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L. Fernandez-Jambrina

Publications and source records attributed to L. Fernandez-Jambrina.

At least 19 recordsLinked to original sources
arXiv2025

Rational complex Bezier curves

In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex values. One of the major advantages of this extension is that we may make use of two different groups of projective transformations. Besides the group of projective transformations of the real plane, we have the group of complex projective transformations. This allows us to apply useful transformations like the geometric inversion to curves in design. In addition to this, the use of the complex formulation allows to lower the degree of the curves in some cases. This can be checked using the resultant of two polynomials and provides a simple formula for determining whether a rational cubic curve is a conic or not. Examples of application of the formalism to classical curves are included.

math.NA↗
arXiv2024

Ripped ΛCDM: an observational contender to the consensus cosmological model

Current observations do not rule out the possibility that the Universe might end up in an abrupt event. Different such scenarios may be explored through suitable parameterizations of the dark energy and then confronted to cosmological background data. Here we parameterize a pseudorip scenario using a particular sigmoid function and carry an in-depth multifaceted examination of its evolutionary features and statistical performance. This depiction of a non violent final fate of our cosmos seems to be arguably statistically favoured over the consensus ΛCDM model according to some Bayesian discriminators.

astro-ph.CO↗
arXiv2021

Flux through a Möbius strip?

Integral theorems such as Stokes' and Gauss' are fundamental in many parts of Physics. For instance, Faraday's law allows computing the induced electric current on a closed circuit in terms of the variation of the flux of a magnetic field across the surface spanned by the circuit. The key point for applying Stokes' theorem is that this surface must be orientable. Many students wonder what happens to the flux through a surface when this is not orientable, as it happens with a Möbius strip. On an orientable surface one can compute the flux of a solenoidal field using Stokes' theorem in terms of the circulation of the vector potential of the field along the oriented boundary of the surface. But this cannot be done if the surface is not orientable, though in principle this quantity could be measured on a laboratory. For instance, checking the induced electric current on a circuit along the boundary of a surface if the field is a variable magnetic field. We shall see that the answer to this puzzle is simple and the problem lies in the question rather than in the answer.

physics.ed-ph↗
arXiv2016

Initial directional singularity in inflationary models

In [1] a new cosmological model is proposed with no big bang singularity in the past, though past geodesically incomplete. This model starts with an inflationary era, follows with a stiff matter dominated period and evolves to accelerated expansion in an asymptotically de Sitter regime in a realistic fashion. The big bang singularity is replaced by a directional singularity. This singularity cannot be reached by comoving observers, since it would take them an infinite proper time lapse to go back to it. On the contrary, observers with nonzero linear momentum have the singularity at finite proper time in their past, though arbitrarily large. Hence, the time lapse from the initial singularity can be as long as desired, even infinity, depending on the linear momentum of the observer. This conclusion applies to similar inflationary models. Due to the interest of these models, we address here the properties of such singularities.

gr-qc↗
arXiv2016

Implicit equations of non-degenerate rational Bezier quadric triangles

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bezier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.

cs.GR↗
arXiv2010

Cosmological singularities in FLRW spacetimes

In this talk we review the appearance of new types of singularities (big rip, sudden singularities...) in FLRW cosmological models that have arisen on considering explanations for accelerated expansion of our universe.

gr-qc↗
arXiv2010

Equation of state and singularities in FLRW cosmological models

We consider FLRW cosmological models with standard Friedmann equations, but leaving free the equation of state. We assume that the dark energy content of the universe is encoded in an equation of state $p=f(ρ)$, which is expressed with most generality in the form of a power expansion. The inclusion of this expansion in Friedmann equations allows us to construct a perturbative solution and to relate the coefficients of the equation of state with the formation of singularities of different types.

gr-qc↗
arXiv2007

Hidden past of dark energy cosmological models

In this paper we analyse the possibility of having homogeneous isotropic cosmological models with observers reaching $t=\infty$ in finite proper time. It is shown that just observationally-suggested dark energy models with $w\in(-5/3,-1)$ show this feature and that they are endowed with an exotic curvature singularity. Furthermore, it is shown that non-accelerated observers in these models may experience a duration of the universe as short as desired by increasing their linear momentum. A subdivision of phantom models in two families according to this behavior is suggested.

gr-qc↗
arXiv2006

Classification of cosmological milestones

In this paper causal geodesic completeness of FLRW cosmological models is analysed in terms of generalised power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Krolak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally alllowed models which have been proposed recently are lightlike geodesically complete.

gr-qc↗
arXiv2005

Comment on Singularity-free Cosmological Solutions with Non-rotating Perfect Fluids

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz-Senovilla and Fernandez-Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.

gr-qc↗
arXiv2004

Non-singular G2 stiff fluid cosmologies

In this paper we analyse Abelian diagonal orthogonally transitive spacetimes with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic completeness. A sufficient condition on the metric of these spacetimes is obtained, that is fairly easy to check and to implement in exact solutions. These results confirm that non-singular spacetimes are abundant among stiff fluid cosmologies.

gr-qc↗
arXiv2004

High Order Relativistic Corrections To Keplerian Motion

The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a non-equatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch-Hansen multipoles and the energy and angular momentum of the orbit.

gr-qc↗
arXiv2004

Singularity-Free Cylindrical Cosmological Model

A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic.

gr-qc↗
arXiv2004

Magnetic Surfaces in Stationary Axisymmetric General Relativity

In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization of some classical potential theory results, since lack of continuity of the potential is related to dipole density and lack of smoothness, to monopole density. In particular this approach is useful for constructing the dipole source for the magnetic field. This formalism involves solving a linear elliptic differential equation with boundary conditions at infinity. As an example, two different models of surface densities for the Kerr-Newman electrovac spacetime are derived.

gr-qc↗
arXiv2004

Differential Form Approach for Stationary Axisymmetric Maxwell Fields in General Relativity

A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different features of the fields, such as the derivation of electromagnetic sources for the Maxwell field in the form of thin layers, construction of new solutions, and generation techniques.

gr-qc↗
arXiv2004

Moment Density of Zipoy's Dipole Solution

Zipoy used spheroidal coordinates to construct a family of static axisymmetric gravitational fields included in Weyl's class. We calculate the mass moment source for the dipole solution using techniques previously developed for magnetic and angular momentum densities and compare it with the Newtonian analog studied by Bonnor and Sackfield.

gr-qc↗
arXiv2004

Angular Momentum Surface Density of the Kerr Metric

A method for interpreting discontinuities of the twist potential of vacuum stationary axisymmetric solutions of Einstein's equations is introduced. Surface densities for the angular momentum of the source can be constructed after solving a linear partial differential equation with boundary conditions at infinity. This formalism is applied to the Kerr metric, obtaining a regularized version of the density calculated with other formalisms. The main result is that the integral defining the total angular momentum is finite for the Kerr metric.

gr-qc↗