Reissner Nordstrom

General Relativity · Part 4

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Table of Contents

  1. 1.Introduction
  2. 2.The Einstein-Maxwell System
  3. 3.Deriving the Metric
  4. 4.The Two Horizons
  5. 5.Surface Gravity and Temperature
  6. 6.Three Qualitative Cases
  7. 7.Case 2: Extremal ()
  8. 8.Case 3: Super-extremal ()

Key Equations

$$S = \int d^4x\,\sqrt{-g}\left[\frac{R}{16\pi G} - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\right]$$
$$\nabla_\mu F^{\mu\nu} = 0, \qquad \nabla_{[\mu}F_{\nu\rho]} = 0$$
$$T^t_{\ t} = T^r_{\ r} = -\frac{Q^2}{8\pi r^4}, \qquad T^\theta_{\ \theta} = T^\phi_{\ \phi} = +\frac{Q^2}{8\pi r^4}$$
$$\boxed{ds^2 = -\left(1 - \frac{2M}{r} + \frac{Q^2}{r^2}\right)dt^2 + \left(1 - \frac{2M}{r} + \frac{Q^2}{r^2}\right)^{-1}dr^2 + r^2\,d\Omega^2}$$

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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