88 research outputs found
Nonsingular, big-bounce cosmology from spinor-torsion coupling
The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of
general relativity that the affine connection be symmetric by regarding its
antisymmetric part, the torsion tensor, as a dynamical variable. The minimal
coupling between the torsion tensor and Dirac spinors generates a spin-spin
interaction which is significant in fermionic matter at extremely high
densities. We show that such an interaction averts the unphysical big-bang
singularity, replacing it with a cusp-like bounce at a finite minimum scale
factor, before which the Universe was contracting. This scenario also explains
why the present Universe at largest scales appears spatially flat, homogeneous
and isotropic.Comment: 7 pages; published versio
All "static" spherically symmetric perfect fluid solutions of Einstein's equations with constant equation of state parameter and finite-polynomial "mass function"
We look for "static" spherically symmetric solutions of Einstein's Equations
for perfect fluid source with equation of state . In order to include
the possibilities of recently popularized dark energy and phantom energy
possibly pervading the spacetime, we put no constraints on the constant . We
consider all four cases compatible with the standard ansatz for the line
element, discussed in previous work. For each case we derive the equation
obeyed by the mass function or its analogs. For these equations, we find {\em
all} finite-polynomial solutions, including possible negative powers.
For the standard case, we find no significantly new solutions, but show that
one solution is a static phantom solution, another a black hole-like solution.
For the dynamic and/or tachyonic cases we find, among others, dynamic and
static tachyonic solutions, a Kantowski-Sachs (KS) class phantom solution,
another KS-class solution for dark energy, and a second black hole-like
solution.
The black hole-like solutions feature segregated normal and tachyonic matter,
consistent with the assertion of previous work. In the first black hole-like
solution, tachyonic matter is inside the horizon, in the second, outside.
The static phantom solution, a limit of an old one, is surprising at first,
since phantom energy is usually associated with super-exponential expansion.
The KS-phantom solution stands out since its "mass function" is a ninth order
polynomial.Comment: 24 standard LaTeX pages, 4 tables, no figures. -Title changed to
avoid equation in title. -The set of solutions and their interpretation
remains unchanged, but new classification of solutions (solution labels also
changed), consolidation of appendix into a table (omitting calculation
details) resulted in shorter paper. -Updated Publication info for preprints
in Reference
Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity
An analysis of insular solutions of Einstein's field equations for static,
spherically symmetric, source mass, on the basis of exterior Schwarzschild
solution is presented. Following the analysis, we demonstrate that the {\em
regular} solutions governed by a self-bound (that is, the surface density does
not vanish together with pressure) equation of state (EOS) or density variation
can not exist in the state of hydrostatic equilibrium, because the source mass
which belongs to them, does not represent the `actual mass' appears in the
exterior Schwarzschild solution. The only configuration which could exist in
this regard is governed by the homogeneous density distribution (that is, the
interior Schwarzschild solution). Other structures which naturally fulfill the
requirement of the source mass, set up by exterior Schwarzschild solution (and,
therefore, can exist in hydrostatic equilibrium) are either governed by
gravitationally-bound regular solutions (that is, the surface density also
vanishes together with pressure), or self-bound singular solutions (that is,
the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for
publication in Modern Physics Letters
The standard "static" spherically symmetric ansatz with perfect fluid source revisited
Considering the standard "static" spherically symmetric ansatz ds2 = -B(r)
dt2 + A(r) dr2 + r2 dOmega2 for Einstein's Equations with perfect fluid source,
we ask how we can interpret solutions where A(r) and B(r) are not positive, as
they must be for the static matter source interpretation to be valid.
Noting that the requirement of Lorentzian signature implies A(r) B(r) >0, we
find two possible interpretations:
(i) The nonzero component of the source four-velocity does not have to be u0.
This provides a connection from the above ansatz to the Kantowski-Sachs (KS)
spacetimes.
(ii) Regions with negative A(r) and B(r) of "static" solutions in the
literature must be interpreted as corresponding to tachyonic source.
The combinations of source type and four-velocity direction result in four
possible cases. One is the standard case, one is identical to the KS case, and
two are tachyonic. The dynamic tachyonic case was anticipated in the
literature, but the static tachyonic case seems to be new. We derive
Oppenheimer-Volkoff-like equations for each case, and find some simple
solutions. We conclude that new "simple" black hole solutions of the above
form, supported by a perfect fluid, do not exist.Comment: 24 standard LaTeX pages, no figures. Some change in emphasis; changes
in parametrizations of some of the solutions (ND2, TD2, TD3, NS1); one new
solution (TS4); removal of an incorrect statement (about ND4
Spacetime geometry of static fluid spheres
We exhibit a simple and explicit formula for the metric of an arbitrary
static spherically symmetric perfect fluid spacetime. This class of metrics
depends on one freely specifiable monotone non-increasing generating function.
We also investigate various regularity conditions, and the constraints they
impose. Because we never make any assumptions as to the nature (or even the
existence) of an equation of state, this technique is useful in situations
where the equation of state is for whatever reason uncertain or unknown.
To illustrate the power of the method we exhibit a new form of the
``Goldman--I'' exact solution and calculate its total mass. This is a
three-parameter closed-form exact solution given in terms of algebraic
combinations of quadratics. It interpolates between (and thereby unifies) at
least six other reasonably well-known exact solutions.Comment: Plain LaTeX 2e -- V2: now 22 pages; minor presentation changes in the
first part of the paper -- no physics modifications; major additions to the
examples section: the Gold-I solution is shown to be identical to the G-G
solution. The interior Schwarzschild, Stewart, Buch5 XIII, de Sitter, anti-de
Sitter, and Einstein solutions are all special cases. V3: Reference,
footnotes, and acknowledgments added, typos fixed -- no physics
modifications. V4: Technical problems with mass formula fixed -- affects
discussion of our examples but not the core of the paper. Version to appear
in Classical and Quantum Gravit
Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
We propose a cosmological model in the framework of the Poincar\'e gauge
theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature
and torsion. In our specific model, the Lagrangian contains (i) the curvature
scalar and the curvature pseudo-scalar linearly and quadratically
(including an term) and (ii) pieces quadratic in the torsion {\it vector}
and the torsion {\it axial} vector (including a term). We show generally that in quadratic PG models we have nearly
the same number of parity conserving terms (`world') and of parity violating
terms (`shadow world'). This offers new perspectives in cosmology for the
coupling of gravity to matter and antimatter. Our specific model generalizes
the fairly realistic `torsion cosmologies' of Shie-Nester-Yo (2008) and Chen et
al.\ (2009). With a Friedman type ansatz for an orthonormal coframe and a
Lorentz connection, we derive the two field equations of PG in an explicit form
and discuss their general structure in detail. In particular, the second field
equation can be reduced to first order ordinary differential equations for the
curvature pieces and . Including these along with certain
relations obtained from the first field equation and curvature definitions, we
present a first order system of equations suitable for numerical evaluation.
This is deferred to the second, numerical part of this paper.Comment: Latex computerscript, 25 pages; mistakes corrected, references added,
notation and title slightly changed; accepted by Phys. Rev.
Exact General Relativistic Perfect Fluid Disks with Halos
Using the well-known ``displace, cut and reflect'' method used to generate
disks from given solutions of Einstein field equations, we construct static
disks made of perfect fluid based on vacuum Schwarzschild's solution in
isotropic coordinates. The same method is applied to different exactsolutions
to the Einstein'sequations that represent static spheres of perfect fluids. We
construct several models of disks with axially symmetric perfect fluid halos.
All disks have some common features: surface energy density and pressures
decrease monotonically and rapidly with radius. As the ``cut'' parameter
decreases, the disks become more relativistic, with surface energy density and
pressure more concentrated near the center. Also regions of unstable circular
orbits are more likely to appear for high relativistic disks. Parameters can be
chosen so that the sound velocity in the fluid and the tangential velocity of
test particles in circular motion are less then the velocity of light. This
tangential velocity first increases with radius and reaches a maximum.Comment: 22 pages, 25 eps.figs, RevTex. Phys. Rev. D to appea
Collapsing shear-free perfect fluid spheres with heat flow
A global view is given upon the study of collapsing shear-free perfect fluid
spheres with heat flow. We apply a compact formalism, which simplifies the
isotropy condition and the condition for conformal flatness. This formalism
also presents the simplest possible version of the main junction condition,
demonstrated explicitly for conformally flat and geodesic solutions. It gives
the right functions to disentangle this condition into well known differential
equations like those of Abel, Riccati, Bernoulli and the linear one. It yields
an alternative derivation of the general solution with functionally dependent
metric components. We bring together the results for static and time- dependent
models to describe six generating functions of the general solution to the
isotropy equation. Their common features and relations between them are
elucidated. A general formula for separable solutions is given, incorporating
collapse to a black hole or to a naked singularity.Comment: 26 page
Chiral fermions and torsion in the early Universe
Torsion arising from fermionic matter in the Einstein-Cartan formulation of
general relativity is considered in the context of Robertson-Walker geometries
and the early Universe. An ambiguity in the way torsion arising from hot
fermionic matter in chiral models should be implemented is highlighted and
discussed. In one interpretation, chemical potentials in chiral models can
contribute to the Friedmann equation and give a negative contribution to the
energy density.Comment: 5 pages revtex4; error in v1 corrected
Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff
fluid in general relativity is performed using the 1+3 covariant approach that
enables the dynamics of the fluid to be determined without assuming any
particular form for the space-time metric. The spin contributions to the field
equations produce a bounce that averts an initial singularity, provided that
the spin density exceeds the rate of shear. At later times, when the spin
contribution can be neglected, a Weyssenhoff fluid reduces to a standard
cosmological fluid in general relativity. Numerical solutions for the time
evolution of the generalised scale factor in spatially-curved models are
presented, some of which exhibit eternal oscillatory behaviour without any
singularities. In spatially-flat models, analytical solutions for particular
values of the equation-of-state parameter are derived. Although the scale
factor of a Weyssenhoff fluid generically has a positive temporal curvature
near a bounce, it requires unreasonable fine tuning of the equation-of-state
parameter to produce a sufficiently extended period of inflation to fit the
current observational data.Comment: 34 pages, 18 figure
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