Andrew P. Lundgren, Mihai Bondarescu, Ruxandra Bondarescu
In this paper we focus on the gravitational thermodynamics of the far future.
Cosmological observations suggest that most matter will be diluted away by the
cosmological expansion, with the rest collapsing into supermassive black holes.
The likely future state of our local universe is a supermassive black hole
slowly evaporating in an empty universe dominated by a positive cosmological
constant. We describe some overlooked features of how the cosmological horizon
responds to the black hole evaporation. The presence of a black hole depresses
the entropy of the cosmological horizon by an amount proportional to the
geometric mean of the entropies of the black hole and cosmological horizons. As
the black hole evaporates and loses its mass in the process, the total entropy
increases obeying the second law of thermodynamics. The entropy is produced by
the heat from the black hole flowing across the extremely cold cosmological
horizon. Once the evaporation is complete, the universe becomes empty de Sitter
space that (in the presence of a true cosmological constant) is the maximum
entropy thermodynamic equilibrium state. We propose that flat Minkowski space
is an improper limit of this process which obscures the thermodynamics. The
cosmological constant should be regarded not only as an energy scale, but also
as a scale for the maximum entropy of a universe. In this context, flat
Minkowski space is indistinguishable from de Sitter with extremely small
cosmological constant, yielding a divergent entropy. This introduces an
unregulated infinity in black hole thermodynamics calculations, giving possibly
misleading results.
View original:
http://arxiv.org/abs/1201.1298
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