437 research outputs found
Quasi-homogeneous black hole thermodynamics
Although the fundamental equations of ordinary thermodynamic systems are
known to correspond to first-degree homogeneous functions, in the case of
non-ordinary systems like black holes the corresponding fundamental equations
are not homogeneous. We present several arguments, indicating that black holes
should be described by means of quasi-homogeneous functions of degree different
from one. In particular, we show that imposing the first-degree condition leads
to contradictory results in thermodynamics and geometrothermodynamics of black
holes. As a consequence, we show that in generalized gravity theories the
coupling constants like the cosmological constant, the Born-Infeld parameter or
the Gauss-Bonnet constant must be considered as thermodynamic variables
Gowdy Cosmological Models in N=1 Supergravity
We investigate the canonical quantization of supergravity N=1 in the case of
a midisuperspace described by Gowdy cosmological models. The quantum
constraints are analyzed and the wave function of the universe is derived
explicitly. Unlike the minisuperspace case, we show the existence of physical
states in midisuperspace models. The analysis of the wave function of the
universe leads to the conclusion that the classical curvature singularity
present in the evolution of Gowdy models is removed at the quantum level due to
the presence of the Rarita-Schwinger field.Comment: 25 pages and 2 figure
Curvature as a Measure of the Thermodynamic Interaction
We present a systematic and consistent construction of geometrothermodynamics
by using Riemannian contact geometry for the phase manifold and harmonic maps
for the equilibrium manifold. We present several metrics for the phase manifold
that are invariant with respect to Legendre transformations and induce
thermodynamic metrics on the equilibrium manifold. We review all the known
examples in which the curvature of the thermodynamic metrics can be used as a
measure of the thermodynamic interaction
Geometrothermodynamics of asymptotically anti - de Sitter black holes
We apply the formalism of geometrothermodynamics to the case of black holes
with cosmological constant in four and higher dimensions. We use a
thermodynamic metric which is invariant with respect to Legendre
transformations and determines the geometry of the space of equilibrium states.
For all known black holes in higher dimensions, we show that the curvature
scalar of the thermodynamic metric in all the cases is proportional to the heat
capacity. As a consequence, phase transitions, which correspond to divergencies
of the heat capacity, are represented geometrically as true curvature
singularities. We interpret this as a further indication that the curvature of
the thermodynamic metric is a measure of thermodynamic interaction.Comment: Section on statistical ensembles and new references adde
Thermodynamic systems as extremal hypersurfaces
We apply variational principles in the context of geometrothermodynamics. The
thermodynamic phase space and the space of equilibrium states turn out to be described by Riemannian metrics which are invariant with
respect to Legendre transformations and satisfy the differential equations
following from the variation of a Nambu-Goto-like action. This implies that the
volume element of is an extremal and that and
are related by an embedding harmonic map.
We explore the physical meaning of geodesic curves in as
describing quasi-static processes that connect different equilibrium states. We
present a Legendre invariant metric which is flat (curved) in the case of an
ideal (van der Waals) gas and satisfies Nambu-Goto equations. The method is
used to derive some new solutions which could represent particular
thermodynamic systems
On the local Lorentz invariance in N=1 supergravity
We discuss the local Lorentz invariance in the context of N=1 supergravity
and show that a previous attempt to find explicit solutions to the Lorentz
constraint in terms of matrices is not correct. We improve that
solution by using a different representation of the Lorentz operators in terms
of the generators of the rotation group, and show its compatibility with the
matrix representation of the fermionic field. We find the most general wave
functional that satisfies the Lorentz constraint in this representation
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