black hole horizon is a future horizon, things can go in, but don't come out. The cosmological horizon in a Big Bang type cosmology is a past horizon, things come out, but nothing goes in. But in a semi-classical treatment, the de Sitter cosmological horizon can be thought of as absorbing or emitting depending on the point of view. Similarly, for a black hole that has been around for a long time, the horizon can be thought of as emitting or absorbing depending on whether you take the point of view of infalling matter or outgoing Hawking radiation. Hawking argued based on thermodynamics that the past horizon of a white hole is in fact physically the same as the future horizon of a black hole, so that past and future horizons are physically identical. This was elaborated by Susskind into black hole complementarity, which states that any interior parts of a black hole solution, in either the past and future horizon interpretation, can be holographically related by a unitary change of basis to the quantum mechanical description of the horizon itself. The Nariai solution is the limit of the largest black hole in a space which is de Sitter at large distances, it has two horizons, the cosmological de Sitter horizon and a Schwarzschild black hole horizon. For small mass black holes, the two are very different--- there is a singularity at the center of the black hole, and there is no singularity past the cosmological horizon. But the Nariai limit considers making the black hole bigger and bigger, until its event horizon has the same area as the cosmological de Sitter horizon. At this point, the space-time becomes regular, the black hole singularity runs off to infinity, and the two horizons are related by a space-time symmetry. In the Nariai limit, the black hole and de Sitter horizon can be interchanged just by changing the sign of the coordinate z. When there is additional matter density, the solution can be thought of as an Einstein spherical universe with two antipodal black holes. Whichever black hole becomes larger becomes the cosmological horizon. Nariai solution Starting with de Sitter–Schwarzschild: with The two parameters a and b give the black hole mass and the cosmological constant respectively. In higher dimensions, the power law for the black hole part is faster. When a is small, ƒ(r) has two zeros at positive values of