black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
A field configuration of the physical theory of gravity on a spacetime $X$ is equivalently
a vielbein field, hence a reduction of the structure group of the tangent bundle along $\mathbf{B} O(n-1,1) \to \mathbf{B}GL(n)$, defining a pseudo-Riemannian metric;
a connection that is locally a Lie algebra-valued 1-form with values in the Poincare Lie algebra.
such that this is a Cartan connection.
(This parameterization of the gravitational field is called the first-order formulation of gravity.) The component $E$ of the connection is the vielbein that encodes a pseudo-Riemannian metric $g = E \cdot E$ on $X$ and makes $X$ a pseudo-Riemannian manifold. Its quanta are the gravitons.
The non-propagating field? $\Omega$ is the spin connection.
The action functional on the space of such connection which defines the classical field theory of gravity is the Einstein-Hilbert action.
More generally, supergravity is a gauge theory over a supermanifold $X$ for the super Poincare group. The field of supergravity is a Lie-algebra valued form with values in the super Poincare Lie algebra.
The additional fermionic field $\Psi$ is the gravitino field.
So the configuration space of gravity on some $X$ is essentially the moduli space of Riemannian metrics on $X$.
for the moment see D'Auria-Fre formulation of supergravity for further details
Penrose-Hawking theorem?, cosmic censorship hypothesis
gravitational entropy
Historical texts:
Textbook accounts:
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]
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)
See also
Discussion of classical gravity via its perturbative quantum field theory:
Günter Scharf, Quantum Gauge Theories – A True Ghost Story, Wiley 2001
Gustav Uhre Jakobsen, General Relativity from Quantum Field Theory (arXiv:2010.08839)
This way the theory of gravity based on the standard Einstein-Hilbert action may be regarded as just an effective quantum field theory, which makes some of its notorious problems be non-problems:
See also the references at general relativity.
The (reduced) covariant phase space of gravity (presented for instance by its BV-BRST complex, see there fore more details) is discussed for instance in
which is surveyed in
Careful discussion of observables in gravity is in
Further discussion of the phase space of gravity in first-order formulation via BV-BFV formalism:
Michele Schiavina, BV-BFV approach to general relativity (2015) [pdf, pdf]
Alberto Cattaneo, Michele Schiavina, BV-BFV approach to General Relativity, Einstein-Hilbert action, J. Math. Phys. 57 023515 (2016) [arXiv:1509.05762, doi:10.1063/1.4941410]
Alberto Cattaneo, Michele Schiavina, The reduced phase space of Palatini-Cartan-Holst theory, Ann. Henri Poincaré 20 (2019) 445 [arXiv:1707.05351, doi:10.1007/s00023-018-0733-z]
Alberto Cattaneo, Michele Schiavina, BV-BFV approach to General Relativity: Palatini-Cartan-Holst action, Adv. Theor. Math. Phys. 23 (2019) 1801-1835 [arXiv:1707.06328, doi:10.4310/ATMP.2019.v23.n8.a3]
Alberto S. Cattaneo, Phase space for gravity with boundaries, Encyclopedia of Mathematical Physics (2023) [arXiv:2307.04666]
(following Kijowski & Tulczyjew (2005))
The result that gravity is not renormalizable is due to:
Review:
.
Last revised on July 13, 2023 at 12:14:22. See the history of this page for a list of all contributions to it.