Flrw

General Relativity · Part 4

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Table of Contents

  1. 1.The Cosmological Principle
  2. 2.The FLRW Metric
  3. 3.Spatial Curvature: Three Geometries
  4. 4.Deriving the Friedmann Equations
  5. 5.The Continuity Equation
  6. 6.Interactive Simulation: Universe Evolution
  7. 7.Homogeneity
  8. 8.Isotropy
  9. 9.k = +1: Closed
  10. 10.k = 0: Flat

Key Equations

$$ds^2 = -c^2\,dt^2 + a(t)^2\left[\frac{dr^2}{1-kr^2} + r^2\left(d\theta^2 + \sin^2\theta\,d\phi^2\right)\right]$$
$$d\Sigma^2 = d\chi^2 + \sinh^2\chi\,d\Omega^2$$
$$R_{00} = -\frac{3\ddot{a}}{ac^2}$$
$$H^2 \equiv \left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}$$

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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