Pair Creation of Black Holes in Anti-de Sitter Space Background

For a spherically symmetric vacuum model with a negative cosmological constant, a complex constrained instanton is considered as the seed for quantum pair creation of Schwarzschild-anti-de Sitter black holes. The relative creation probability is found to be the exponential of the negative of one quarter of the black hole horizon area or the black hole entropy. In the absence of a general no-boundary proposal for open creation, the constrained instanton approach is used in treating both the open and closed paircreation of black holes.