15,211 research outputs found
Black Hole Thermodynamics and Riemann Surfaces
We use the analytic continuation procedure proposed in our earlier works to
study the thermodynamics of black holes in 2+1 dimensions. A general black hole
in 2+1 dimensions has g handles hidden behind h horizons. The result of the
analytic continuation is a hyperbolic 3-manifold having the topology of a
handlebody. The boundary of this handlebody is a compact Riemann surface of
genus G=2g+h-1. Conformal moduli of this surface encode in a simple way the
physical characteristics of the black hole. The moduli space of black holes of
a given type (g,h) is then the Schottky space at genus G. The (logarithm of
the) thermodynamic partition function of the hole is the Kaehler potential for
the Weil-Peterson metric on the Schottky space. Bekenstein bound on the black
hole entropy leads us to conjecture a new strong bound on this Kaehler
potential.Comment: 17+1 pages, 9 figure
Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume
We study a metric version of the simplicial volume on Riemannian manifolds,
the Lipschitz simplicial volume, with applications to degree theorems in mind.
We establish a proportionality principle and a product inequality from which we
derive an extension of Gromov's volume comparison theorem to products of
negatively curved manifolds or locally symmetric spaces of non-compact type. In
contrast, we provide vanishing results for the ordinary simplicial volume; for
instance, we show that the ordinary simplicial volume of non-compact locally
symmetric spaces with finite volume of Q-rank at least 3 is zero.Comment: 33 pages; corrected the vanishing result (and adapted Section 5
accordingly), minor expository changes in the introductio
On the Patterns of Principal Curvature Lines around a Curve of Umbilic Points
In this paper is studied the behavior of principal curvature lines near a
curve of umbilic points of a smooth surface.Comment: 12 pages, 5 figure
Some remarks on the simplicial volume of nonpositively curved manifolds
We show that any closed manifold with a metric of nonpositive curvature that
admits either a single point rank condition or a single point curvature
condition has positive simplicial volume. We use this to provide a differential
geometric proof of a conjecture of Gromov in dimension three.Comment: 14 pages, 1 figure. Minor revision
Cosmological Hysteresis and the Cyclic Universe
A Universe filled with a homogeneous scalar field exhibits `Cosmological
hysteresis'. Cosmological hysteresis is caused by the asymmetry in the equation
of state during expansion and contraction. This asymmetry results in the
formation of a hysteresis loop: , whose value can be non-vanishing
during each oscillatory cycle. For flat potentials, a negative value of the
hysteresis loop leads to the increase in amplitude of consecutive cycles and to
a universe with older and larger successive cycles. Such a universe appears to
possess an arrow of time even though entropy production is absent and all of
the equations respect time-reversal symmetry ! Cosmological hysteresis appears
to be widespread and exists for a large class of scalar field potentials and
mechanisms for making the universe bounce. For steep potentials, the value of
the hysteresis loop can be positive as well as negative. The expansion factor
in this case displays quasi-periodic behaviour in which successive cycles can
be both larger as well as smaller than previous ones. This quasi-regular
pattern resembles the phenomenon of BEATS displayed by acoustic systems.
Remarkably, the expression relating the increase/decrease in oscillatory cycles
to the quantum of hysteresis appears to be model independent. The cyclic
scenario is extended to spatially anisotropic models and it is shown that the
anisotropy density decreases during successive cycles if the hysteresis loop is
negative.Comment: 31 pages, 8 figures. Matches version published in Phys Rev D85,
123542 (2012
- …