General Relativity and the Einstein Equations

2008/12/04 by Yvonne Choquet–Bruhat · 7 citations
Physics and Astronomy · #Relativity and Gravitational Theory #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Einstein #Theory of relativity #General relativity #Physics #Mathematical physics #Theoretical physics

paper · doi:10.1093/acprof:oso/9780199230723.001.0001

openalex publication_date 2008/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Abstract General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. This book overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.

Citations

• Domain of Dependence
• Numerical simulations of general gravitational singularities
• Gravitational Waves in Closed Universes
• A Class of Exact Solutions of Einstein's Field Equations
• Describing general cosmological singularities in Iwasawa variables
• Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy
• Fixation of Coordinates in the Hamiltonian Theory of Gravitation
• Numerical investigation of cosmological singularities
• Symmetric hyperbolic linear differential equations
• Oscillatory approach to a singular point in the relativistic cosmology
• The mass of an asymptotically flat manifold
• Gravitational Collapse and Space-Time Singularities
• Universality and scaling in gravitational collapse of a massless scalar field
• Solutions of the Einstein-Maxwell equations with many black holes
• Motion of isolated bodies
• Propagation and Quantization of Rarita-Schwinger Waves in an External Electromagnetic Potential
• Approche comparative de la conception des droits de l'homme, dans la philosophie occidentale et africaine
• Strengths of naked singularities in Tolman-Bondi spacetimes
• Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions
• The Instability of Naked Singularities in the Gravitational Collapse of a Scalar Field
• On Continued Gravitational Contraction
• The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid
• Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
• A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds
• Consistent supergravity

Cited by

• The Shell Collapsar—A Possible Alternative to Black Holes
• Superradiant instabilities of asymptotically anti-de Sitter black holes
• Testing General Relativity with Present and Future Astrophysical Observations
• Relic neutrino freeze-out: Dependence on natural constants
• On the Choquet-Bruhat–York–Friedrich formulation of the Einstein–Euler equations
• Smooth Gowdy-symmetric generalized Taub–NUT solutions
• Shing-Tung Yau [wikipedia]