16 research outputs found
Thermodynamics, stability and Hawking-Page transition of Kerr black holes from R\'enyi statistics
Thermodynamics of rotating black holes described by the R\'enyi formula as
equilibrium and zeroth law compatible entropy function is investigated. We show
that similarly to the standard Boltzmann approach, isolated Kerr black holes
are stable with respect to axisymmetric perturbations in the R\'enyi model. On
the other hand, when the black holes are surrounded by a bath of thermal
radiation, slowly rotating black holes can also be in stable equilibrium with
the heat bath at a fixed temperature, in contrast to the Boltzmann description.
For the question of possible phase transitions in the system, we show that a
Hawking-Page transition and a first order small black hole/large black hole
transition occur, analogous to the picture of rotating black holes in AdS
space. These results confirm the similarity between the R\'enyi-asymptotically
flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating
case as well. We derive the relations between the thermodynamic parameters
based on this correspondence.Comment: 29 pages, 20 figure
Thick brane solutions and topology change transition on black hole backgrounds
We consider static, axisymmetric, thick brane solutions on higher
dimensional, spherically symmetric black hole backgrounds. It was found
recently [1], that in cases when the thick brane has more than 2 spacelike
dimensions, perturbative approaches break down around the corresponding thin
solutions for Minkowski type topologies. This behavior is a consequence of the
fact that thin solutions are not smooth at the axis, and for a general
discussion of possible phase transitions in the system, one needs to use a
non-perturbative approach. In the present paper we provide an exact, numerical
solution of the problem both for black hole- and Minkowski type topologies with
arbitrary number of brane and bulk dimensions. We also illustrate a topology
change transition in the system for a 5-dimensional brane embedded in a
6-dimensional bulk.Comment: 11 pages, 10 figures, accepted for publication in Phys. Rev.
Revisiting Rotational Perturbations and the Microwave Background
We consider general-relativistic rotational perturbations in homogeneous and
isotropic Friedman - Robertson - Walker (FRW) cosmologies. Taking linear
perturbations of FRW models, the general solution of the field equations
contains tensorial, vectorial and scalar functions. The vectorial terms are in
connection with rotations in the given model and due to the Sachs - Wolfe
effect they produce contributions to the temperature fluctuations of the cosmic
microwave background radiation (CMBR). In present paper we obtain the analytic
time dependence of these contributions in a spatially flat, FRW model with
pressureless ideal fluid, in the presence and the absence of a cosmological
constant. We find that the solution can be separated into an integrable and a
non-integrable part as is the situation in the case of scalar perturbations.
Analyzing the solutions and using the results of present observations we
estimate the order of magnitude of the angular velocity corresponding to the
rotation tensor at the time of decoupling and today.Comment: accepted for publication in Int. J. Mod. Phys.
Black hole horizons can hide positive heat capacity
Regarding the volume as independent thermodynamic variable we point out that
black hole horizons can hide positive heat capacity and specific heat. Such
horizons are mechanically marginal, but thermally stable. In the absence of a
canonical volume definition, we consider various suggestions scaling
differently with the horizon radius. Assuming Euler-homogeneity of the entropy,
besides the Hawking temperature, a pressure and a corresponding work term
render the equation of state at the horizon thermally stable for any meaningful
volume concept that scales larger than the horizon area. When considering also
a Stefan--Boltzmann radiation like equation of state at the horizon, only one
possible solution emerges: the Christodoulou--Rovelli volume, scaling as , with an entropy .Comment: 5 pages, no figures, to be published in Phys. Lett.
Cosmological Perturbations from a Group Theoretical Point of View
We present a new approach to cosmological perturbations based on the theory
of Lie groups and their representations. After re-deriving the standard
covariant formalism from SO(3) considerations, we provide a new expansion of
the perturbed Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in terms of
irreducible representations of the Lorentz group. The resulting decomposition
splits into (scalar, scalar), (scalar, vector) and (vector, vector) terms.
These equations directly correspond to the standard Lifshitz classification of
cosmological perturbations using scalar, vector and tensor modes which arise
from the irreducible SO(3) representation of the spatial part of the metric.
While the Lorentz group basis matches the underlying local symmetries of the
FLRW spacetime better than the SO(3), the new equations do not provide further
simplification compared to the standard cosmological perturbation theory. We
conjecture that this is due to the fact that the so(3,1) ~ su(2) x su(2)
Lorentz algebra has no pair of commuting generators commuting with any of the
translation group generators.Comment: To be published in Classical and Quantum Gravit
Relative information entropy in cosmology: The problem of information entanglement
The necessary information to distinguish a local inhomogeneous mass density
field from its spatial average on a compact domain of the universe can be
measured by relative information entropy. The Kullback-Leibler (KL) formula
arises very naturally in this context, however, it provides a very complicated
way to compute the mutual information between spatially separated but causally
connected regions of the universe in a realistic, inhomogeneous model. To
circumvent this issue, by considering a parametric extension of the KL measure,
we develop a simple model to describe the mutual information which is entangled
via the gravitational field equations. We show that the Tsallis relative
entropy can be a good approximation in the case of small inhomogeneities, and
for measuring the independent relative information inside the domain, we
propose the R\'enyi relative entropy formula.Received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under the grant agreement No. PCOFUND-GA-2009-246542; from CMAT through FEDER Funds COMPETE, and also from FCT projects Est-OE/MAT/UI0013/2014, SFRH/BCC/105835/2014 and CERN/FP/123609/2011
Rényi entropy and the thermodynamic stability of black holes
Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.V.G.Cz. is grateful for discussions with Prof. T.S. Biro. The research leading to this result has received funding from: the European Union Seventh Framework Programme (FP7/2007-2013) under the grant agreement No. PCOFUND-GA-2009-246542; the FCT project SFRH/BCC/105835/2014; the Japanese Ministry of Education, Science, Sports, and Culture Grant-in-Aid for Scientific Research (C) (No. 23540319), and also from the Japan Society for the Promotion of Science L14710 grant
Black holes, gravitational waves and fundamental physics: a roadmap
The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions.
The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature.
The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'