Generalized second law of thermodynamics in the Bianchi type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs' law of thermodynamics, it is proved that the generalized second law of thermodynamics does not always satisfied throughout the history of the universe when we assume the universe is enclosed by the generalized Ricci scalar radius Rgr. It becomes invalid in the near past to the future, and the formation of the galaxies will be helpful in explaining such phenomenon, for that the galaxies's formation is an entropy increase process. The negative change rates of the horizon entropy and internal entropy occur in different period indicates that the influences of galaxies formation is wiped from internal to the universe's horizon.
The modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter is considered in the nonflat Friedmann-Robertson-Walker universe. Through examining the deceleration parameter, one can find that the transition time of the Universe from decelerating to accelerating phase in the interacting holographic Ricci dark energy model is close to that in the Λ cold dark matter model. The evolution of modified holographic Ricci dark energy's state parameter and the evolution of dark matter and dark energy's densities shows that the dark energy holds the dominant position from the near past to the future. By studying the statefinder diagnostic and the evolution of the total pressure, one can find that this model could explain the Universe's transition from the radiation to accelerating expansion stage through the dust stage. According to the Om diagnostic, it is easy to find that when the interaction is weak and the proportion of relativistic dark matter in total dark matter is small, this model is phantom-like. Through our studying, we find the interaction and the relativistic dark matter's proportion all have great influence on the evolution of the Universe.
In this paper, we study the orbital dynamics of the gravitational field of stringy black holes by analyzing the effective potential and the phase plane diagram. By solving the equation of Lagrangian, the general relativistic equations of motion in the gravitational field of stringy black holes are given. It is easy to find that the motion of test particles depends on the energy and angular momentum of the test particles. Using the phase plane analysis method and combining the conditions of the stability, we discuss different types of the test particles' orbits in the gravitational field of stringy black holes. We get the innermost stable circular orbit which occurs at r min = 5.47422 and when the angular momentum b ≤ 4.3887 the test particles will fall into the black hole.
The evolution of a bound system in the expanding background has been investigated in this paper. The background is described by a FRW universe with the modified holographic dark energy model, whose equation of state parameter changes with time and can cross the phantom boundary. To study the evolution of the bound system, an interpolating metric is considered, and on this basis the geodesics of a test particle are given. The equation of motion and the effective potential are also derived from the geodesics. By studying the the effective potential and the evolution of the radius of a test particle in the bound system of the Milky Way galaxy, we have found that the galaxy would go through three stages: expands from a singular point; stays in a discoid for a period of time; big rip in the future. With the help of analysing the critical angular momentum, we find that the test particle needs less angular momentum to escape from the center mass as time passes. keywords: bound system; expanding background; modified holographic dark energy *
This paper studies the accretion of dark energy onto a stringy electrically charged black hole. Solution for a general spherical accretion of the ideal fluid onto a black hole is given first. It is shown that the location of the critical point lies inside the event horizon. In our paper, two solvable models of dark energy are considered. For the linearized model, the expression for the mass of the black hole is derived. And for the Chaplygin gas model, the change rate of the black hole mass is obtained. The results show that the mass of the stringy electrically charged black hole is fixed when ρ + p = 0, but decreases at ρ + p < 0 and increases at ρ +p > 0. Then, we conclude that the accretion of phantomlike dark energy makes the mass of the black hole decrease, and the accretion of the quintessence-like dark energy can increase the black hole mass. The bigger the absolute value of the pressure is, the faster the black hole mass decreases.
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