65,213 research outputs found
Configurational entropy of charged AdS black holes
When we consider charged AdS black holes in higher dimensional spacetime and
a molecule number density along coexistence curves is numerically extended to
higher dimensional cases. It is found that a number density difference of a
small and large black holes decrease as a total dimension grows up. In
particular, we find that a configurational entropy is a concave function of a
reduced temperature and reaches a maximum value at a critical (second-order
phase transition) point. Furthermore, the bigger a total dimension becomes, the
more concave function in a configurational entropy while the more convex
function in a reduced pressure.Comment: 6 pages, 4 figures, typos corrected, version to appear in PL
The Extended Thermodynamic Properties of a topological Taub-NUT/Bolt-AdS spaces
We consider higher dimensional topological Taub-NUT/Bolt-AdS solutions where
a cosmological constant is treated as a pressure. The thermodynamic quantities
of these solutions are explicitly calculated. Furthermore, we find these
thermodynamic quantities satisfy the Clapeyron equation. In particular, a new
thermodynamically stable region for the NUT solution is found by studying the
Gibbs free energy. Intriguingly, we also find that like the AdS black hole
case, the G-T diagram of the Bolt solution has two branches which are joined at
a minimum temperature. The Bolt solution with the large radius, at the lower
branch, becomes stable beyond a certain temperature while the Bolt solution
with the small radius, at the upper branch, is always unstable.Comment: 7 pages, 6 figures, typos corrected, version to appear in PL
The Extended Thermodynamic Properties of Taub-NUT/Bolt-AdS spaces
We investigate the extended thermodynamic properties of higher-dimensional
Taub-NUT/Bolt-AdS spaces where a cosmological constant is treated as a
pressure. We find a general form for thermodynamic volumes of Taub-NUT/Bolt-AdS
black holes for arbitrary dimensions. Interestingly, it is found that the
Taub-NUT-AdS metric has a thermodynamically stable range when the total number
of dimensions is a multiple of 4 (4, 8, 12, ...). We also explore their phase
structure and find the first order phase transition holds for
higher-dimensional cases.Comment: 18 pages, 5 figures, typos corrected, references added, version to
appear in PL
Effective Circle Count for Apollonian packings and Closed horospheres
The main result of this paper is an effective count for Apollonian circle
packings that are either bounded or contain two parallel lines. We obtain this
by proving an effective equidistribution of closed horospheres in the unit
tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite
volume, whose fundamental group has critical exponent bigger than 1. We also
discuss applications to Affine sieves. Analogous results for surfaces are
treated as well.Comment: 43 pages, 2 figures, To appear in GAF
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