Cosmic strings in a model of non-relativistic gravity

Ho$\check{\textbf{r}}$ava proposed a non-relativistic renormalizable theory of gravitation, which is reduced to general relativity (GR) in large distances (infra-red regime (IR)). It is believed that this theory is an ultra-violet (UV) completion for the classical theory of gravitation. In this paper, after a brief review of some fundamental features of this theory, we investigate it for a static cylindrical symmetric solution which describes \emph{Cosmic string} as a special case. We have also investigated some possible solutions, and have seen that how the classical GR field equations are modified for generic potential $V (g)$. In one case there is an algebraic constraint on the values of three coupling constants. Finally as a pioneering work we deduce the most general \emph{cosmic string} in this theory. We explicitly show that how the \emph{coupling constants} distort the mass parameter of \emph{cosmic string}. We deduce an explicit function for mass per unit length of the space-time as a function of the \emph{coupling constants}. We compare this function with another which Aryal et al [58] have found in GR.Also we calculate the self-force on a massive particle near Ho$\check{\textbf{r}}$ava-Lifshitz straight string and we give a typical order for the \emph{coupling constants} $g_{9}$. This order of magnitude proposes a cosmological test for validity of this theory.Comment: 30pages,It has been accepted for publication in International Journal of Theoretical Physics-Extended version with 2 new sections about (Thermodynamics and Dark energy in Horava-Lifshitz gravity),(About the existence of non-static cylindrical solutions

Ferromagnetism of electron gas

In current work, we investigate the density and temperature dependence of polarization parameter; using the relativistic formalism for the electron-electron interaction within the Fermi liquid model. we calculate the spin dependent scattering matrix elements in relativistic region, and then obtain the non-relativistic behavior to study the magnetic properties of an electron gas. By varying the polarization parameter, we minimized the free energy and then obtain the polarization of the system as a function of density and temperature. At zero temperature the exact results for polarization and magnetic susceptibility have obtained. It has been shown that for a given temperature (density) there is critical density (temperature) that the ferromagnetic phase can appears in electron gas. Our results show that at nonzero temperatures and in very low and very high densities the ferromagnetism phase can not be exist.Comment: 11 pages, 4 figures, Accepted to Publish in "Journal of Statistical physics(Springer)",In pres

Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields

In this paper, we investigate the Noether symmetries of $F(T)$ cosmology involving matter and dark energy. In this model, the dark energy is represented by a canonical scalar field with a potential. Two special cases for dark energy are considered including phantom energy and quintessence. We obtain $F(T)\sim T^{3/4},$ and the scalar potential $V(\phi)\sim\phi^2$ for both models of dark energy and discuss quantum picture of this model. Some astrophysical implications are also discussed.Comment: 15 pages,4 figure

Plane symmetric solutions in Horava-Lifshitz theory

The purpose of this paper is to find and analyze plane symmetric, static(non static) solutions in Ho\v{r}ava- Lifshitz gravity. We discussed two versions of Horava gravity. First we showed that if the detailed balance principle have considered, there are both static and non-static solutions. We show that in static case there are two family of solvable models which either of them has a well defined EOS, in analogous to the perfect fluid solutions in GR. In non-static case we find a family of solutions. Some physical properties of these solutions was discussed. Secondly we investigated the plane symmetric solutions for a new modified version of Ho\v{r}avaa gravity \cite{bla}, which has the new terms inserted action in it.Comment: 16 pages, no figure, references added, re-organized and re-writtend, typos corrected, main results unchange

Quantized Black Hole and Heun function

Following the simple proposal by He and Ma for quantization of a black hole(BH) by Bohr's idea about the atoms, we discussed the solvability of the wave equation for such a BH. We superficial solved the associated Schrodinger equation. The eigenfunction problem reduces to HeunB $H$ differential equation which is a natural generalization of the hypergeometric differential equation. In other words, the spectrum can be determined by solving the Heun's differential equation.Comment: 9 pages,Title Changed, 3 figures, Refrences adde