arXiv subjects

Juan Antonio Morales-Lladosa

Publications and source records attributed to Juan Antonio Morales-Lladosa.

18 recordsLinked to original sources

arXiv2025

Violation of Bell inequalities from Cosmic Microwave Background data

In a recent paper [R. Dale. R. Lapiedra, and J. A. Morales-Lladosa, Phys. Rev. D {\bf 107}, 023506 (2023)] a cosmic-like Clauser-Horne-Shimony-Holt (CHSH) inequality was proved for the temperature fluctuations $δT$ of the perturbed Cosmic Microwave Background (CMB), assuming local realism. This inequality can be tested from observational data. In fact, no violation for it has been found from the CMB data provided by the COBE satellite in different sky directions. This is a result which, being negative, is not conclusive in relation to the possible violation of the CHSH inequality in a cosmological context. So, the preceding analysis needs to be extended by using more precise current CMB data, like those provided by WMAP and Planck satellites. This is a task of considerable importance but, technically, much more involved in data treatments. In this work, assuming again local realism behind measurements and observational data, this extension is accomplished. The result is that a sound violation of the CHSH inequality is found, which would mean the failure of the assumed local realism in accordance with the quantum origin of the primordial temperature fluctuations in the framework of standard inflation and the orthodox interpretation of the Quantum Mechanics.

gr-qc↗

arXiv2024

Cosmic primordial density fluctuations and Bell inequalities

The temperature measurements, $T$, of the perturbed cosmic microwave background, performed by the cosmic background explorer satellite (COBE), are considered. A dichotomist function, $f = \pm 1$, is defined such that $f =+1$ if $δT > 0$ and $f =-1$ if $δT < 0$, where $δT$ stands for the fluctuation of $T$. Then, it is assumed that behind the appearance of these fluctuations there is local realism. Under this assumption, some specific Clauser-Horne-Shimony-Holt (CHSH) inequalities are proved for these fluctuation temperatures measured by COBE in the different sky directions. The calculation of these inequalities from the actual temperature measurements shows that these inequalities are not violated. This result cannot be anticipated by calculating the commutators of the cosmic density quantum operators. This must be remarked here since, in the case of a system of two entangled spin ${\textstyle{1 \over 2}}$ particles, its CHSH inequalities violation can be inferred from the nonvanishing value of the corresponding spin measurement commutators. The above nonviolation of the observed cosmic CHSH inequalities is compatible with the existence of local realism behind the cosmic measurement results. Nevertheless, assuming again local realism, some new cosmic CHSH inequalities can be derived for the case of the WMAP measurements whose accuracy is better than the one of the above considered COBE measurements. More specifically, in the WMAP case, some significant cross correlations between the temperature and polarization maps are detected, and the new cosmic CHSH inequalities are the ones built with these cross correlations. Now, the occasional violation of these CHSH inequalities would mean the failure of the assumed local realism in accordance with the quantum origin of the primordial temperature and polarization fluctuations in the framework of standard inflation.

gr-qc↗

arXiv2024

Vector Field Dynamics: Field Equations and Energy Tensor

Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the general Euler-Lagrange equations for the field are derived and the existence of a conserved current is achieved. The field equations are also analyzed from an eikonal-like point of view. The Hilbert energy-momentum tensor of the field is also derived and the influence of each one of the irreducible pieces appearing in the Lagrangian is studied. Particular values of the free parameters allow to retrieve known results.

gr-qc↗

arXiv2022

Essential Fierz identities for a fermionic field

For a single fermionic field, an interpretation of the Fierz identities (which establish relations between the bilinear field observables) is given. They appear closely related to the algebraic class (regular or singular) of the spin 2-form $S$ associated to the spinor field. If $S \neq 0$, the Fierz identities follow from the 3+1 decomposition of the eigenvector equations for $S$ with respect to an inertial laboratory, which makes this interpretation suitable for fermionic particle physics models. When $S= 0$, the Fierz identities reduce to three constraints on the current densities associated with the spinor field, saying that they are orthogonal, equimodular, the vector current being timelike and the axial one being spacelike.

hep-th↗

arXiv2019

Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects

We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $δ$ functions) discontinuities, the Dirac $δ$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the Einstein field equations can only exist in the sense of distributions. Then, we assume that the metric considered is ${\cal C}^1$ class everywhere and is a solution of the Einstein field equations in this sense. We explore the consequences of these two assumptions, and in doing so we derive the general conditions that constrain the jumps in the second partial derivatives across the boundary. The example of the Oppenheimer-Snyder metric is considered and some new results are obtained on it. Then, the formalism developed in this exploration is applied to a different situation, i.e., to a given generalization of the Einstein field equations for the case where the partial second derivatives of the metric exist but are not symmetric.

gr-qc↗

arXiv2018

Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy

The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cloud), and the consequences of such a tentative assumption are explored. The whole analytical family of resulting models is obtained and some of them are picked out as physical better models on the basis of the finite and constant value of its {\em intrinsic} energy.

gr-qc↗

arXiv2017

Cosmic censorship conjecture in some matching spherical collapsing metrics

A physically plausible Lema{\^ı}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that its {\em intrinsic} energy is, as due, stationary and finite. It is proved for this Lema{\^ı}tre-Tolman-Bondi collapse, for some parameter values, that its intrinsic central singularity is globally naked, thus violating the cosmic censorship conjecture with, for each direction, one photon, or perhaps a pencil of photons, leaving the singularity and reaching the null infinity. Our result is discussed in relation to some other cases in the current literature on the subject in which some of the central singularities are globally naked too.

gr-qc↗

arXiv2015

Geodesic family of spherical instantons and cosmic quantum creation

The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\^ı}tre-Tolman-Bondi family and for a general $Λ$-Friedmann-Lema{\^ı}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $Λ$FLRW model is quantically creatable while the open and flat models are not. That is so since it can be seen that this closed model has vanishing energy while the open model and the limiting flat case (suitably perturbed) have both infinite energy.

gr-qc↗

arXiv2014

Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero. Thus, the global vanishing previously found for the Schwarzschild metric remains linearly stable under slow rotational perturbations of this metric.

gr-qc↗

arXiv2014

Intrinsic energy of Lemaître-Tolman-Bondi models and cosmological implications

Recently, some Lema{\^ı}tre-Tolman-Bondi metrics have been considered as models alternative to the dark energy within the Friedmann-Lema{\^ı}tre-Robertson-Walker universes. The vanishing of the intrinsic energy of these metrics is examined since such a vanishing, in the present case and in general, could be interpreted as a necessary condition to consider the possibility of the quantum creation of a metric. More specifically, this vanishing is examined in the particular case where the Lema{\^ı}tre-Tolman-Bondi metrics behave asymptotically like a Friedmann-Lema{\^ı}tre-Robertson-Walker universe. Finally, we deal with a particular model ruled out after being confronted with cosmic observations. In a minimal agreement with this negative result, leaving aside an unstable case, the value of the intrinsic energy of this particular model does not vanish and becomes in fact minus infinite.

gr-qc↗

arXiv2013

On the uniqueness of the space-time energy in General Relativity. The illuminating case of the Schwarzschild metric

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in particular to the Schwarzschild metric, obtaining a vanishing energy for this space-time. This result is compared with the result of some known theorems on the uniqueness of the energy of any asymptotic Minkowskian space, showing that there is no contradiction between both results, the differences becoming from the use of coordinates with different operational meanings. The suitability of Gauss coordinates when defining an {\em intrinsic} energy is considered and it is finally concluded that a Schwarzschild metric is a particular case of space-times with vanishing {\em intrinsic} 4-momenta.

gr-qc↗

arXiv2013

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.

gr-qc↗

arXiv2011

Maximal slicings in spherical symmetry: local existence and construction

We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.

gr-qc↗

arXiv2011

Intrinsic vanishing of energy and momenta in a universe

We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in general relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular three-momenta vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lema{\^ı}tre-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.

gr-qc↗

arXiv2010

Painlevé-Gullstrand synchronizations in spherical symmetry

A Painlevé-Gullstrand synchronization is a slicing of the space-time by a family of flat spacelike 3-surfaces. For spherically symmetric space-times, we show that a Painlevé-Gullstrand synchronization only exists in the region where $(dr)^2 \leq 1$, $r$ being the curvature radius of the isometry group orbits ($2$-spheres). This condition says that the Misner-Sharp gravitational energy of these 2-spheres is not negative and has an intrinsic meaning in terms of the norm of the mean extrinsic curvature vector. It also provides an algebraic inequality involving the Weyl curvature scalar and the Ricci eigenvalues. We prove that the energy and momentum densities associated with the Weinberg complex of a Painlevé-Gullstrand slice vanish in these curvature coordinates, and we give a new interpretation of these slices by using semi-metric Newtonian connections. It is also outlined that, by solving the vacuum Einstein's equations in a coordinate system adapted to a Painlevé-Gullstrand synchronization, the Schwarzschild solution is directly obtained in a whole coordinate domain that includes the horizon and both its interior and exterior regions.

gr-qc↗

arXiv2010

Positioning in a flat two-dimensional space-time: the delay master equation

The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. We illustrate these results with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.

gr-qc↗

arXiv2010

Positioning systems in Minkowski space-time: from emission to inertial coordinates

The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of an emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a `central' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.

gr-qc↗

arXiv2010

On the local existence of maximal slicings in spherically symmetric spacetimes

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.

gr-qc↗