783 research outputs found
Orbital stability of the restricted three body problem in General Relativity
We consider the problem of orbital stability of the motion of a test particle
in the restricted three-body problem, by using the orbital moment and its time
derivative. We show that it is possible to get some insight into the stability
properties of the motion of test particles, without knowing the exact solutions
of the motion equations.Comment: 2 page
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
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
Geometrothermodynamics
We present the fundamentals of geometrothermodynamics, an approach to study
the properties of thermodynamic systems in terms of differential geometric
concepts. It is based, on the one hand, upon the well-known contact structure
of the thermodynamic phase space and, on the other hand, on the metric
structure of the space of thermodynamic equilibrium states. In order to make
these two structures compatible we introduce a Legendre invariant set of
metrics in the phase space, and demand that their pullback generates metrics on
the space of equilibrium states. We show that Weinhold's metric, which was
introduced {\it ad hoc}, is not contained within this invariant set. We propose
alternative metrics which allow us to redefine the concept of thermodynamic
length in an invariant manner and to study phase transitions in terms of
curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy
Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory
We investigate the thermodynamic properties of 5D static and spherically
symmetric black holes in (i) Einstein-Maxwell-Gauss-Bonnet theory, (ii)
Einstein-Maxwell-Gauss-Bonnet theory with negative cosmological constant, and
in (iii) Einstein-Yang-Mills-Gauss-Bonnet theory. To formulate the
thermodynamics of these black holes we use the Bekenstein-Hawking entropy
relation and, alternatively, a modified entropy formula which follows from the
first law of thermodynamics of black holes. The results of both approaches are
not equivalent. Using the formalism of geometrothermodynamics, we introduce in
the manifold of equilibrium states a Legendre invariant metric for each black
hole and for each thermodynamic approach, and show that the thermodynamic
curvature diverges at those points where the temperature vanishes and the heat
capacity diverges.Comment: New sections added, references adde
Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
We study the thermodynamics and the thermodynamic geometries of charged
rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the
thermodynamics of these systems within the context of the Weinhold and
Ruppeiner thermodynamic geometries and the recently developed formalism of
geometrothermodynamics (GTD). Considering the behavior of the heat capacity and
the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot
describe completely the thermodynamics of these black holes and of their
limiting case of vanishing electric charge. In contrast, the Legendre
invariance imposed on the metric in GTD allows one to describe the CR-BTZ black
holes and their limiting cases in a consistent and invariant manner
Geometric Thermodynamics of Schwarzschild-AdS black hole with a Cosmological Constant as State Variable
The thermodynamics of the Schwarzschild-AdS black hole is reformulated within
the context of the recently developed formalism of geometrothermodynamics
(GTD). Different choices of the metric in the equilibrium states manifold are
used in order to reproduce the Hawking-Page phase transition as a divergence of
the thermodynamical curvature scalar. We show that the enthalpy and total
energy representations of GTD does not reproduce the transition while the
entropy rep- resentation gives the expected behavior.Comment: 14 page
Extending the generalized Chaplygin gas model by using geometrothermodynamics
We use the formalism of geometrothermodynamics (GTD) to derive fundamental
thermodynamic equations that are used to construct general relativistic
cosmological models. In particular, we show that the simplest possible
fundamental equation, which corresponds in GTD to a system with no internal
thermodynamic interaction, describes the different fluids of the standard model
of cosmology. In addition, a particular fundamental equation with internal
thermodynamic interaction is shown to generate a new cosmological model that
correctly describes the dark sector of the Universe and contains as a special
case the generalized Chaplygin gas model.Comment: 18 pages, 7 figures. Section added: Basics aspects of
geometrothermodynamic
Time and "angular" dependent backgrounds from stationary axisymmetric solutions
Backgrounds depending on time and on "angular" variable, namely polarized and
unpolarized Gowdy models, are generated as the sector inside
the horizons of the manifold corresponding to axisymmetric solutions. As is
known, an analytical continuation of ordinary -branes, -branes allows
one to find -brane solutions. Simple models have been constructed by means
of analytic continuation of the Schwarzchild and the Kerr metrics. The
possibility of studying the -Gowdy models obtained here is outlined with an
eye toward seeing if they could represent some kind of generalized -branes
depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde
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Development Of Third Harmonic Generation As A Short Pulse Probe Of Shock Heated Material
We are studying high-pressure laser produced shock waves in silicon (100). To examine the material dynamics, we are performing pump-probe style experiments utilizing 600 ps and 40 fs laser pulses from a Ti:sapphire laser. Two-dimensional interferometry reveals information about the shock breakout, while third harmonic light generated at the rear surface is used to infer the crystalline state of the material as a function of time. Sustained third harmonic generation (THG) during a similar to 100 kbar shock breakout indicate that the rear surface remains crystalline for at least 3 ns. However, a decrease in THG during a similar to 300 kbar shock breakout suggests a different behavior, which could include a change in crystalline structure.Mechanical Engineerin
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