0000000000719109
AUTHOR
Juan Antonio Morales
Creatable universes
We consider the question of properly defining energy and momenta for non asymptotic Minkowskian spaces in general relativity. Only spaces of this type, whose energy, linear 3-momentum, and intrinsic angular momentum vanish, would be candidates for creatable universes, that is, for universes which could have arisen from a vacuum quantum fluctuation. Given a universe, we completely characterize the family of coordinate systems for which one could sensibly say that this universe is a creatable universe.
Inhomogeneous space-times admitting isotropic radiation: Vorticity-free case
The energy-momentum tensor of space-times admitting a vorticity-free and a shear-free timelike congruence is obtained. This result is used to write Einstein equations in a convenient way in order to get inhomogeneous space-times admitting an isotropic distribution of photons satisfying the Liouville equation. Two special cases with anisotropic pressures in the energy flow direction are considered.
Two-Perfect Fluid Interpretation of an Energy Tensor
The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained.
Symmetric frames on Lorentzian spaces
Symmetric frames (those whose vectors are metrically indistinguishable) are studied both, from the algebraic and differential points of view. Symmetric frames which, in addition, remain indistinguishable for a given set of concomitants of the metric are analyzed, and the necessary and sufficient conditions for a space‐time to admit them are given. A new version of the cosmological principle then follows. Natural symmetric frames (induced by local charts) are also considered, and the space‐times admitting them are obtained.
Evolution of polarization orientations in a flat universe with vector perturbations: CMB and quasistellar objects
Various effects produced by vector perturbations (vortical peculiar velocity fields) of a flat Friedmann-Robertson-Walker background are considered. In the presence of this type of perturbations, the polarization vector rotates. A formula giving the rotation angle is obtained and, then, it is used to prove that this angle depends on both the observation direction and the emission redshift. Hence, rotations are different for distinct quasars and also for the Cosmic Microwave Background (CMB) radiation coming along different directions (from distinct points of the last scattering surface). As a result of these rotations, some correlations could appear in an initially random field of quasar po…
Method to obtain shear-free two-fluid solutions of Einstein's equations.
We use the Einstein equations, stated as an initial-value problem (3+1 formalism), to present a method for obtaining a class of solutions which may be interpreted as the gravitational field produced by a mixture of two perfect fluids. The four-velocity of one of the components is assumed to be a shear-free, irrotational, and geodesic vector field. The solutions are given up to a set of a hyperbolic quasilinear system.
Intrinsic characterization of space‐time symmetric tensors
This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.
Positioning with stationary emitters in a two-dimensional space-time
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coord…
Two-dimensional approach to relativistic positioning systems
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.
Lorentzian Comments on Stokes Parameters
The popular Stokes statements about polarized light are interpreted in a Minkowskian language using a Lorentzian representation for the Stokes parameters and the degree of polarization. The evolution equations for Stokes parameters on a curved space-time are obtained using the parallel transport of the polarization vector along a null geodesic. The interest of these equations in Astrophysics and Relativistic Cosmology is outlined.
Cosmological Vector Perturbations and CMB Anomalies
Recently, it has been proved that large scale vector modes could explain most of the CMB anomalies in the first temperature multipoles. Some divergenceless (vortical) velocity fields–which are superimpositions of vector modes–can explain both the alignment of the second and third multipoles and the planar character of the octopole. In this paper we comment: (a) some papers trying to account for the mentioned anomalies, (b) our explanation based on vector modes, and (c) some current ideas about the possible origin of these modes.
On Newtonian frames
In Newtonian space-time there exist four, and only four, causal classes of frames. Natural frames allow to extend this result to coordinate systems, so that coordinate systems may be also locally classified in four causal classes. These causal classes admit simple geometric descriptions and physical interpretations. For example, one can generate representatives of the four causal classes by means of the {\em linear synchronization group}. Of particular interest is the {\em local Solar time synchronization}, which reveals the limits of the frequent use of the concept of `causally oriented oordinate', such as that of `time-like coordinate'. Classical {\em positioning systems}, based in sound …
Residual fluctuations in the microwave background at large angular scales: Revision of the Sachs-Wolfe effect
In this paper we revise the Sachs-Wolfe (SW) computation of large-scale an isotropies of the microwave background temperature, taking into account the properties of the metrics admitting an isotropic distribution of collisionless photons. We show that the metric used by SW belongs to the aforementioned class, and conclude that the microwave background (once the dipolar anisotropy has been subtracted) should now be isotropic at large angular scales, provided that it was isotropic on the last scattering surface and assuming that the growing mode of a pressureless Einstein-de Sitter perturbation is a good description of the metric.
Radial conformal motions in Minkowski space–time
A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.
Minkowskian description of polarized light and polarizers.
A conventional Stokes description of polarized light is considered in a four-dimensional Lorentzian space, developing a seminal idea of Paul Soleillet [Ann. Phys. (Paris) 12, 23 (1929)]. This provides a striking interpretation for the degree of polarization and the Stokes decomposition of light beams. Malus law and reciprocity theorems for polarizers are studied using this Lorentzian formalism.
A kinematic method to obtain conformal factors
Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson-Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi-Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson-Walker space-times.
Comments on space–time signature
In terms of three signs associated to two vectors and to a 2-plane, a formula for the signature of any four-dimensional metric is given. In the process, a simple expression for the sign of the Lorentzian metric signature is obtained. The rela- tionship between these results and those already known are commented upon.
199 Causal Classes of Space-Time Frames
It is shown that from the causal point of view Minkowskian space-time admits 199, and only 199, different classes of frames.
Potential perturbation to Friedmann universes
The energy-momentum tensor of perturbed Friedmann universes in the longitudinal gauge (depending on only one gravitational potential) is obtained in order to clarify the physical meaning of two important cases: (1) conformally static perturbations (when the potential is independent of time), and (2) nonstatic perturbations in the case where the potential allows a particular separation of time and space coordinates. The statement according to which the longitudinal gauge allows a description of high-density-contrast regions is analyzed. In the conformally static case we suggest interpreting the energy-momentum tensor as representing a set of particles in gravitational interaction, suitable f…
The momentum and the angular momentum of the Universe revisited. Some preliminary results
We consider the question of properly defining energy and momenta for non asymptotic Minkowskian spaces in general relativity. Only those of these spaces which have zero energy, zero linear 3-momentum, and zero intrinsic angular momentum would be candidates to creatable universes, that is, to universes which could have arisen from a vacuum quantum fluctuation. Given a universe, we completely characterize the family of coordinate systems in which it would make sense saying that this universe can be a creatable universe.
Covariant determination of the Weyl tensor geometry
We give a covariant and deductive algorithm to determine, for every Petrov type, the geometric elements associated with the Weyl tensor: principal and other characteristic 2-forms, Debever null directions and canonical frames. We show the usefulness of these results by applying them in giving the explicit characterization of two families of metrics: static type I spacetimes and type III metrics with a hypersurface-orthogonal Killing vector. PACS numbers: 0240M, 0420C
Schwarzschild Interior in Conformally Flat Form
A unified conformally flat form of the static Schwarzschild interior space–times is provided. A new parameter that allows us to analyze the symmetry (spherical, plane or hyperbolic) of the three well known classes of metrics is introduced. In the spherically symmetric case, this parameter is related to the historical limit value of the mass to radius ratio found by Schwarzschild for a sphere of incompressible fluid.