A general relativity workbook

Review of special relativity

Four-vectors

Index notation

Arbitrary coordinates

Tensor equations

Maxwell's equations

Geodesics

The Schwarzschild metric

Particle orbits

Precession of the perihelion

Photon orbits

Deflection of light

Event horizon

Alternative coordinates

Black hole thermodynamics

The absolute gradient

Geodesic deviation

The Riemann tensor

The stress-energy tensor

The Einstein equation

Interpreting the equation

The Schwarzschild solution

The universe observed

A metric for the cosmos

Evolution of the universe

Cosmic implications

The early universe

CMB fluctuations and inflation

Gauge freedom

Detecting gravitational waves

Gravitational wave energy

Generating gravitational waves

Gravitational wave astronomy

Gravitomagnetism

The Kerr metric

Particle orbits in Kerr spacetime

Ergoregion and horizon

Negative-energy orbits.