undergoing chaotic Mixmaster oscillations towards the singularity. We demonstrate that for couplings larger than some threshold value, two Mixmaster spatial points $A,B$, with $A$ in the past of $B$, synchronize and thereby proceed in perfect unison towards the...

I will present recent developments on the geometric analysis of Einstein's field equations for spacetimes containing singularity hypersurfaces, which represent gravitational waves, shock waves, or phase interfaces. I will explain the formulation and classification of scattering laws and junction conditions at singularities, and will discuss bouncing cosmologies (big bang, big crunch). I will...

We present new results on the singularity structure and asymptotic analysis of a brane-world that consists of a flat 3-brane embedded in a five-dimensional bulk. The bulk matter is modelled by a fluid that satisfies a non-linear equation of state of the form $p=\gamma\rho^{\lambda}$, where p is the ‘pressure’ and $\rho$ is the ‘density’ of the fluid. We show that for appropriate ranges of the...

A class of naked strong curvature singularities is ruled out in Bakry-Emery spacetimes by using techniques of differential topology in Lorentzian manifolds.

These spacetimes adimit a Bakry-Emery-Ricci tensor which is a generalization of the Ricci tensor. This result supports to validity of Penrose's strong cosmic censorship conjecture in scalar-tensor gravitational theories, which include...

In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space-times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space-time for which null and...

I will discuss the status of our understanding of singularities in general relativistic spacetimes. I will cover briefly their definition, location, and existence, while focusing on their classical and quantum nature. I will emphasize what we know, and what we do not know about the effect of test particles and waves on a zoo of singularities, from quasiregular to nonscalar curvature to scalar...