arXiv:1503.01011v1 [gr-qc] 3 Mar 2015 Equation of hydrostatic equilibrium for stars in dilaton gravity S. H. Hendi 1,2∗ , M. Najafi 1 and B. Eslam Panah 1† 1 Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454, Iran 2 Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha, Iran In this paper, we present a new the hydrostatic equilibrium equation related to dilaton gravity. To determine an interior solution of a compact star in the presence of dilaton field, we need a generalization of the Tolman- Oppenheimer-Volkoff hydrostatic equilibrium equation. We consider a spherical symmetric spacetime to obtain the hydrostatic equilibrium equation of stars in the presence of dilaton field. I. INTRODUCTION Our observations of Supernova type Ia [1] confirm that the expansion of our Universe is currently undergoing a period of acceleration. But Einstein (EN) gravity can not explain this acceleration. Secondly, although Einstein’s theory can explain the solar system phenomena successfully, when we want to study beyond the solar system or when the gravity is so strong, this theory encounters with some problems, so we need to modify EN gravity. In order to improve EN gravity, one may add a (cosmological) constant to its Lagrangian [2]. Moreover, we can regard other modifications of Einstein gravity are such as, Lovelock gravity [3], brane world cosmology [4], scalar-tensor theories [5, 6], F (R) gravity [7]. On the other hand, dark energy and dark matter have received a lot of attention in recent years. Theoretical physicists introduced a model for dark matter that according to it the dark matter is non–baryonic [8], for this kind of dark matter three models were proposed, cold, warm and hot. Among them cold dark matter model has the highest agreement with the experimental observations. It is worthwhile to mention that, dilaton field is one of the most interesting candidates for cold dark matter [9]. On the other hand, the best approach for finding the nature of dark energy is taking into account new scalar field [10]. In addition, the low energy limit of string theory contains of a dilaton field. Physical properties, thermodynamics, and thermal stability of the black object solutions in the context of dilaton theory have been investigated before [11]. The hydrostatic equilibrium equation (HEE) plays crucial role in studying the evolution of the stars. This equation is giving an insight regarding the equilibrium state between internal pressure and gravitational force of the stars. It is important to note that the neutron and quark stars have large amount of mass concentrated in small radius, so they are in the category of highly dense objects and therefore they are called compact stars. Due to this fact, we need to take into account effects of general relativity such as the curvature of spacetime in the studying the compact stars. The first HEE for stars in the Einstein gravity and for 4-dimensions of spacetime was studied by Tolman, Oppenheimer and Volkoff (TOV) [12]. Also, the physical characteristics of stars using TOV equation have been investigated in [13]. On the other hand, if one is interested in studying the structure and evolution of stars in different gravities, one should obtained the HEE in those gravities. Therefore, in recent years, the generalizations and modifications of this equation were of special interests for many authors (for more details see [14]), for example: the HEE equation in EN gravity for d-dimensions was investigated in [15] and in EN-Λ gravity for arbitrary dimensions was obtained in [16]. Also, the HEE equation for 5 and higher dimensions in Gauss-Bonnet (GB) was extracted in [17] and [16], respectively. Recently, in [16, 18] the (2 + 1)-dimensional HEE was obtained for a static star in the presence of cosmological constant. In this paper, we want to obtain exact solution of HEE equation in the presence of dilaton field in 4-dimensions. We consider a spherical symmetric metric and obtain the HEE in dilaton gravity. In addition, we consider dilaton gravity as a correction of Einstein gravity and we will obtain related HEE. II. EQUATION OF HYDROSTATIC EQUILIBRIUM IN DILATON GRAVITY The action of dilaton gravity is given by I G = 1 16π  d 4 x √ −g{R − 2g µν ∂ µ Φ∂ ν Φ − V (Φ)} + I M , (1) * email address: hendi@shirazu.ac.ir † email address: behzad - eslampanah@yahoo.com