Rotating Black Holes and Causal Structure

Analyze the Kerr metric for a rotating black hole, identifying its horizons and the static limit.

Define the ergosphere and derive the frame-dragging effect (Lense-Thirring effect).

Describe the Penrose process for extracting energy from a rotating black hole.

Construct the Penrose diagram for the maximal analytic extension of the Kerr spacetime.

Define surface gravity (κ) for a stationary black hole.

State and interpret the four laws of black hole mechanics.

Explain the physical analogy between black hole mechanics and the laws of thermodynamics.

Derive the Raychaudhuri equation and use it to prove the Penrose-Hawking singularity theorems under specific energy conditions.