22 research outputs found
Thermodynamic Metrics and Black Hole Physics
We give a brief survey of thermodynamic metrics, in particular the Hessian of
the entropy function, and how they apply to black hole thermodynamics. We then
provide a detailed discussion of the Gibbs surface of Kerr black holes. In
particular we analyze its global properties, and extend it to take the entropy
of the inner horizon into account. A brief discussion of Kerr-Newman black
holes is included.Comment: 21 pages, new figures adde
On Geometro-thermodynamics of Dilaton Black Holes
In this talk we present the latest results from our ongoing project on
geometro-thermodynamics (also known as information geometry of thermodynamics
or Ruppeiner geometry) of dilaton BHs in 4D in both Einstein and string frames
and a dyonic dilaton BH and at the end we report very briefly results from this
approach to the 2D dilaton BHs.Comment: Talk given at 30th Spanish Relativity Meeting (ERE 2007):
Relativistic Astrophysics And Cosmology, 10-14 Sep 2007, Puerto de La Cruz,
Tenerife, Spain. Typos correcte
Ruppeiner theory of black hole thermodynamics
The Ruppeiner metric as determined by the Hessian of the Gibbs surface
provides a geometric description of thermodynamic systems in equilibrium. An
interesting example is a black hole in equilibrium with its own Hawking
radiation. In this article, we present results from the Ruppeiner study of
various black hole families from different gravity theories e.g. 2D dilaton
gravity, BTZ, general relativity and higher-dimensional Einstein-Maxwell
gravity.Comment: 10 pages, 1 figure. Talk given by N Pidokrajt at ERE2006 in Palma de
Mallorca, Spai
Geometry of Higher-Dimensional Black Hole Thermodynamics
We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstr\"om
(RN) black holes in spacetime dimensions higher than four. These black holes
possess thermodynamic geometries similar to those in four dimensional
spacetime. The thermodynamic geometries are the Ruppeiner geometry and the
conformally related Weinhold geometry. The Ruppeiner geometry for Kerr
black hole is curved and divergent in the extremal limit. For Kerr
black hole there is no extremality but the Ruppeiner curvature diverges where
one suspects that the black hole becomes unstable. The Weinhold geometry of the
Kerr black hole in arbitrary dimension is a flat geometry. For RN black hole
the Ruppeiner geometry is flat in all spacetime dimensions, whereas its
Weinhold geometry is curved. In the Kerr black hole can possess more
than one angular momentum. Finally we discuss the Ruppeiner geometry for the
Kerr black hole in with double angular momenta.Comment: 8 pages, 2 figures, RevTex, References adde
Information geometry of asymptotically AdS black holes
We investigate thermodynamic geometries of two families of asymptotically
Anti-de Sitter black holes, i.e. the Reissner-Nordstr\"om Anti-de Sitter in
four dimensions and the BTZ black hole. It is found that the Anti-de Sitter
space renders the geometry nontrivial (c.f. the Reissner-Nordstr\"om black hole
in asymptotically flat background). The BTZ black hole's thermodynamic geometry
is trivial despite the fact that it is characterized by the (negative)
cosmological constant. As a matter of curiosity we compute thermodynamic
geometry of these black holes regarding the cosmological constant as a true
parameter but no physically significant results can be derived.Comment: Contribution to proceedings of ERE2008, 4 page
Anti-de Sitter Quotients, Bubbles of Nothing, and Black Holes
In 3+1 dimensions there are anti-de quotients which are black holes with
toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de
Sitter solution (and appropriate identifications) one finds two one parameter
families of spacetimes that contain these quotient black holes. One of these
families consists of B-metrics ("bubbles of nothing"), the other of black hole
spacetimes. All of them have vanishing conserved charges.Comment: 14 pages, 3 figures. References added, one explanation improve
Flat Information Geometries in Black Hole Thermodynamics
The Hessian of either the entropy or the energy function can be regarded as a
metric on a Gibbs surface. For two parameter families of asymptotically flat
black holes in arbitrary dimension one or the other of these metrics are flat,
and the state space is a flat wedge. The mathematical reason for this is traced
back to the scale invariance of the Einstein-Maxwell equations. The picture of
state space that we obtain makes some properties such as the occurence of
divergent specific heats transparent.Comment: 14 pages, one figure. Dedicated to Rafael Sorkin's birthda
Geometro-thermodynamics of tidal charged black holes
Tidal charged spherically symmetric vacuum brane black holes are
characterized by their mass m and tidal charge q, an imprint of the
5-dimensional Weyl curvature. For q>0 they are formally identical to the
Reissner-Nordstr\"om black hole of general relativity. We study the
thermodynamics and thermodynamic geometries of tidal charged black holes and
discuss similarities and differences as compared to the Reissner-Nordstr\"om
black hole. As a similarity, we show that (for q>0) the heat capacity of the
tidal charged black hole diverges on a set of measure zero of the parameter
space, nevertheless both the regularity of the Ruppeiner metric and a
Poincar\'e stability analysis shows no phase transition at those points. The
thermodynamic state spaces being different indicates that the underlying
statistical models could be different. We find that the q<0 parameter range,
which enhances the localization of gravity on the brane, is thermodynamically
preferred. Finally we constrain for the first time the possible range of the
tidal charge from the thermodynamic limit on gravitational radiation efficiency
at black hole mergers.Comment: v3: 23 pages, 8 figures, 1 table, published versio