13 research outputs found
Description of Friedmann Observables in Quantum Universe
The solution of the problem of describing the Friedmann observables (the
Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis
of the method of gaugeless Hamiltonian reduction in which the gravitational
part of the energy constraint is considered as a new momentum. We show that the
conjugate variable corresponding to the new momentum plays a role of the
invariant time parameter of evolution of dynamical variables in the sector of
the Dirac observables of the general Hamiltonian approach. Relations between
these Dirac observables and the Friedmann observables of the expanding Universe
are established for the standard Friedmann cosmological model with dust and
radiation. The presented reduction removes an infinite factor from the
functional integral, provides the normalizability of the wave function of the
Universe and distinguishes the conformal frame of reference where the Hubble
law is caused by the alteration of the conformal dust mass.Comment: 10 pages, LaTe
On perfect fluid models in non-comoving observational spherical coordinates
We use null spherical (observational) coordinates to describe a class of
inhomogeneous cosmological models. The proposed cosmological construction is
based on the observer past null cone. A known difficulty in using inhomogeneous
models is that the null geodesic equation is not integrable in general. Our
choice of null coordinates solves the radial ingoing null geodesic by
construction. Furthermore, we use an approach where the velocity field is
uniquely calculated from the metric rather than put in by hand. Conveniently,
this allows us to explore models in a non-comoving frame of reference. In this
frame, we find that the velocity field has shear, acceleration and expansion
rate in general. We show that a comoving frame is not compatible with expanding
perfect fluid models in the coordinates proposed and dust models are simply not
possible. We describe the models in a non-comoving frame. We use the dust
models in a non-comoving frame to outline a fitting procedure.Comment: 8 pages, 1 figure. To appear in 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
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
A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints
We compare higher order gravity models to observational constraints from
magnitude-redshift supernova data, distance to the last scattering surface of
the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed
systematic approach to higher order gravity models based on minimal sets of
curvature invariants, and select models that pass some physical acceptability
conditions (free of ghost instabilities, real and positive propagation speeds,
and free of separatrices). Models that satisfy these physical and observational
constraints are found in this analysis and do provide fits to the data that are
very close to those of the LCDM concordance model. However, we find that the
limitation of the models considered here comes from the presence of
superluminal mode propagations for the constrained parameter space of the
models.Comment: 12 pages, 6 figure
A re-interpretation of the concept of mass and of the relativistic mass-energy relation
For over a century the definitions of mass and derivations of its relation
with energy continue to be elaborated, demonstrating that the concept of mass
is still not satisfactorily understood. The aim of this study is to show that,
starting from the properties of Minkowski spacetime and from the principle of
least action, energy expresses the property of inertia of a body. This implies
that inertial mass can only be the object of a definition - the so called
mass-energy relation - aimed at measuring energy in different units, more
suitable to describe the huge amount of it enclosed in what we call the
"rest-energy" of a body. Likewise, the concept of gravitational mass becomes
unnecessary, being replaceable by energy, thus making the weak equivalence
principle intrinsically verified. In dealing with mass, a new unit of
measurement is foretold for it, which relies on the de Broglie frequency of
atoms, the value of which can today be measured with an accuracy of a few parts
in 10^9
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