104 research outputs found
Ultimate gravitational mass defect
We present a new type of gravitational mass defect in which an infinite
amount of matter may be bounded in a zero ADM mass. This interpolates between
effects typical of closed worlds and T-spheres. We consider the Tolman model of
dust distribution and show that this phenomenon reveals itself for a solution
that has no origin on one side but is closed on the other side. The second
class of examples corresponds to smooth gluing T-spheres to the portion of the
Friedmann-Robertson-Walker solution. The procedure is generalized to
combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In
particular, in this approach a finite T-sphere is obtained that looks for
observers in two R-regions as the Schwarzschild metric with two different
masses one of which may vanish.Comment: 9 pages. 1 reference added. To appear in Gen. Rel. Gra
Ideal Stars and General Relativity
We study a system of differential equations that governs the distribution of
matter in the theory of General Relativity. The new element in this paper is
the use of a dynamical action principle that includes all the degrees of
freedom, matter as well as metric. The matter lagrangian defines a relativistic
version of non-viscous, isentropic hydrodynamics. The matter fields are a
scalar density and a velocity potential; the conventional, four-vector velocity
field is replaced by the gradient of the potential and its scale is fixed by
one of the eulerian equations of motion, an innovation that significantly
affects the imposition of boundary conditions. If the density is integrable at
infinity, then the metric approaches the Schwarzschild metric at large
distances. There are stars without boundary and with finite total mass; the
metric shows rapid variation in the neighbourhood of the Schwarzschild radius
and there is a very small core where a singularity indicates that the gas laws
break down. For stars with boundary there emerges a new, critical relation
between the radius and the gravitational mass, a consequence of the stronger
boundary conditions. Tentative applications are suggested, to certain Red
Giants, and to neutron stars, but the investigation reported here was limited
to polytropic equations of state. Comparison with the results of Oppenheimer
and Volkoff on neutron cores shows a close agreement of numerical results.
However, in the model the boundary of the star is fixed uniquely by the
required matching of the interior metric to the external Schwarzschild metric,
which is not the case in the traditional approach.Comment: 26 pages, 7 figure
Thermodynamics with long-range interactions: from Ising models to black-holes
New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22
pages, 2 figure
Hard-Sphere Fluids in Contact with Curved Substrates
The properties of a hard-sphere fluid in contact with hard spherical and
cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is
applied to determine the density profile and surface tension for wide
ranges of radii of the curved walls and densities of the hard-sphere fluid.
Particular attention is paid to investigate the curvature dependence and the
possible existence of a contribution to that is proportional to the
logarithm of the radius of curvature. Moreover, by treating the curved wall as
a second component at infinite dilution we provide an analytical expression for
the surface tension of a hard-sphere fluid close to arbitrary hard convex
walls. The agreement between the analytical expression and DFT is good. Our
results show no signs for the existence of a logarithmic term in the curvature
dependence of .Comment: 15 pages, 6 figure
Interior of a Schwarzschild black hole revisited
The Schwarzschild solution has played a fundamental conceptual role in
general relativity, and beyond, for instance, regarding event horizons,
spacetime singularities and aspects of quantum field theory in curved
spacetimes. However, one still encounters the existence of misconceptions and a
certain ambiguity inherent in the Schwarzschild solution in the literature. By
taking into account the point of view of an observer in the interior of the
event horizon, one verifies that new conceptual difficulties arise. In this
work, besides providing a very brief pedagogical review, we further analyze the
interior Schwarzschild black hole solution. Firstly, by deducing the interior
metric by considering time-dependent metric coefficients, the interior region
is analyzed without the prejudices inherited from the exterior geometry. We
also pay close attention to several respective cosmological interpretations,
and briefly address some of the difficulties associated to spacetime
singularities. Secondly, we deduce the conserved quantities of null and
timelike geodesics, and discuss several particular cases in some detail.
Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly
from the interior solution. In concluding, it is important to emphasize that
the interior structure of realistic black holes has not been satisfactorily
determined, and is still open to considerable debate.Comment: 15 pages, 7 figures, Revtex4. V2: Version to appear in Foundations of
Physic
All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity
Via a straightforward integration of the Einstein equations with cosmological
constant, all static circularly symmetric perfect fluid 2+1 solutions are
derived. The structural functions of the metric depend on the energy density,
which remains in general arbitrary. Spacetimes for fluids fulfilling linear and
polytropic state equations are explicitly derived; they describe, among others,
stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate
fermions, incoherent and pure radiation. As a by--product, we demonstrate the
uniqueness of the constant energy density perfect fluid within the studied
class of metrics. A full similarity of the perfect fluid solutions with
constant energy density of the 2+1 and 3+1 gravities is established.Comment: revtex4, 8 page
Strange Stars with a Density-Dependent Bag Parameter
We have studied strange quark stars in the framework of the MIT bag model,
allowing the bag parameter B to depend on the density of the medium. We have
also studied the effect of Cooper pairing among quarks, on the stellar
structure. Comparison of these two effects shows that the former is generally
more significant. We studied the resulting equation of state of the quark
matter, stellar mass-radius relation, mass-central-density relation,
radius-central-density relation, and the variation of the density as a function
of the distance from the centre of the star. We found that the
density-dependent B allows stars with larger masses and radii, due to
stiffening of the equation of state. Interestingly, certain stellar
configurations are found to be possible only if B depends on the density. We
have also studied the effect of variation of the superconducting gap parameter
on our results.Comment: 23 pages, 8 figs; v2: 25 pages, 9 figs, version to be published in
Phys. Rev. (D
Holography, Fractionalization and Magnetic Fields
Four dimensional gravity with a U(1) gauge field, coupled to various fields
in asymptotically anti-de Sitter spacetime, provides a rich arena for the
holographic study of the strongly coupled (2+1)-dimensional dynamics of finite
density matter charged under a global U(1). As a first step in furthering the
study of the properties of fractionalized and partially fractionalized degrees
of freedom in the strongly coupled theory, we construct electron star solutions
at zero temperature in the presence of a background magnetic field. We work in
Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source
is cloaked by an event horizon. A key ingredient of our solutions is our
observation that starting with the standard Landau level structure for the
density of states, the electron star limits reduce the charge density and
energy density to that of the free fermion result. Using this result we
construct three types of solution: One has a star in the infra-red with an
electrically neutral horizon, another has a star that begins at an electrically
charged event horizon, and another has the star begin a finite distance from an
electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly
interacting matter in magnetic fields. v2: Updated references and adjusted
some phrasing in the introductio
The importance of the mixed phase in hybrid stars built with the Nambu-Jona-Lasinio model
We investigate the structure of hybrid stars based on two different
constructions: one is based on the Gibbs condition for phase coexistence and
considers the existence of a mixed phase (MP), and the other is based on the
Maxwell construction and no mixed phase is obtained. The hadron phase is
described by the non-linear Walecka model (NLW) and the quark phase by the
Nambu-Jona-Lasinio model (NJL). We conclude that the masses and radii obtained
are model dependent but not significantly different for both constructions.Comment: 8 pages, 7 figures, 3 table
Equilibrium and stability of neutrino lumps as TOV solutions
We report about stability conditions for static, spherically symmetric
objects that share the essential features of mass varying neutrinos in
cosmological scenarios. Compact structures of particles with variable mass are
held together preponderantly by an attractive force mediated by a background
scalar field. Their corresponding conditions for equilibrium and stability are
given in terms of the ratio between the total mass-energy and the spherical
lump radius, . We show that the mass varying mechanism leading to lump
formation can modify the cosmological predictions for the cosmological neutrino
mass limits. Our study comprises Tolman-Oppenheimer-Volkoff solutions of
relativistic objects with non-uniform energy densities. The results leave open
some questions concerning stable regular solutions that, to an external
observer, very closely reproduce the preliminary conditions to form
Schwarzschild black holes.Comment: 20 pages, 5 figure
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