GRG Editor's Choice: Mathematical general relativity

Coley, A.A., Mathematical general relativity, Gen Relativ Gravit (2019) 51: 78. https://doi.org/10.1007/s10714-019-2559-5

Editor's Choice (Invited Report: State of the Field)

First Online: 24 June 2019

Abstract:

We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship hypothesis and the Penrose inequality, the uniqueness of black hole solutions and the stability of Kerr spacetime and the final state conjecture, critical phenomena and the Einstein–Yang–Mills equations, and a number of other problems in classical general relativity. We then broaden the scope and discuss some mathematical problems motivated by quantum gravity, including AdS/CFT correspondence and problems in higher dimensions and, in particular, the instability of anti-de Sitter spacetime, and in cosmology, including the cosmological constant problem and dark energy, the stability of de Sitter spacetime and cosmological singularities and spikes. Finally, we briefly discuss some problems in numerical relativity and relativistic astrophysics.

The author: 

Alan A. Coley is Professor at the Department of Mathematics and Statistics of Dalhousie University, Halifax, Canada.

His research interests are General Relativity, Mathematical Cosmology, Differential Geometry and Dynamical Systems.

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community. 

“Invited Reports: State of the Field” are detailed status reports addressed to experts and researchers who would like to understand the subject thoroughly.