Einstein Equations

General Relativity · Part 3

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Table of Contents

  1. 1.The Einstein Field Equations
  2. 2.The Field Equations
  3. 3.Left Side: Geometry
  4. 4.Right Side: Matter
  5. 5.10 Coupled Nonlinear PDEs
  6. 6.Key Properties
  7. 7.Alternative Forms
  8. 8.Geometric Content
  9. 9.No Superposition
  10. 10.Self-Interaction

Key Equations

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}\, T_{\mu\nu}$$
$$G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi\, T_{\mu\nu}$$
$$R_{\mu\nu} - \frac{1}{2}\, g_{\mu\nu}\, R = \frac{8\pi G}{c^4}\, T_{\mu\nu}$$
$$R_{\mu\nu} = 0 \qquad \text{(when } T_{\mu\nu} = 0, \Lambda = 0 \text{)}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the General Relativity course on CoursesHub.World. Explore Einstein's theory of gravity as curved spacetime. Covers differential geometry, curvature tensors, Einstein field equations, classic solutions including Schwarzschild and Kerr black holes, gra...

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