Gravitational Waves

General Relativity · Part 4

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Table of Contents

  1. 1.Linearized Gravity
  2. 2.Trace-Reversed Perturbation
  3. 3.Gauge Freedom: The Lorenz Gauge
  4. 4.Transverse-Traceless (TT) Gauge
  5. 5.The Two Polarization States
  6. 6.Effect on Test Particles: The Geodesic Deviation
  7. 7.Interactive Simulation: Binary Inspiral Waveform

Key Equations

$$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}, \quad |h_{\mu\nu}| \ll 1$$
$$\bar{h}_{\mu\nu} = h_{\mu\nu} - \frac{1}{2}\eta_{\mu\nu}h$$
$$\Box \bar{h}_{\mu\nu} = -\frac{16\pi G}{c^4} T_{\mu\nu}$$
$$\partial_j h^{TT}_{ij} = 0 \quad \text{(transverse)}$$

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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