- Introduction
- The space-time
- Verification of the Einstein–Maxwell equations
- Extremal horizons
- The inadmissible scenarios: horizons 4 & 2+2
- Horizons 1+3**
- Horizons 1+1+2
- Extremal black holes with disappearing horizons
- Extremal naked singularities
- Extremal black holes: summary
- Perturbing the parameters
- On conformal diagrams
- Comparison with extremal Kerr–Newman scenarios
- Frame-dragging***
- Electrogeodesics
- Integrals of motion
- On the normalisation equation
- The static case
- The axis
- The equatorial plane
- Motion in the equatorial plane
- Stationary circular orbits**
- Photon orbits
- Effective potential
- Radial motion along the axis of rotation
- Null geodesics & near-horizon approximation
- Effective potential & static particles revisited
- Quantum tunnelling & horizon temperature
- The null geodesic method fundamentals
- Horizon temperatures
- Horizons of multiplicity one**
- Extremal horizons
- The space-time
- Appendices
- A. A tale of two Lagrangians
- B. The road not taken
- C. Positive roots of polynomials