arXiv subjects

Edgar Gasperín

Publications and source records attributed to Edgar Gasperín.

6 recordsLinked to original sources

arXiv2026

An empirically constrained Covariant Modified Gravity: exact reconstruction of galactic rotation curves and lensing

We present a covariant modified gravity theory which reproduces all the galactic phenomenology usually attributed to dark matter in the low acceleration regime, including the flat rotation curves of massive tracers, and the deflection angles of photons as inferred through gravitational lensing. We first derive a fully covariant description of galactic space-times under a spherically symmetric and static approximation. This description accounts for flat rotation curves, observed gravitational lensing phenomenology and the Tully-Fisher mass scalings of the above. The resulting covariant description is then used to constrain the parameters of a minimally coupled gravitational action using power laws for both the Ricci scalar and the matter Lagrangian. The action presented hence leads to field equations whose trace, under the approximations taken, has as solutions metric coefficients which exactly reproduce flat rotation curves, gravitational lensing observations and observationally determined Tully-Fisher galactic mass scalings of any required index. This last allowing for an accurate fitting of observational dynamics up to galaxy cluster scales.

physics.gen-ph↗

arXiv2025

An asymptotic systems approach for the good-bad-ugly model with application to general relativity

We employ an adapted version of Hörmander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our heuristics were unable to capture potential leading order logarithmic terms appearing in the asymptotic solution of the good equation (the standard wave equation). Presently, we work with an improved method which overcomes this shortcoming, allowing the faithful treatment of a larger class of initial data in which such logarithmic terms are manifest. We then generalize this method to encompass models that include stratified null forms as sources and whose wave operators are built from an asymptotically flat metric. We then apply this result to the Einstein field equations in generalized harmonic gauge and compute the leading decay in~$R^{-1}$ of the Weyl scalars, where~$R$ is a suitably defined radial coordinate. We detect an obstruction to peeling, a decay statement on the Weyl scalars~$Ψ_n$ that is ensured by smoothness of null infinity. The leading order obstruction appears in~$Ψ_2$ and, in agreement with the literature, can only be suppressed by a careful choice of initial

gr-qc↗

arXiv2025

Numerical evolutions of the linearised conformal Einstein field equations in the inversion-Minkowski spacetime

Numerical evolutions of a system of equations close to null infinity in the geometric background of the inversion-Minkowski spacetime are performed. The evolved equations correspond to the linearisation of a second order metric formulation of the conformal Einstein field equations (CEFEs). These linear equations were first presented in [1] and the main purpose of this paper is to illustrate, through numerical evolutions, the scri-fixing technique via gauge source functions introduced [1] for the linearised CEFEs. A comparison of evolutions using scri-fixing gauge sources and trivial gauge source function in spherical and axial symmetry is presented.

gr-qc↗

arXiv2025

Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces

We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-$0$ fields (solutions to the wave equation) on $n$-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions written in terms of series expansions close to spatial and null infinity and use them to compute non-trivial asymptotic spin-$0$ charges. It is shown that if one considers the most general initial data within the class considered in this paper, the expansion is poly-homogeneous and hence of restricted regularity at null infinity. Furthermore, we derive the conditions on the initial data needed to obtain regular solutions and well-defined limits for the asymptotic charges at the critical sets where null infinity and spatial infinity meet. In even dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for odd higher dimensions there exists no non-trivial asymptotic charges that remain regular at the critical sets.

gr-qc↗

arXiv2022

Regularizing Dual-Frame Generalized Harmonic Gauge at Null Infinity

The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise to logarithmically divergent terms that would result in irregular variables and equations on the compactified domain, which would in turn prevent accurate numerical approximation. It has been shown, however, that a suitable choice of gauge and constraint addition can be used to prevent their appearance. Presently we give a first order symmetric hyperbolic reduction of general relativity in GHG on compactified hyperboloidal slices that exploits this knowledge and eradicates these log-terms at leading orders. Because of their effect on the asymptotic solution space, specific formally singular terms are systematically chosen to remain. Such formally singular terms have been successfully treated numerically in toy models and result in a formulation with the desirable property that unphysical radiation content near infinity is suppressed.

gr-qc↗

arXiv2019

Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law

We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded, and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a "Lorenz gauge"), one can still obtain a well-posed problem that is stable in the sense that the corresponding Hamiltonian is positive definite. An analysis of the resulting Komar currents reveals an exact Gauss law for a system of black holes in vacuum spacetimes and suggests a possible measure of matter content in asymptotically flat spacetimes.

gr-qc↗