Numerical simulations of general gravitational singularities

Abstract

This paper covers some of the current techniques and issues involved in performing numerical simulations of the formation of singularities.

This work was part of the 2006 AEI conference on New Frontiers in Numerical Relativity and was published in an issue of Classical and Quantum Gravity on that conference

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• A Hamiltonian Formulation of the BKL Conjecture
• Numerical simulations of loop quantum Bianchi-I spacetimes
• Describing general cosmological singularities in Iwasawa variables
• Numerical loop quantum cosmology: an overview
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• Loop Quantum Cosmology: A brief review
• Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture
• Chimera: A hybrid approach to numerical loop quantum cosmology
• Spike behavior in the approach to spacetime singularities
• Bianchi I model in terms of nonstandard loop quantum cosmology: Classical dynamics
• Mathematical General Relativity
• Cosmology using numerical relativity
• Big Bang Singularity Resolution In Quantum Cosmology
• Arithmetic and Hyperbolic Structures in String Theory
• A New Class of Asymptotically Non-Chaotic Vacuum Singularities
• Open problems in mathematical physics
• Localized big bang stability for the Einstein-scalar field equations
• Numerical Relativity Beyond Astrophysics
• Non-orthogonally transitive $G_2$ spike solution
• Electrocardiogram of the Mixmaster Universe
• Mixmaster Fluids Near the Big Bang
• Crossing the singularity of a gravitational wave collision
• Space-like Singularities of General Relativity: A Phantom menace?
• Examination of the nature of the Bianchi type cosmological singularities