Einstein’s Field Equations

  • Norbert Straumann
Part of the Graduate Texts in Physics book series (GTP)


The hard core of the theory consists of Einstein’s field equation, which relates the metric field to matter. After a discussion of the physical meaning of the curvature tensor, we shall first give a simple physical motivation for the field equation and will then show that it is determined by only a few natural requirements (Lovelock theorem), with two coupling constants. One is just Newtons gravitational constant, and the other is the much discussed cosmological constant, whose observational magnitude is a complete mystery for present day fundamental physics. This long chapter of about ninety pages, is devoted to various qualitative aspects of Einstein’s field equation. We treat the Lagrangian formalism, the role of diffeomorphism invariance, the tetrad formalism, energy, momentum, and angular momentum for isolated systems, the initial value problem, the 3+1 formalism, causality of matter propagation, and conclude with a careful treatment of the general relativistic Boltzmann equation.


Field Equation Partial Differential Equation Lorentz Manifold Spacelike Hypersurface Cauchy Surface 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Norbert Straumann
    • 1
  1. 1.Mathematisch-Naturwiss. Fakultät, Institut für Theoretische PhysikUniversität ZürichZürichSwitzerland

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