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.
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 o
rder 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 Milgroms acceleration constant which sheds light into to the non-necessity of a dark matter component as well.
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.
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.
Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Greens function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of ap
proximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called one-point model) that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff-Baym equation for the one-body Greens function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.
We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effe
ctive three-dimensional shift current ($sim$100 $mu$A/V$^2$), larger than has been previously observed in other polar systems. Moreover, we show that the integral of the shift-current tensor is correlated to the large spontaneous effective three-dimensional electric polarization ($sim$1.9 C/m$^2$). Our calculations indicate that the shift current will be largest in the visible spectrum, suggesting that these monochalcogenides may be promising for polar optoelectronic devices. A Rice-Mele tight-binding model is used to rationalize the shift-current response for these systems, and its dependence on polarization, in general terms with implications for other polar materials
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 cu
rve 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.
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 wit
h 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.
In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity $ f(chi) = chi^{3/2} $ developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the ph
enomenology 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 Riemanns 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.
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.
