FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

Noncommutative black holes in non-asymptotically flat backgrounds and gauge-gravity duality
Collaborators: P. Nicolini 1 , R.B. Mann 2,3 , G. Torrieri 1 , S. Lottini 4 , I. Mishustin 1
1 Frankfurt Institute for Advanced Studies, 2 Perimeter Institute for Theoretical Physics, Canada, 3 University of Waterloo,
Canada, 4 Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität.
In 2011 we faced the problem of regular noncommutative black holes in non-asympotically flat backgrounds.
Specifically we considered two cases: a deSitter background and an Anti-deSitter one. The two cases have
relevance respectively in early Universe cosmology and in the context of the gauge-gravity duality paradigm.
In inflationary epochs, the Universe is well described by the deSitter geometry, which is known to be stable
under classical perturbations. However at quantum mechanical level, the deSitter space exhibits instability due
to the spontaneous nucleation of black holes. The standard semiclassical formalism for pair creation is based
on the study of instantons, i.e. stationary points of the gravitational action which permit the evaluation of amplitudes
within the Euclidean quantum gravity path integral formalism. We showed that noncommutative black
holes would have plentifully been produced during inflationary times for Planckian values of the cosmological
constant. However, as a special result we found that, in these early epochs of the universe, Planck size black
holes production would have been largely disfavoured. We remark that noncommutative black holes are longerlived
with respect to conventional black holes, since they do not completely evaporate. Thus their production
could have potential repercussions for Planck-scale inflation as well as for the production of primordial black
holes.
A radiating black hole in Anti-deSitter space corresponds to a heat source in a reflecting box of finite volume.
Thermodynamically these black holes are dual to systems described by particular kinds of gauge field theory
in one dimension fewer. In this spirit we considered noncommutative black holes as a model for a ultraviolet
completion of the conventional Anti-deSitter black hole geometry. As a consequence of the profile of their
temperature, we showed that the phase structure of the solution is modified: the conventional Hawking-Page
phase transition extends into a van der Waals-like phase diagram, with a critical point and a smooth crossover
thereafter. This result has profound and intriguing repercussions: one may think to exploit such a new black
hole phase transition to describe, via the gauge-gravity duality paradigm, the nuclear matter transition from the
“classical” skyrme crystal to a phase where quantum effects weaken the bond between baryons and eventually
melt the crystal into a nuclear gas with consequent switch of the deconfinement phase into a cross over.
On the left: a representation of the Anti-deSitter space. On the right: the phase diagram of nuclear matter.
Related publications in 2011:
1) R. B. Mann and P. Nicolini, Cosmological production of noncommutative black holes, Physical Review D
84 (2011) 064014.
2) P. Nicolini and G. Torrieri, The Hawking-Page crossover in noncommutative anti-deSitter space, JHEP 1108
(2011) 097.
3) G. Torrieri, S. Lottini, I. Mishustin and P. Nicolini, “The Phase diagram in T –µ–Nc space”, arXiv:1110.6219
[nucl-th].
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