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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 $\mathbf{B} O(n1,1) \to \mathbf{B}GL(n)$, defining a pseudoRiemannian metric;
a connection that is locally a Lie algebravalued 1form with values in the Poincare Lie algebra.
such that this is a Cartan connection.
(This parameterization of the gravitational field is called the firstorder formulation of gravity.) The component $E$ of the connection is the vielbein that encodes a pseudoRiemannian metric $g = E \cdot E$ on $X$ and makes $X$ a pseudoRiemannian manifold. Its quanta are the gravitons.
The nonpropagating 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 EinsteinHilbert action.
More generally, supergravity is a gauge theory over a supermanifold $X$ for the super Poincare group. The field of supergravity is a Liealgebra 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'AuriaFre formulation of supergravity for further details
gravitational entropy
Textbooks include
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
The theory of gravity based on the standard EinsteinHilbert action may be regarded as just an effective quantum field theory, which makes some of its notorious problems be nonproblems:
See also the references at general relativity.
The (reduced) covariant phase space of gravity (presented for instance by its BVBRST complex, see there fore more details) is discussed for instance in
which is surveyed in
Careful discussion of observables in gravity is in
The result that gravity is not renormalizable is due to
Review includes
.
Last revised on July 24, 2018 at 01:18:45. See the history of this page for a list of all contributions to it.