Kerr Metric

Black Holes · Part 2

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Table of Contents

  1. 1.1. Boyer-Lindquist Coordinates
  2. 2.2. Event Horizons
  3. 3.3. Ring Singularity
  4. 4.4. Frame Dragging (Lense-Thirring Effect)
  5. 5.5. Killing Vectors and Conserved Quantities
  6. 6.6. Innermost Stable Circular Orbit (ISCO)
  7. 7.7. Experimental Verification
  8. 8.Key Takeaways
  9. 9.Limits
  10. 10.Special Cases

Key Equations

$$r_+ = r_s = 2GM/c^2, \quad r_- = 0$$
$$r_+ \approx 1.0 - 1.4\, GM/c^2$$
$$E = -\xi_\mu u^\mu = -g_{tt} \frac{dt}{d\tau} - g_{t\phi} \frac{d\phi}{d\tau}$$
$$Q = p_\theta^2 + \cos^2\theta \left[a^2(m^2 - E^2) + \frac{L_z^2}{\sin^2\theta}\right]$$

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

Course Context

This PDF is part of the Black Holes course on CoursesHub.World. Study the physics of black holes from Schwarzschild geometry to Hawking radiation. Covers rotating and charged black holes, thermodynamics, the information paradox, holographic principle, and astrophy...

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