Mathematics – Logic
Scientific paper
Jun 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997pthph..97..859c&link_type=abstract
Prog. Theor. Phys., Vol. 97, No. 6, p. 859 - 871
Mathematics
Logic
4
Black Holes: Quantum Gravity, Black Holes: Cosmology
Scientific paper
Using the Hartle-Hawking no-boundary proposal for the wave function of the universe, one can study the wave function and probability of a single black hole created at the birth of the universe. The author begins with a quantum spherically symmetric model. At the semi-classical level, this turns out to be a S2×S1 model. The black hole originates from a gravitational instanton with conical singularities. The wave function and probability of a universe with a black hole are calculated at the WKB level. The probability of black hole creation is the exponential of one quarter of the sum of the areas of the black hole and cosmological horizons. One quarter of this sum is the total entropy of the universe. The probability is an exponentially decreasing function of its mass parameter. It is conjectured that these arguments apply to all types of black holes in the de Sitter space background.
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