gravity/gravity.tex at master · mnieper/gravity · GitHub

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\documentclass[a4paper,12pt]{report}

\input{preamble}

\title{General Relativity and Einstein--Cartan Theory}
\author{Marc A. Nieper-Wi\ss kirchen}
\date{\today}

\begin{document}

  \maketitle

  \include{preface}
  \include{thanks}
  \include{history}
  \include{notations}

  \tableofcontents

  \include{spacetime}
  \include{infinitesimal}

  \include{motions} % Equations of motions
  % Introduction
  % Affine manifolds, connection coefficients
  % Constant tensor fields & parallel displacement
  % Second derivative & torsion
  % Autoparallel
  % Exponential map, normal coordinates

  \include{forces} % Tidal forces
  % Introduction
  % Riemann curvature
  % Jacobi fields
  % Bianchi identities
  % Exponential map

  \include{vacuum} %
  % Introduction
  % Riemannian and Pseudo-riemannian manifolds
  % Levi-Civita connection
  % Geodesics
  % Riemannian curvature
  % Interpretation of Riemannian curvature
  % Interpretation of scalar curvature
  % Interpretation of Ricci curvature in Lorentzian manifolds

  \include{relativity} % General relativity
  % Introduction
  % Einstein tensor
  % Mass density
  % Einstein's field equations
  % Newton's theory of gravity
  % Equations of motion
  % Killing vector fields
  % Schwarzschild metric
  % Schwarzschild potential

  \include{maxwell}
  % Introduction
  % Differential forms
  % Hodge dual
  % Maxwell theory
  % energy momentum tensor of electrodynamic
  % charged black hole

  \include{action} % Action principle
  % Introduction
  % Euler-Lagrange eqn. for fields
  % Currents
  % Maxwell theory
  % Relativity

  \include{gauge} % Gauge theories
  % Introduction
  % Fibre bundles
  % Ehresmann connections
  % U(1) theory
  % Cartan connections
  % SO(1,4) theory
  % eq. of motion with torsion
  % spin/fermions

	\appendix

  \include{topology}
  % Topological spaces
  % Continuous maps
  % Hausdorff spaces
  % Normal spaces
  % Compact spaces
  % Locally compact spaces
  % Paracompact Hausdorff spaces

  \include{analysis}
  % Bump functions

\end{document}