arXiv subjects
Publications and source records attributed to S. Mendoza.
In this chapter it is shown how the introduction of 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.
Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.
We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity.
We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity. We also prove that a Noether's symmetry approach to the problem yields a conserved quantity coherent with this relativistic MONDian extension.
The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a difference approximation to the solution of a Poisson equation using these kind of structured grids have been recently reported. In this paper, we compare the accuracy of the numerical solution calculated by applying those structured grids with finite differences against the the solution obtained with Delaunay-like triangulations on irregular regions.
The motion of knots in astrophysical jets is commonly interpreted as shock waves moving along it. Observations of the HST-1 knot during extended periods of time have produced complicated light curves on many wavelengths which are difficult to account using standard hydrodynamical models. Here we reproduce these light curves using the semi-analytical approach developed by Mendoza et al. (2009), developed to reproduce light curves of working surfaces moving along relativistic jets. These working surfaces are generated by periodic oscillations of the injected flow velocity and discharge at the base of the jet. In particular, we use this approach to reproduce the exotic observed features of the light curves of the HST-1 knot in M87. We show that the complicated fits to the light curves are reproduced with high accuracy in all wavelengths. As a bonus, we show that this model is also able to reproduce the light curve of the micro-qsr A06200-00 with high accuracy.
In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through the inclusion of Milgrom's acceleration constant into a gravitational theory, we show that very general formulas can be constructed for the acceleration felt by a particle. Dimensional analysis shows that this inclusion naturally leads to the appearance of a mass-length scale in gravity, breaking its scale invariance. A particular form of the modified gravitational force is constructed and tested for consistency with observations over a wide range of astrophysical environments, from solar system to extragalactic scales. We show that over any limited range of physical parameters, which define a specific class of astrophysical objects, the dispersion velocity of a system must be a power law of its mass and size. These powers appear linked together through a natural constraint relation of the theory. This yields a generalised gravitational equilibrium relation valid for all astrophysical systems. A general scheme for treating spherical symmetrical density distributions is presented, which in particular shows that the fundamental plane of elliptical galaxies, the Newtonian virial equilibrium, the Tully-Fisher and the Faber-Jackson relations, as well as the scalings observed in local dwarf spheroidal galaxies, are nothing but particular cases of that relation when applied to the appropriate mass-length scales. We discuss the implications of this approach for a modified theory of gravity and emphasise the advantages of working with the force, instead of altering Newton's second law of motion, in the formulation of a gravitational theory.
We use a specific form of the interpolation function in the MOND formalism, which optimally accounts for the internal structure of dwarf spheroidal (dSph) galaxies, to explore the consequences it has on the scaling relations seen in these systems.}} {The particular form of the interpolation function we used leads to a law of gravity that does not degrade the good fit of the MOND proposal on galactic scales, and in fact, slightly improves the accordance with observations at dSph scales. This formalism yields a good description of gravitational phenomena without the need of invoking any still undetected and hypothetically dominant dark matter, in the weak field regime probed by local dSph galaxies.} {Isothermal equilibrium density profiles then yield projected surface density profiles for the local dSph galaxies in very good agreement with observational determinations, for values of the relevant parameters as inferred from recent observations of these Galactic satellites. The observed scaling relations for these systems are also naturally accounted for within the proposed scheme, including a previously unrecognised correlation of the inferred mass-to-light ratios of local dSph's with the ages of their stellar populations, which is natural in modified gravity schemes in the absence of dark matter.} {The results shed some light on the form that the MOND interpolating function may have in the most challenging regime, which occurs at moderate accelerations and intermediate mass--weighted lengths.
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value $c$, for wavelengths larger than $R_{s}$, in the vicinity of $R_{s}$. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent 'particle' description fails, and the wave nature becomes apparent.
We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible and so, the flow is ballistic. We also assume a steady flow and consider the particles at the boundary of the spherical cloud to be rotating as a rigid body, with a fixed amount of inwards radial velocity. This represents a generalisation to the traditional infinite gas cloud model described by Ulrich (1976). We show that the streamlines and density profiles obtained deviate largely from the ones calculated by Ulrich. The extra freedom in the choice of the parameters on the model can naturally account for the study of protostars formed in dense clusters by triggered mechanisms, where a wide variety of external physical mechanisms determine the boundary conditions. Also, as expected, the model predicts the formation of an equatorial accretion disc about the central object with a radius different from the one calculated by Ulrich (1976).
We present a ballistic description of the formation and propagation of the working surface of a relativistic jet. Using simple laws of conservation of mass and linear momentum at the working surface, we obtain a full description of the working surface flow parametrised by the initial velocity and mass injection rate. This allows us to compute analytically the energy release at any time in the working surface. We compare this model with the results obtained numerically through a new hydrodynamical code applied to the propagation of a relativistic fluid in one dimension in order to test the limits of our study. Finally, we compare our analytical results with observed light curves of five long gamma ray bursts and show that our model is in very good agreement with observations using simple periodic variations of the injected velocity profiles. This simple method allows us to recover initial mass discharge and energy output ejected during the burst.
We investigate in detail two physical properties of the metric f(R) theory developed by Sobouti (2007). We first look for the possibility of producing gravitational waves that travel at the speed of light. We then check the possibility of producing extra bending in the lenses produced by the theory. We do this by using standard weak field approximations to the gravitational field equations that appear in Sobouti's theory. We show in this article that the metric theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is proved in general terms for all metric theories of gravity which can be expressed as powers of Ricci's scalar. We also show that an extra additional lensing as compared to the one predicted by standard general relativity is produced. These two points are generally considered to be of crucial importance in the development of relativistic theories of gravity that could provide an alternative description to the dark matter paradigm.
We construct a simple accretion model of a rotating pressureless gas sphere onto a Schwarzschild black hole. We show how to build analytic solutions in terms of Jacobi elliptic functions. This construction represents a general relativistic generalisation of the Newtonian accretion model first proposed by Ulrich (1976). In exactly the same form as it occurs for the Newtonian case, the flow naturally predicts the existence of an equatorial rotating accretion disc about the hole. However, the radius of the disc increases monotonically without limit as the flow reaches its maximum allowed angular momentum.
We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $λ=αR_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields (α= 4 π^2 / \ln(2)) and a total entropy of the system $S=k_{B}N \ln(2)$, in agreement with the Bekenstein entropy of a black hole . It is shown that the critical temperature for Bose-Einstein condensation for relativistic particles of $λ=αR_{s}$ is always well below the Hawking temperature of a black hole, in support of the proposed internal configuration. We then examine our results from the point of view of recent loop quantum gravity ideas and find that a natural consistency of both approaches appears. We show that the Jeans criterion for gravitational instability can be generalised to the special and general relativistic regimes and holds for any type of mass--energy distribution.
The Neutrinos at the Main Injector (NuMI) facility is a conventional neutrino beam which produces muon neutrinos by focusing a beam of mesons into a long evacuated decay volume. We have built four arrays of ionization chambers to monitor the position and intensity of the hadron and muon beams associated with neutrino production at locations downstream of the decay volume. This article describes the chambers' construction, calibration, and commissioning in the beam.
The idea of a unified model for all astrophysical jets has been considered for quite some time. We present here a few scaling laws relevant to all type of astrophysical jets, analogous to those of \citet{sams96} which are widely used for astrophysical black holes. We use Buckingham's $ Π$ theorem of dimensional analysis to obtain a family of dimensional relations among the physical quantities associated to astrophysical jets.
Self-similar solutions to the problem of a strong imploding relativistic shock wave are calculated. These solutions represent the relativistic generalisation of the Newtonian Gouderley-Landau-Stanyukovich problem of a strong imploding spherical shock wave converging to a centre. The solutions are found assuming that the pre-shocked flow has a uniform density, and are accurate for sufficiently large times after the formation of the shock wave.
The Neutrinos at the Main Injector (NuMI) beamline will deliver an intense muon neutrino beam by focusing a beam of mesons into a long evacuated decay volume. We have built 4 arrays of ionization chambers to monitor the neutrino beam direction and quality. The arrays are located at 4 stations downstream of the decay volume, and measure the remnant hadron beam and tertiary muons produced along with neutrinos in meson decays.