arXiv subjects

Marcelo E. Rubio

Publications and source records attributed to Marcelo E. Rubio.

14 recordsLinked to original sources

arXiv2026

Orbital evolution of asymmetric binaries within accreting environments

Extreme mass-ratio inspirals embedded in accretion disks provide a natural arena for studying the interplay between relativistic orbital dynamics and environmental effects. In this work, we develop a framework to investigate the secular evolution of compact objects repeatedly crossing an accretion disk around a supermassive black hole. The orbital motion is modeled through Kerr geodesics, while disk interactions are encoded through effective prescriptions for mass accretion and dynamical friction. We find that disk-induced dissipation generically drives a two-stage evolution characterized by rapid alignment of the orbital plane with the disk, followed by slower eccentricity damping. By systematically comparing the dynamics with a purely Keplerian treatment, we show that cumulative relativistic effects produce deviations even at large orbital separations, where the Keplerian approximation would naively be expected to remain accurate. These discrepancies grow through repeated disk crossings and become increasingly pronounced in more relativistic orbital configurations. We further investigate the impact of the accretion-disk model by comparing the Sirko-Goodman and Novikov-Thorne prescriptions. Relativistic disk structures predict systematically lower densities and larger scale heights, leading to weaker orbital dissipation and slower secular evolution. By contrast, the spin of the central black hole has only a minor effect on the overall circularization efficiency. Our results demonstrate the importance of consistently modeling both relativistic orbital dynamics and disk structure when studying compact objects embedded in AGN disks, and provide a framework for exploring their long-term evolution, as well as a possible connection to quasi-periodic eruptions.

gr-qc↗

arXiv2025

Constraint evolution in first-order viscous relativistic fluids

Relativistic hydrodynamics provides a solid framework for evolving matter and energy in a wide variety of phenomena. Nevertheless, the inclusion of dissipative effects in realistic scenarios through causal, stable, and well-posed theories still constitutes an open problem. In this paper, we study the evolution of the algebraic and differential constraints stemmed from the first-order reduction proposed by Bemfica, Disconzi, Noronha and Kovtun (BDNK), for proving the local well-posedness of conformally-invariant viscous fluids in Sobolev spaces. First, we show analytically that the whole set of constraints satisfies a homogeneous, strongly-hyperbolic system of equations, ensuring a correct propagation as a consequence of the fluid equations. Motivated by this result, we explore their numerical stability by performing simulations of the BDNK reduction restricted to plane-symmetric configurations, in flat spacetime. We report on different initial data sets initially satisfying the constraints, and whose evolution leads to stable configurations. This result suggests that the proposed reduction by BDNK is suitable for numerical evolutions, keeping the constraints accurate under small numerical errors.

gr-qc↗

arXiv2025

Bekenstein bounds in maximally symmetric nonlinear electrodynamics

We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as ``ModMax'' electrodynamics. This family of theories is the only one that preserves all the symmetries of Maxwell's theory, having applications in the study of regular black hole solutions and supersymmetry. The purpose of this article is three-fold. Firstly, we study the initial-value problem of ModMax and show, by means of a simple geometric criterion, that such a theory admits a well-posed formulation. Secondly, we prove a series of geometric inequalities relating energy, charge, angular momentum, and size in ModMax. The validity of these bounds gives strong evidence of an universal inequality conjectured by Bekenstein for macroscopic systems. Finally, we perform the first stable numerical simulations of ModMax in the highly nonlinear regime. We apply our simulations for verifying an inequality between energy, size and angular momentum in bounded domains, and for showing birefringence as a function of the nonlinear parameter, comparing with other nonlinear nonlinear extensions.

gr-qc↗

arXiv2024

Fixing the dynamical evolution of self-interacting vector fields

Numerical simulations of the Cauchy problem for self-interacting massive vector fields often face instabilities and apparent pathologies. We explicitly demonstrate that these issues, previously reported in the literature, are actually due to the breakdown of the well-posedness of the initial-value problem. This is akin to shortcomings observed in scalar-tensor theories when derivative self-interactions are included. Building on previous work done for k-essence, we characterize the well-posedness breakdowns, differentiating between Tricomi and Keldysh-like behaviors. We show that these issues can be avoided by ``fixing the equations'', enabling stable numerical evolutions in spherical symmetry. Additionally, we show that for a class of vector self-interactions, no Tricomi-type breakdown takes place. Finally, we investigate initial configurations for the massive vector field which lead to gravitational collapse and the formation of black holes.

gr-qc↗

arXiv2023

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time

Partial differential equations exhibiting an anisotropic scaling between space and time -- such as those of Horava-Lifshitz gravity -- have a dispersive nature. They contain higher-order spatial derivatives, but remain second order in time. This is inconvenient for performing long-time numerical evolutions, as standard explicit schemes fail to maintain convergence unless the time step is chosen to be very small. In this work, we develop an implicit evolution scheme that does not suffer from this drawback, and which is stable and second-order accurate. As a proof of concept, we study the numerical evolution of a Lifshitz scalar field on top of a spherically symmetric black hole space-time. We explore the evolution of a static pulse and an (approximately) ingoing wave-packet for different strengths of the Lorentz-breaking terms, accounting also for the effect of the angular momentum eigenvalue and the resulting effective centrifugal barrier. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.

gr-qc↗

arXiv2023

Numerical simulations of divergence-type theories for conformal dissipative fluids

We present the first numerical simulations of the symmetric--hyperbolic theory for conformal dissipative relativistic fluids developed in [1]. In this theory, the information of the fluid dynamics is encoded in a scalar generating function which depends on three free parameters. By adapting the WENO-Z high-resolution shock-capturing central scheme, we show numerical solutions restricted to planar symmetry in Minkowski spacetime, from two qualitatively different initial data: a smooth bump and a discontinuous step. We perform a detailed exploration of the effect of the different parameters of the theory, and numerically assess the constitutive relations associated with the shear viscosity by analyzing the entropy production rate when shocks are produced.

gr-qc↗

arXiv2023

Dark matter from primordial black holes would hold charge

We explore the possibility that primordial black holes (PBHs) contain electric charge down to the present day. We find that PBHs should hold a non-zero net charge at their formation, due to either Poisson fluctuations at horizon crossing or high-energy particle collisions. Although initial charge configurations are subject to fast discharge processes through particle accretion or quantum particle emission, we show that maximally rotating PBHs could produce magnetic fields able to shield them from discharge. Moreover, given that electrons are the lightest and fastest charge carriers, we show that the plasma within virialised dark matter haloes can endow PBHs with net negative charge. We report charge-to-mass ratios between $10^{-31}\,C/\mbox{kg}$ and $10^{-15}\,C/\mbox{kg}$ for PBHs within the mass windows that allow them to constitute the entirety of the dark matter in the Universe.

astro-ph.CO↗

arXiv2023

Extended primordial black hole mass functions with a spike

We introduce a modification of the Press-Schechter formalism aimed to derive general mass functions for primordial black holes (PBHs). In this case, we start from primordial power spectra (PPS) which include a monochromatic spike, typical of ultra slow-roll inflation models. We consider the PBH formation as being associated to the amplitude of the spike on top of the linear energy density fluctuations, coming from a PPS with a blue index. By modelling the spike with a log-normal function, we study the properties of the resulting mass function spikes, and compare these to the underlying extended mass distributions. When the spike is at PBH masses which are much lower than the exponential cutoff of the extended distribution, very little mass density is held by the PBHs within the spike, and it is not ideal to apply the Press-Schechter formalism in this case as the resulting characteristic overdensity is too different from the threshold for collapse. It is more appropriate to do so when the spike mass is similar to, or larger than the cutoff mass. Additionally, it can hold a similar mass density as the extended part. Such particular mass functions also contain large numbers of small PBHs, especially if stable PBH relics are considered, and they can provide $\sim 1000M_\odot$ seeds for the supermassive black holes at the centres of present-day galaxies. The constraints on the fraction of dark matter in PBHs for monochromatic mass functions are somewhat relaxed when there is an additional underlying extended distribution of masses.

astro-ph.CO↗

arXiv2022

Isotropization of a rotating and longitudinally expanding $ϕ^4$ scalar system

We present numerical simulations for the evolution of an expanding system of massless scalar fields with quartic coupling. By setting a rotating, non-isotropic initial configuration, we compute the energy density, the transverse and longitudinal pressures and the angular momentum of the system. We compare the time scales associated with the isotropization and the decay of the initial angular momentum due to the expansion, and show that even for fairly large initial angular momentum, it decays significantly faster than the pressure anisotropy.

hep-th↗

arXiv2021

Ill-posedness of the mean-field dynamo equations with a linear electromotive force

We show that the initial-value problem for the non-relativistic magnetic dynamo equation turns out to be ill-posed when the electromotive force depends linearly on the magnetic field. This result implies that the increasing of magnetic energy does not necessarily come from physical amplification mechanisms, since certain magnetic modes could arbitrarily grow as wave-frequency increases, despite any dynamo-like process. Thus, up to this order, the theory is not suitable for astrophysical simulations. We then study the case when electromotive forces are linear in magnetic field derivatives, showing that the resulting system has a well-posed problem. Finally, we apply the well-posed theory to the force-free regime, for which we find bounds for the corresponding magnetic energy analyzing the evolution of the magnetic helicity.

astro-ph.HE↗

arXiv2021

Magnetic field generation from primordial black hole distributions

We introduce a statistical method for estimating magnetic field fluctuations generated from primordial black hole (PBH) populations. To that end, we consider monochromatic and extended Press-Schechter PBH mass functions, such that each constituent is capable of producing its own magnetic field due to some given physical mechanism. Assuming linear correlation between magnetic field fluctuations and matter over-densities, our estimates depend on the mass function, the physical field generation mechanism by each PBH constituent, and the characteristic PBH separation. After computing the power spectrum of magnetic field fluctuations, we apply our formalism to study the plausibility that two particular field generation mechanisms could have given rise to the expected seed fields according to current observational constraints. The first mechanism is the Biermann battery and the second one is due to the accretion of magnetic monopoles at PBH formation, constituting magnetic PBHs. Our results show that, for monochromatic distributions, it does not seem to be possible to generate sufficiently intense seed fields in any of the two field generation mechanisms. For extended distributions, it is also not possible to generate the required seed field by only assuming a Biermann battery mechanism. In fact, we report an average seed field by this mechanism of about 10^{-47} G, at z = 20. For the case of magnetic monopoles we instead assume that the seed values from the literature are achieved and calculate the necessary number density of monopoles. In this case we obtain values that are below the upper limits from current constraints.

astro-ph.CO↗

arXiv2019

Generic instabilities in the relativistic Chapman-Enskog heat conduction law

We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the relativistic Chapman-Enskog procedure. The resulting system of equations is shown to be non hyperbolic, by considering general perturbations over the whole set of equations written with respect to a generic time direction. The obtained eigenvalues are not purely imaginary and their real part grows without bound as the wave-number increases. Unlike Eckart's theory, this instability is not present when the time direction is aligned with the fluid's direction. However, since in general the fluid velocity is not surface-forming, the instability can only be avoided in the particular case where no rotation is present.

gr-qc↗

arXiv2017

A hyperbolic theory of relativistic conformal dissipative fluids

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of evolution variables whose dynamics is governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory, as well as to derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories-- and near equilibrium configurations-- there exist symmetric hyperbolic ones, implying that for them one can define well posed initial value problems.

gr-qc↗

arXiv2017

On the ill posedness of Force-Free Electrodynamics in Euler Potentials

We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed. We establish this result by showing that a well-posedness criterion provided by Kreiss fails to hold for this theory, and using a theorem provided by Strang. To show the nature of the problem we display a particular bounded (in Sobolev norms) sequence of initial data for the Force-free equations such that at any given time as close to zero as one wishes, the corresponding evolution sequence is not bounded. Thus, the Force-free evolution is non continuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.

gr-qc↗