Numerical methods for finding stationary gravitational solutions

Abstract

The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory–Laflamme zero modes of small rotating black holes in AdS. We also include several tools and tricks that have been useful throughout the literature.

Locations

• Classical and Quantum Gravity - View
• arXiv (Cornell University) - View - PDF
• ePrints Soton (University of Southampton) - View - PDF
• Apollo (University of Cambridge) - View - PDF
• DataCite API - View