black hole spacetimes | vanishing angular momentum | positive angular momentum |
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vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
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Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
The theory called the theory of general relativity is a classical field theory that in physics describes the field of gravity.
In general relativity, physical spacetime is modeled in terms of differential geometry as a Lorentzian manifold whose pseudo-Riemannian metric – or rather the Levi-Civita connection that corresponds to it – encodes the field of gravity.
The action functional describing the dynamics of this field is the Einstein-Hilbert action, in which the field of gravity enters in terms of the integral of the scalar curvature of the Levi-Civita connection over spacetime.
As is usual in classical field theory, the physically realized configurations – here: Levi-Civita connections – are those that extremize this functional. The Euler-Lagrange equations characterizing these extrema are the Einstein equations.
Historically the theory of general relativity was developed by Albert Einstein based on the theory known as special relativity. Given the conceptual simplicity of the Einstein-Hilbert action, there are several variations of his original version of the theory that are immediately obtained by adding certain terms to the action functional. One of these generalization is supergravity, which extends the theory from ordinary differential geometry to supergeometry.
Textbook accounts:
Steven Weinberg: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley (1972, 2013) [ISBN:978-0-471-92567-5, ark:/13960/t13n7rw1f, spire:1410180]
Charles Misner, Kip Thorne, John Wheeler, Gravitation (1973)
Robert Wald, General Relativity, University of Chicago Press (1984) [doi:10.7208/chicago/9780226870373.001.0001, pdf]
Thanu Padmanabhan, Gravitation – Foundations and Frontiers, Cambridge University Press (2012) [doi:10.1017/CBO9780511807787, spire:852758, toc: pdf]
Pietro Fré, Gravity, a Geometrical Course, Volume 1: Development of the Theory and Basic Physical Applications, Spinger (2013) [doi:10.1007/978-94-007-5361-7]
Pietro Fré, Gravity, a Geometrical Course, Volume 2: Black Holes, Cosmology and Introduction to Supergravity, Springer (2013) [doi:10.1007/978-94-007-5443-0]
on black holes, cosmology and the (D'Auria-Fré formulation of) supergravity
Kirill Krasnov, Formulations of General Relativity – Gravity, Spinors and Differential Forms, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2020) [doi:10.1017/9781108674652, taster:pdf]
Lecture notes:
Matthias Blau, Lecture notes on general relativity (web)
Emil T. Akhmedov, Lectures on General Theory of Relativity (arXiv:1601.04996)
Pietro Menotti, Lectures on gravitation (arXiv:1703.05155)
Daniel Baumann, General Relativity, 2021 (pdf)
Edward Witten, Light Rays, Singularities, and All That, Rev. Mod. Phys. 92 45004 (2020) [arXiv:1901.03928, doi:10.1103/RevModPhys.92.045004, lecture: video 1, 2, 3, 4, 5, 6, 7, 8, 9]
(with focus on causal structure, the Penrose singularity theorem and related aspects)
Kirill Krasnov, Formulations of General Relativity, PIRSA lecture series (Feb 2019) [part 1:doi:10.48660/19020079, 2:doi:10.48660/19020080, 3:doi:10.48660/19020081, 4:doi:10.48660/19020082]
Background on pseudo-Riemannian geometry:
Barrett O'Neill, Semi-Riemannian Geometry With Applications to Relativity, Pure and Applied Mathematics 103, Academic Press (1983) [ISBN:9780125267403]
Shlomo Sternberg, Semi-Riemannian Geometry and General Relativity (2003) [pdf, ark:/13960/t5m927d2v]
Shlomo Sternberg, Curvature in Mathematical Physics, Dover (2012) [ISBN:9780486478555]
Emphasis on mathematical physics
Alan Coley, Mathematical General Relativity (arXiv:1807.08628)
José Natário, Mathematical relativity (arXiv:2003.02855)
Introductory exposition:
See also
See also the references at gravity.
In relation to thermodynamics
Patrick Iglesias-Zemmour, Jean-Marie Souriau Heat, cold and Geometry, in: M. Cahen et al (eds.) Differential geometry and mathematical physics, 37-68, D. Reidel 1983 (web, pdf)
(on thermodynamics and general relativity)
Peter Coles, Einstein, Eddington, and the 1919 Eclipse (arxIv:astro-ph/0102462)
(on the experimental confirmation of general relativity)
Last revised on June 6, 2024 at 09:10:54. See the history of this page for a list of all contributions to it.