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\begin{document}

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\section*{gravity}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{details}{Details}\dotfill \pageref*{details} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{CovariantPhaseSpaceReferences}{Covariant phase space}\dotfill \pageref*{CovariantPhaseSpaceReferences} \linebreak
\noindent\hyperlink{nonrenormalizability}{Non-renormalizability}\dotfill \pageref*{nonrenormalizability} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

A [[field (physics)|field]] configuration of the [[physical theory]] of \emph{gravity} on a [[spacetime]] $X$ is equivalently

\begin{itemize}%
\item 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]];


\item a [[connection on a bundle|connection]] that is locally a [[Lie algebra-valued 1-form]] with values in the [[Poincare Lie algebra]].

\begin{displaymath}
(E, \Omega) : T X \to \mathfrak{iso}(d-1,1)
\end{displaymath}
such that this is a [[Cartan connection]].



\end{itemize}
(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 [[graviton]]s.

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 Euclidean group|super Poincare group]]. The field of supergravity is a Lie-algebra valued form with values in the [[super Poincare Lie algebra]].

\begin{displaymath}
(E,\Omega, \Psi) : T X \to \mathfrak{siso}(d-1,1)
\end{displaymath}
The additional [[fermion]]ic field $\Psi$ is the [[gravitino]] field.

So the [[configuration space]] of gravity on some $X$ is essentially the [[moduli space of Riemannian metrics]] on $X$.

\hypertarget{details}{}\subsection*{{Details}}\label{details}

\begin{quote}%
for the moment see [[D'Auria-Fre formulation of supergravity]] for further details


\end{quote}
\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item [[Einstein-Hilbert action]], [[Einstein equation]]


\item [[rubber-sheet analogy of gravity]]


\item [[general covariance]]


\item [[Penrose-Hawking theorem]], [[cosmic censorship hypothesis]]


\item [[weak gravity conjecture]]


\item [[first order formulation of gravity]]

\begin{itemize}%
\item [[Plebanski formulation of gravity]], [[gravity as a BF-theory]], [[teleparallel gravity]]


\item [[Chern-Simons gravity]]



\end{itemize}

\item [[Einstein-Maxwell theory]], [[Einstein-Yang-Mills theory]]


\item [[higher order curvature corrections]]


\item [[supergravity]]


\item 2d gravity

\begin{itemize}%
\item [[Liouville theory]]


\item [[Jackiw-Teitelboim gravity]]



\end{itemize}

\item [[spacetime]]

\begin{itemize}%
\item [[black hole]]


\item [[gravitational wave]]



\end{itemize}

\item gravitational entropy

\begin{itemize}%
\item [[Bekenstein-Hawking entropy]]


\item [[generalized second law of thermodynamics]]



\end{itemize}

\item [[energy condition]]


\item [[positive energy theorem]]


\item [[asymptotic safety]]


\item [[cosmology]]

\begin{itemize}%
\item [[standard model of cosmology]]

\end{itemize}

\item [[MOND]]


\item [[computer experiment]]: [[gevolution]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\hypertarget{general}{}\subsubsection*{{General}}\label{general}

Textbooks include

\begin{itemize}%
\item [[Charles Misner]], [[Kip Thorne]], [[John Wheeler]], \emph{[[Gravitation]]}, 1973

\end{itemize}
Lecture notes

\begin{itemize}%
\item [[Matthias Blau]], \emph{Lecture notes on general relativity} (\href{http://www.blau.itp.unibe.ch/GRLecturenotes.html}{web})


\item Emil T. Akhmedov, \emph{Lectures on General Theory of Relativity} (\href{https://arxiv.org/abs/1601.04996}{arXiv:1601.04996})


\item Pietro Menotti, \emph{Lectures on gravitation} (\href{https://arxiv.org/abs/1703.05155}{arXiv:1703.05155})



\end{itemize}
See also

\begin{itemize}%
\item [[Alan Coley]], \emph{Mathematical General Relativity} (\href{https://arxiv.org/abs/1807.08628}{arXiv:1807.08628})

\end{itemize}
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:

\begin{itemize}%
\item [[John Donoghue]], \emph{Introduction to the Effective Field Theory Description of Gravity} (\href{http://arxiv.org/abs/gr-qc/9512024}{arXiv:gr-qc/9512024})

\end{itemize}
See also the references at \emph{[[general relativity]]}.

\hypertarget{CovariantPhaseSpaceReferences}{}\subsubsection*{{Covariant phase space}}\label{CovariantPhaseSpaceReferences}

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

\begin{itemize}%
\item [[Romeo Brunetti]], [[Klaus Fredenhagen]], \emph{Towards a Background Independent Formulation of Perturbative Quantum Gravity} (\href{http://arxiv.org/abs/gr-qc/0603079}{arXiv:gr-qc/0603079})

\end{itemize}
which is surveyed in

\begin{itemize}%
\item Katarzyna Rejzner, \emph{The BV formalism applied to classical gravity} (\href{http://rejzner.com/talks/Karlsruhe2011.pdf}{pdf})

\end{itemize}
Careful discussion of [[observables]] in gravity is in

\begin{itemize}%
\item [[Igor Khavkine]], \emph{Local and gauge invariant observables in gravity}, talk at \href{http://www.science.unitn.it/~moretti/convegno/convegno.html}{Operator and Geometric Analysis on Quantum Theory}, preprint \href{https://arxiv.org/abs/1503.03754}{arXiv:1503.03754}

\end{itemize}
\hypertarget{nonrenormalizability}{}\subsubsection*{{Non-renormalizability}}\label{nonrenormalizability}

The result that gravity is not [[renormalization|renormalizable]] is due to

\begin{itemize}%
\item [[Gerard `t Hooft]] and [[Martinus Veltman]], \emph{One loop divergencies in the theory of gravitation}, Ann. Inst. Poincar \'e{} 20 (1974) 69.

\end{itemize}
Review includes

\begin{itemize}%
\item [[Zvi Bern]], \emph{Perturbative quantum gravity and its relation to gauge theory}, Living reviews in relativity, \href{www.livingreviews.org/Articles/Volume5/2002-5bern}{www.livingreviews.org/Articles/Volume5/2002-5bern} .
\item Assaf Shomer, \emph{A pedagogical explanation for the non-renormalizability of gravity} (\href{https://arxiv.org/abs/0709.3555}{arXiv:0709.3555})

\end{itemize}
[[!redirects Einstein gravity]]



\end{document}