A new approach toward geometrical concept of black hole thermodynamics

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity.Comment: 13 pages with 7 figures, accepted in EPJ

Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow

Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge and energy functions.Comment: 13 pages, 5 figure

Three dimensional nonlinear magnetic AdS solutions through topological defects

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known BornInfeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and in other words, we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appear too.Comment: 22 pages with 24 figures. Accepted for publication in Eur. Phys. J.

Geometrical thermodynamics and P-V criticality of the black holes with power-law Maxwell field

We study thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of the temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying phase transition. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on thermodynamical structure of these black holes are investigated. In addition, some thermodynamical properties such as volume expansion coefficient, speed of sound and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.Comment: 18 pages with 12 captioned figures. Published versio

Three-dimensional accelerating AdS black holes in F(R)F(R) gravity

Considering a three-dimensional $C-$metric, we obtain the exact accelerating black holes in the $F(R)$ theory of gravity coupled with and without a matter field. First, we extract uncharged accelerating AdS black hole solutions in $F(R)$ gravity. Then, we study the effects of various parameters on metric function, roots, and the temperature of these black holes. The temperature is always positive for the radii less than $\frac{1}{\alpha }$, and it is negative for the radii more than $\frac{1}{\alpha }$. We extend our study by coupling nonlinear electrodynamics as a matter filed to $F(R)$ gravity to obtain charged black holes in this theory. Next, we evaluate the effects of different parameters such as the electrical charge, accelerating parameter, angular, $F(R)$ gravity, and scalar curvature on the obtained solutions, roots, and temperature of three-dimensional charged accelerating AdS black holes. The results indicate that there is a root in which it depends on various parameters. The temperature of these black holes is positive after this root.Comment: 11 pages, 3 figure

The analysis of the effect of tax on profitability indices in listed companies of Tehran Stock Exchange

Profitability is considered as the most complicated feature for a company to be understood and evaluated. These ratios included in profitability are applied for evaluating business capabilities and making the wages in comparison with all cost during a specific period of time. In a more accurate way, the ratios indicate the profitability of a company, having calculated the total costs and tax on revenue, operational efficiency, company pricing policies, assets profitability and company’s shareholders. The approach applied in this research is descriptive-analytic. Using the data of 28 companies listed in Tehran Stock Exchange from 2004 to 2010 and using panel data approach, the tax effects over the paid profitability indices were studied in this paper. The results achieved from all estimation cases point out a negative significant effects on various profitability indices. It should be mentioned that in order to relate the taxes to the profitability indices, the costs and the debts of a corporation can be referred. Results of the study indicated that the debts ratio to asset and the type of the industry showed a negative effect on profitability and capital ratio to asset and the size of the company indicated positive significant effects on profitability index

The analysis of the effect of tax on profitability indices in listed companies of Tehran Stock Exchange

Profitability is considered as the most complicated feature for a company to be understood and evaluated. These ratios included in profitability are applied for evaluating business capabilities and making the wages in comparison with all cost during a specific period of time. In a more accurate way, the ratios indicate the profitability of a company, having calculated the total costs and tax on revenue, operational efficiency, company pricing policies, assets profitability and company’s shareholders. The approach applied in this research is descriptive-analytic. Using the data of 28 companies listed in Tehran Stock Exchange from 2004 to 2010 and using panel data approach, the tax effects over the paid profitability indices were studied in this paper. The results achieved from all estimation cases point out a negative significant effects on various profitability indices. It should be mentioned that in order to relate the taxes to the profitability indices, the costs and the debts of a corporation can be referred. Results of the study indicated that the debts ratio to asset and the type of the industry showed a negative effect on profitability and capital ratio to asset and the size of the company indicated positive significant effects on profitability index