User:Markus Pössel/WIP
Here is some stuff from the general relativity article, to be moved elsewhere
[edit]More precisely, the horizon is a null hypersurface, and for a black hole in asymptotically flat spacetime, neither null nor timelike geodesics from the inside will never reach infinity. There are several ways of definining horizons. The two most important ones are the event horizon, the boundary from inside which no light and no particles can escape to infinity, and the apparent horizon, the boundary from inside which no light and no particles can escape to the outside; both are defined globally for a whole spacetime.[1] In addition, there are ways to define horizons in a more intuitive way as isolated horizons, namely surfaces that can be defined for isolated systems without knowing spacetime properties at infinity.[2]
Even more remarkable, there is a general set of laws known as black hole mechanics, analogous to the laws of thermodynamics. The zeroth law states that the surface gravity of a long-term (in technical terms: stationary) black hole has a constant value on its horizon, just as the temperature is constant throughout a system in thermodynamic equilibrium. The first law states how small changes in the mass of a stationary black hole are related in a specific way to small changes in its area, its angular momentum and its charge, just as changes in the internal energy of a system are related to changes in its generalized volume, temperature, and particle number; among other things, this law sets a limit to the energy that can be extracted from a rotating black hole by means of the so-called Penrose process.[3] The second law states that the area of the event horizon of a general black hole will never decrease with time, just as the entropy of a thermodynamic system. By the third law, it is impossible to reduce the surface gravity to zero in a finite number of steps, in analogy with Nernst's theorem of thermodynamics.[4] In fact, there is strong evidence that the laws of black hole mechanics are indeed a special case of the laws of thermodynamics, and that the black hole area does indeed denote its entropy:<ref>See Bekenstein 1973,
- ^ Cf. Hawking & Ellis 1973, pp. 312–320 or Wald 1984, sec. 12.2.
- ^ Cf. Ashtekar & Krishnan 2004.
- ^ See Penrose 1969.
- ^ The laws of black hole mechanics were first described in Bardeen, Carter & Hawking 1973; a more pedagogical presentation can be found in Carter 1979; for a more recent review, see chapter 2 of Wald 2001. A thorough, book-length introduction including an introduction to the necessary mathematics Poisson 2004.