arXiv subjects

S. Mendoza

Publications and source records attributed to S. Mendoza.

At least 19 recordsLinked to original sources

arXiv2021

Full analytical ultrarelativistic 1D solutions of a planar working surface

We show that the 1D planar ultrarelativistic shock-tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the hydrodynamical quantities of the problem form two shock waves separating from a contact discontinuity. The procedure is based on the extensive use of the Taub jump conditions for relativistic shock waves, the Taub adiabatic and performing Lorentz transformations to present the solution in a system of reference adequate for an external observer at rest. The solutions are found using a set of very useful theorems related to the Lorentz factors when transforming between systems of reference. The energy dissipated inside the working surface is relevant for studies of light curves observed in relativistic astrophysical jets and so, we provide a full analytical solution for this phenomenon assuming an ultrarelativistic periodic velocity injected at the base of the jet.

astro-ph.HE↗

arXiv2021

Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature-matter couplings and their applications to the accelerated expansion of the Universe without dark components

We discuss the advantages of using metric theories of gravity with curvature-matter couplings in order to construct a relativistic generalisation of the simplest version of Modified Newtonian Dynamics (MOND), where Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature-matter couplings. Using the simplest two local constructions in a FLRW universe for dust, we show that there is no need for the introduction of dark matter and dark energy components into the Friedmann equation in order to account for type Ia supernovae observations of an accelerated universe at the present epoch.

gr-qc↗

arXiv2021

Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe

We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives leaving their order as a free parameter. All this with the intention to explain the current observed acceleration of the Universe. We apply the Last Step Modification technique of fractional calculus to construct some useful fractional equations of cosmology. The fits of the unknown fractional derivative order and the fractional cosmographic parameters to SN Ia data shows that this simple construction can explain the current accelerated expansion of the Universe without the use of a dark energy component with a MOND-like behaviour using Milgrom's acceleration constant which sheds light into to the non-necessity of a dark matter component as well.

gr-qc↗

arXiv2020

The matter Lagrangian of an ideal fluid

We show that the matter Lagrangian of an ideal fluid equals (up to a sign -depending on its definition and on the chosen signature of the metric) the total energy density of the fluid, i.e. rest energy density plus internal energy density.

gr-qc↗

arXiv2020

MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling

In this article we construct an extended relativistic f(R) theory of gravity with matter-curvature couplings F(R,L_matt) for which its weak field limit of approximation recovers the simplest version of MOND. We do this by (a) performing an order of magnitude approach and (b) by perturbing the resulting field equations of the theory to the weakest field limit of approximation. We also compute the geodesic equation of the resulting theory and show that it has an extra force, a fact that commonly appears in general matter-curvature couplings. This arxiv version includes a section at the end with an Erratum.

gr-qc↗

arXiv2018

Metric-affine f(R,T) theories of gravity and their applications

We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{μν}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the non-conservation of the energy-momentum tensor, which implies non-geodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

gr-qc↗

arXiv2018

A direct primitive variable recovery scheme for hyperbolic conservative equations: the case of relativistic hydrodynamics

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

physics.comp-ph↗

arXiv2017

MOND as the weak field limit of an extended metric theory of gravity with torsion

In this article we construct a relativistic extended metric theory of gravity, for which its weak field limit reduces to the non-relativistic MOdified Newtonian Dynamics regime of gravity. The theory is fully covariant and the way to achieve this is to introduce torsion in the description of gravity as well as with the addition of a particular function of the matter lagrangian into the gravitational action.

gr-qc↗

arXiv2016

A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity

We construct a relativistic metric description of MOND using the Palatini formalism following the $ f(χ)=χ^b $ description of \citet{mendozatula}. We show that in order to recover the non-relativistic MOND regime where, for circular orbits the Tully-Fisher law replaces Kepler's third law, the value of the parameter $ b = 3/2 $, which is coincident with the value found using a pure metric formalism Capozziello et al. (2011). Unlike the pure metric formalism, which yields 4th order field equations, the Palatini approach yields second order field equations, which is a desirable requirement from a theoretical perspective. Thus, the phenomenology associated to astrophysical phenomena with Tully-Fisher scalings can be accounted for using this proposal, without the need to introduce any non-baryonic dark matter particles.

gr-qc↗

arXiv2016

An eclipsing binary black hole candidate system in the blazar Mrk 421

Removing outbursts from multiwavelength light curves of the blazar Mrk~421, we construct outburstless time series for this system. A model-independent power spectrum light curve analysis in the optical, hard X-ray and gamma-rays for this outburstless state and also the full light-curves, show clear evidence for a periodicity of ~ 310 days across all wavelengths studied. A subsequent full maximum likelihood analysis fitting an eclipse model confirms a periodicity of 310 \pm 1 days. The power spectrum of the signal in the outburstless state of the source does not follow a flicker noise behaviour and so, the system producing it is not self-organised. This and the fact that the periodicity is better defined in the outburstless state, strongly suggests that it is not produced by any internal physical processes associated to the central engine. The simplest physical mechanism to which this periodicity could be ascribed is a dynamical effect produced by an orbiting supermassive black hole companion eclipsing the central engine. Interestingly, the optimal eclipse model infers a brightness enhancement of (136.4 \pm 20 )%, suggesting an eclipse resulting in a gravitational lensing brightening. Consisting with this interpretation, the eclipse occurs for only ( 9.7 \pm 0.2)% of the orbital period.

astro-ph.GA↗

arXiv2015

Modified Newtonian Dynamics as an entropic force

Under natural assumptions on the thermodynamic properties of space and time with the holographic principle we reproduce a MOND-like behaviour of gravity on particular scales of mass and length, where Newtonian gravity requires a modification or extension if no dark matter component is introduced in the description of gravitational phenomena. The result is directly obtained with the assumption that a fundamental constant of nature with dimensions of acceleration needs to be introduced into gravitational interactions. This in turn allows for modifications or extensions of the equipartion law and/or the holographic principle. In other words, MOND-like phenomenology can be reproduced when appropriate generalised concepts at the thermodynamical level of space and/or at the holographic principle are introduced. Thermodynamical modifications are reflected in extensions to the equipartition law which occur when the temperature of the system drops below a critical value, equals to Unruh's temperature evaluated at the acceleration constant scale introduced for the description of the gravitational phenomena. Our calculations extend the ones by Verlinde (2011) in which Newtonian gravity is shown to be an emergent phenomenon, and together with it reinforces the idea that gravity at all scales is emergent.

gr-qc↗

arXiv2015

Understanding the light curves of the HST-1 knot in M87 with internal relativistic shock waves along its jet

Knots or blobs observed in astrophysical jets are commonly interpreted as shock waves moving along them. Long time observations of the HST-1 knot inside the jet of the galaxy M87 have produced detailed multi-wavelength light curves. In this article, we model these light curves using the semi-analytical approach developed by Mendoza et al. (2009). This model was developed to account for the light curves of working surfaces moving along relativistic jets. These working surfaces are generated by periodic oscillations of the injected flow velocity and mass ejection rates at the base of the jet. Using genetic algorithms to fit the parameters of the model, we are able to explain the outbursts observed in the light curves of the HST-1 knot with an accuracy greater than a 2 sigma statistical confidence level.

astro-ph.GA↗

arXiv2015

Evidence for dark matter in the inner Milky Way...Really?

The following is a comment on the recent letter by Iocco et al. (2015, arXiv:1502.03821) where the authors claim to have found "...convincing proof of the existence of dark matter...". The letter in question presents a compilation of recent rotation curve observations for the Milky Way, together with Newtonian rotation curve estimates based on recent baryonic matter distribution measurements. A mismatch between the former and the latter is then presented as "evidence for dark matter". Here we show that the reported discrepancy is the well known gravitational anomaly which consistently appears when dynamical accelerations approach the critical Milgrom acceleration a_0 = 1.2 \times 10^{-10} m / s^2. Further, using a simple modified gravity force law, the baryonic models presented in Iocco et al. (2015), yield dynamics consistent with the observed rotation values.

astro-ph.GA↗

arXiv2014

Hydrodynamics associated to the X-ray light curve of A0620-00

From 1975 to 1976, an outburst was detected in the light curve of the X-ray transient A0620-00 using the Ariel V and SAS-3 experiments. In this letter we model the outburst with the hydrodynamical model proposed by Mendoza et al. (2009). The physical model is constructed assumming basic mass and momentum conservation laws associated to the motion of the shock waves developed inside the expanding relativistic jet of the source. These internal shock waves are produced as a result of periodic variations of the inyected mass and velocity of the flow at the base of the jet. The observations of this X-ray light curve present two clear bumps. The first one is modelled assuming periodic variations of the inyected velocity at the base of the jet, while the second one can either be modelled by a further velocity oscillations, or by a periodic variation of the mass injection rate at the base of the jet at a latter time. The fitting of the data fixes different parameters of the model, such as the mean mass injection rate at the base of the jet and the oscillation frequency of the flow as measured on the rest frame of the central source.

astro-ph.HE↗

arXiv2014

Astrophysical constraints and insights on extended relativistic gravity

We give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure compatible with the Einstein Equivalence Principle. This result is derived on very general grounds without knowing the underlying structure of the gravitational field equations. As such, any developed gravitational theory built to deal with these astrophysical scales needs to reproduce the obtained results of this article.

gr-qc↗

arXiv2013

A hydrodynamical model for the FERMI-LAT gamma-ray light curve of Blazar PKS1510-089

A physical description of the formation and propagation of the working surface inside the relativistic jet of the Blazar PKS 1510-089 are used to model its gamma-ray variability light curve using FERMI-LAT data from 2008 to 2012. The physical model is based on conservation laws of mass and momentum at the working surface as explained by Mendoza et al. (2009). The hydrodynamical description of the working surface is parametrised by the initial velocity and mass injection rate at the base of the jet. We show that periodic variations on the injected velocity profiles are able to account for the observed luminosity. With this, we are able to obtain mass ejection rates of the central engine which are injected at the base of the jet, and oscillation frequencies of the flow, amongst other physical parameters.

astro-ph.HE↗

arXiv2013

Gravitational lensing with $ f(χ)=χ^{3/2} $ gravity in accordance with astrophysical observations

In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity $ f(χ) = χ^{3/2} $ developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann's tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.

astro-ph.CO↗

arXiv2013

A cosmological dust model with extended f(chi) gravity

Introducing a fundamental constant of nature with dimensions of acceleration into the theory of gravity makes it possible to extend gravity in a very consistent manner. At the non-relativistic level a MOND-like theory with a modification in the force sector is obtained, which is the limit of a very general metric relativistic theory of gravity. Since the mass and length scales involved in the dynamics of the whole universe require small accelerations of the order of Milgrom's acceleration constant a_0, it turns out that the relativistic theory of gravity can be used to explain the expansion of the universe. In this work it is explained how to use that relativistic theory of gravity in such a way that the overall large-scale dynamics of the universe can be treated in a pure metric approach without the need to introduce dark matter and/or dark energy components.

astro-ph.CO↗