1,301 research outputs found
Two-dimensional quantum-corrected black hole in a finite size cavity
We consider the gravitation-dilaton theory (not necessarily exactly
solvable), whose potentials represent a generic linear combination of an
exponential and linear functions of the dilaton. A black hole, arising in such
theories, is supposed to be enclosed in a cavity, where it attains thermal
equilibrium, whereas outside the cavity the field is in the Boulware state. We
calculate quantum corrections to the Hawking temperature , with the
contribution from the boundary taken into account. Vacuum polarization outside
the shell tend to cool the system. We find that, for the shell to be in the
thermal equilibrium, it cannot be placed too close to the horizon. The quantum
corrections to the mass due to vacuum polarization vanish in spite of non-zero
quantum stresses. We discuss also the canonical boundary conditions and show
that accounting for the finiteness of the system plays a crucial role in some
theories (e.g., CGHS), where it enables to define the stable canonical
ensemble, whereas consideration in an infinite space would predict instability.Comment: 21 pages. In v.2 misprints corrected. To appear in Phys. Rev.
Hidden symmetries for thermodynamics and emergence of relativity
Erik Verlinde recently proposed an idea about the thermodynamic origin of
gravity. Though this is a beautiful idea which may resolve many long standing
problems in the theories of gravity, it also raises many other problems. In
this article I will comment on some of the problems of Verlinde's proposal with
special emphasis on the thermodynamical origin of the principle of relativity.
It is found that there is a large group of hidden symmetries of thermodynamics
which contains the Poincare group of the spacetime for which space is emergent.
This explains the thermodynamic origin of the principle of relativity.Comment: V1: 4 pages, comments/criticisms welcomed; V2: references added; V3:
typos and minor corrections? V4? substantial changes in Section 3 and other
parts mad
Existence of weak solutions for the generalized Navier-Stokes equations with damping
In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio
Quantum corrections to the entropy of charged rotating black holes
Hawking radiation from a black hole can be viewed as quantum tunneling of
particles through the event horizon. Using this approach we provide a general
framework for studying corrections to the entropy of black holes beyond
semiclassical approximations. Applying the properties of exact differentials
for three variables to the first law thermodynamics, we study charged rotating
black holes and explicitly work out the corrections to entropy and horizon area
for the Kerr-Newman and charged rotating BTZ black holes. It is shown that the
results for other geometries like the Schwarzschild, Reissner-Nordstr\"{o}m and
anti-de Sitter Schwarzschild spacetimes follow easily
Phase transitions in geometrothermodynamics
Using the formalism of geometrothermodynamics, we investigate the geometric
properties of the equilibrium manifold for diverse thermodynamic systems.
Starting from Legendre invariant metrics of the phase manifold, we derive
thermodynamic metrics for the equilibrium manifold whose curvature becomes
singular at those points where phase transitions of first and second order
occur. We conclude that the thermodynamic curvature of the equilibrium
manifold, as defined in geometrothermodynamics, can be used as a measure of
thermodynamic interaction in diverse systems with two and three thermodynamic
degrees of freedom
Efficient Resolution of Anisotropic Structures
We highlight some recent new delevelopments concerning the sparse
representation of possibly high-dimensional functions exhibiting strong
anisotropic features and low regularity in isotropic Sobolev or Besov scales.
Specifically, we focus on the solution of transport equations which exhibit
propagation of singularities where, additionally, high-dimensionality enters
when the convection field, and hence the solutions, depend on parameters
varying over some compact set. Important constituents of our approach are
directionally adaptive discretization concepts motivated by compactly supported
shearlet systems, and well-conditioned stable variational formulations that
support trial spaces with anisotropic refinements with arbitrary
directionalities. We prove that they provide tight error-residual relations
which are used to contrive rigorously founded adaptive refinement schemes which
converge in . Moreover, in the context of parameter dependent problems we
discuss two approaches serving different purposes and working under different
regularity assumptions. For frequent query problems, making essential use of
the novel well-conditioned variational formulations, a new Reduced Basis Method
is outlined which exhibits a certain rate-optimal performance for indefinite,
unsymmetric or singularly perturbed problems. For the radiative transfer
problem with scattering a sparse tensor method is presented which mitigates or
even overcomes the curse of dimensionality under suitable (so far still
isotropic) regularity assumptions. Numerical examples for both methods
illustrate the theoretical findings
Phase transitions for the Lifshitz black holes
We study possibility of phase transitions between Lifshitz black holes and
other configurations by using free energies explicitly. A phase transition
between Lifshitz soliton and Lifshitz black hole might not occur in three
dimensions. We find that a phase transition between Lifshitz and BTZ black
holes unlikely occurs because they have different asymptotes. Similarly, we
point out that any phase transition between Lifshitz and black branes unlikely
occurs in four dimensions since they have different asymptotes. This is
consistent with a necessary condition for taking a phase transition in the
gravitational system, which requires the same asymptote.Comment: 19 pages, 7 figures, a revised version to appear in EPJ
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