Pp Waves
General Relativity · Part 4
224 KB5 sections4 key equationsLaTeX typeset
Table of Contents
- 1.Introduction to PP Waves
- 2.Derivation of the PP-Wave Metric
- 3.Brinkmann vs. Rosen Coordinates
- 4.The Vacuum Einstein Equation
- 5.Physical Interpretation
Key Equations
$$\nabla_\mu k_\nu = 0, \qquad k^\mu k_\mu = 0$$
$$ds^2 = 2\,dU\,dV + g_{ij}(U)\,dX^i\,dX^j, \qquad i,j \in \{1,2\}$$
$$R_{\mu\nu} = -\frac{1}{2}\nabla^2_\perp H\;\delta_\mu^u\,\delta_\nu^u$$
$$H(u, x, y) = \text{Re}\left[f(u, w)\right]$$
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...