Gravitational Waves
General Relativity · Part 4
224 KB7 sections4 key equationsLaTeX typeset
Table of Contents
- 1.Linearized Gravity
- 2.Trace-Reversed Perturbation
- 3.Gauge Freedom: The Lorenz Gauge
- 4.Transverse-Traceless (TT) Gauge
- 5.The Two Polarization States
- 6.Effect on Test Particles: The Geodesic Deviation
- 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.