In an asymptotically predictable spacetime, a black hole is the region that cannot send a causal signal to future null infinity. Its future boundary is the event horizon.
An event horizon is the null boundary of the causal past of future null infinity. Its global definition makes it respond teleologically to matter that falls in later.
A Penrose diagram conformally compactifies a spacetime while preserving causal directions, placing null infinity, timelike infinity, spacelike infinity, horizons, and singularities at finite coordinate locations.
Black-hole thermodynamics relates horizon geometry to thermodynamic laws, assigning temperature and entropy to a stationary black hole.
The physical-process first law derives the area change caused by a small flux of matter through an initially and finally stationary horizon. Linearized Null Raychaudhuri equation evolution converts the Killing-energy flux into .
The Kerr black hole is the asymptotically flat stationary axisymmetric vacuum black hole with mass and angular momentum .
Boyer-Lindquist coordinates adapt the Kerr metric to its stationary and axial symmetries. The horizon radii are the roots of .
The Kerr ergoregion is the region where the asymptotically timelike stationary Killing field becomes spacelike. Its outer boundary is .
The Penrose process extracts rotational energy by allowing a fragment with negative stationary Killing energy to enter the black hole while another fragment escapes with more energy than the original body carried.
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A black hole is a region in space where the gravitational pull is so strong that nothing, not even light, can escape from it. This phenomenon occurs when a massive star collapses under its own gravity at the end of its life cycle. Black holes are characterized by three main properties: 1. **Singularity**: At the center of a black hole lies the singularity, a point where gravity is thought to be infinitely strong, and known laws of physics break down.
