Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson Effect

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordström anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as p _q = ωρ _q in which \(-1<\omega <-\frac {1}{3}\). Our calculations are restricted to ansatz: ω = ??1 (the cosmological constant regime) and \(\omega =-\frac {2}{3}\) (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature T _i of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure P _i . Position of the inverse point {T _i , P _i } is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point versus different numerical values of the mass M and the charge Q of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for M > Q in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point {T _i , P _i } position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge Q. In other words the quintessence dark energy dose not affect on position of the inverse point when the AdS RN black hole takes on small charges.     

Interacting Generalized Ghost Dark Energy in Non-isotropic Background

In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. At first, the non-interacting generalized ghost dark energy in a Bianchi type I (BI) background is discussed. Then the equation of state parameter, ω _D = p _D /ρ _D , the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It was found that, in this case, ω _D cannot cross the phantom line (ω _D >?1) and eventually the universe approaches a de-Sitter phase of expansion (ω _D →?1). Then, this investigation was extended to the interacting ghost dark energy in a non-isotropic universe. It was found that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (ω _D <?1) provided the parameters of the model are chosen suitably. It was considered a specific model which permits the standard continuity equation in this theory. Besides Ω_Λ and Ω _m in standard Einstein cosmology, another density parameter, Ω _σ , is expected by the anisotropy. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration.     

Ghost Dark Energy with Non-Linear Interaction Term

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w _D = p/ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω _D ). We find that in one case, w _D cross the phantom line (w _D < ?1). However in two other classes w _D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w _D , q. We study squared sound speed \({v_{s}^{2}}\), and find that for one case of non-linear interaction term \({v_{s}^{2}}\) can achieves positive values at late time of evolution.     

Dynamics of phantom matter

A spherically symmetric evolution model of self-gravitating matter with the equation of state p = ?(1 + δ)? (where δ = const) is considered. The equations of the model are written in the frame of reference co-moving with matter. A criterion for the existence and formation of a horizon is defined. Part of the Einstein equations is integrated analytically. The initial conditions and the constraints imposed on these conditions in the presence of a horizon are determined. For small δ, an analytic solution to spherically symmetric time-dependent Einstein equations is obtained. Conditions are determined under which the dynamics of matter changes from collapse to expansion. Characteristic times of the evolution of the system are evaluated. It is proved that the accretion of phantom matter (for δ > 0) onto a black hole leads to the decreases of the horizon radius of the black hole (i.e., the black hole is dissolved).     

Holographic Superconductor of Regular Phantom Black Hole

Holographic superconductors containing a non-minimal derivative coupling for the scalar field in a regular phantom plane symmetric black hole have been considered. We show that the parameter of the regular black hole b as well as the non-minimal derivative coupling parameter η affect the formation of the condensate as well as the conductivity in the superconductor. Moreover, b has a critical value in which the critical temperature T_c increases without a bound.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

Noether symmetry of <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) 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)～T ^3/4, and the scalar potential V(?)～? ² for both models of dark energy and discuss quantum picture of this model. Some astrophysical implications are also discussed.     

Instability of Interacting Ghost Dark Energy Model in an Anisotropic Universe

A new dark energy model called “ghost dark energy” was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, ρ _Λ = α H, where α is a constant of order \({\Lambda }^{3}_{QCD}\) and Λ _{Q C D} ～ 100M e V is QCD mass scale. In this paper, we investigate about the stability of generalized QCD ghost dark energy model against perturbations in the anisotropic background. At first, the ghost dark energy model of the universe with spatial BI model with/without the interaction between dark matter and dark energy is discussed. In particular, the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy model are obtained. Then, we use the squared sound speed \({v_{s}^{2}}\) the sign of which determines the stability of the model. We explore the stability of this model in the presence/absence of interaction between dark energy and dark matter in both flat and non-isotropic geometry. In conclusion, we find evidence that the ghost dark energy might can not lead to a stable universe favored by observations at the present time in BI universe.     

Horizon thermodynamics in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) theory

We investigate whether the new horizon first law proposed recently still work in f(R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in f(R) theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in f(R) theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.     

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.     

Effects of dark energy on the efficiency of charged AdS black holes as heat engines

In this paper, we study the heat engine where a charged AdS black hole surrounded by dark energy is the working substance and the mechanical work is done via the PdV term in the first law of black hole thermodynamics in the extended phase space. We first investigate the effects of a kind of dark energy (quintessence field in this paper) on the efficiency of the RN-AdS black holes as the heat engine defined as a rectangular closed path in the P–V plane. We get the exact efficiency formula and find that the quintessence field can improve the heat engine efficiency, which will increase as the field density \(\rho _q\) grows. At some fixed parameters, we find that a larger volume difference between the smaller black holes(\(V_1\)) and the bigger black holes(\(V_2\) ) will lead to a lower efficiency, while the bigger pressure difference \(P_1-P_4\) will make the efficiency higher, but it is always smaller than 1 and will never be beyond the Carnot efficiency, which is the maximum value of the efficiency constrained by thermodynamics laws; this is consistent to the heat engine in traditional thermodynamics. After making some special choices for the thermodynamical quantities, we find that the increase of the electric charge Q and the normalization factor a can also promote the heat engine efficiency, which would infinitely approach the Carnot limit when Q or a goes to infinity.     

Horizon structure of rotating Bardeen black hole and particle acceleration

We investigate the horizon structure and ergosphere in a rotating Bardeen regular black hole, which has an additional parameter (g) due to the magnetic charge, apart from the mass (M) and the rotation parameter (a). Interestingly, for each value of the parameter g, there exists a critical rotation parameter (\(a=a_{E}\)), which corresponds to an extremal black hole with degenerate horizons, while for \(a<a_{E}\) it describes a non-extremal black hole with two horizons, and no black hole for \(a>a_{E}\). We find that the extremal value \(a_E\) is also influenced by the parameter g, and so is the ergosphere. While the value of \(a_E\) remarkably decreases when compared with the Kerr black hole, the ergosphere becomes thicker with the increase in g. We also study the collision of two equal mass particles near the horizon of this black hole, and explicitly show the effect of the parameter g. The center-of-mass energy (\(E_\mathrm{CM}\)) not only depend on the rotation parameter a, but also on the parameter g. It is demonstrated that the \(E_\mathrm{CM}\) could be arbitrarily high in the extremal cases when one of the colliding particles has a critical angular momentum, thereby suggesting that the rotating Bardeen regular black hole can act as a particle accelerator.     

Statefinder—A new geometrical diagnostic of dark energy

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time derivative. The Statefinder pair is calculated for a number of existing models of dark energy having both constant and variable w. For the case of a cosmological constant, the Statefinder acquires a particularly simple form. We demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy. We also show that the mean Statefinder pair can be determined to very high accuracy from a SNAP-type experiment.     

Black hole mass decreasing due to phantom energy accretion

Solution for a stationary spherically symmetric accretion of the relativistic perfect fluid with an equation of state p(rho) onto the Schwarzschild black hole is presented. This solution is a generalization of Michel solution and applicable to the problem of dark energy accretion. It is shown that accretion of phantom energy is accompanied by the gradual decrease of the black hole mass. Masses of all black holes tend to zero in the phantom energy Universe approaching the Big Rip.     

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2ST _H is found in the next to leading order computation in the noncommutative parameter θ (i.e. \({\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})}\)) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point T _H  = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2ST _H , where the mass (M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter–Schwarzschild geometry.     

Quasinormal modes of black holes absorbing dark energy

We study perturbations of black holes absorbing dark energy. Due to the accretion of dark energy, the black hole mass changes. We observe distinct perturbation behaviors for absorption of different forms of dark energy onto the black holes. This provides the possibility of extracting information whether dark energy lies above or below the cosmological constant boundary w=−1$w=-1$. In particular, we find in the late time tail analysis that, differently from the other dark energy models, the accretion of phantom energy exhibits a growing mode in the perturbation tail. The instability behavior found in this work is consistent with the Big Rip scenario, in which all of the bound objects are torn apart with the presence of the phantom dark energy.     

Quasi-normal Modes of Rerssner-Nordström Black Hole

The minimum interval of event horizon area of Rerssner-Nordström black hole was calculated via using the loop quantum gravity theory. Based on the first law of black hole thermodynamics, the real part of quasi-normal modes frequency of the black hole was calculated. The expression of asymptotically quasi-normal mode frequency of Rerssner-Nordström black hole was deduced strictly. By analyzing the value of the minimum spin j _{m i n} , the two families of quasi-normal mode spectra of the charged black hole were obtained for j _{m i n} = 1/2 and j _{m i n} = 1 respectively. Our conclusion is in complete agreement with the analytical results of Hod. Our results provide the theoretical basis for the source of the real part of the quasi-normal mode frequency of the black hole.     

A Note on Holographic Dark Energy with Varying <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript> Term

We reconsider the holographic dark energy (HDE) model with a slowly time varying c ²(z) parameter in the energy density, namely \(\rho _{D}=3{M_{p}^{2}} c^{2}(z)/L^{2}\), where L is the IR cutoff and z is the redshift parameter. As the system’s IR cutoff we choose the Hubble radius and the Granda-Oliveros (GO) cutoffs. The latter inspired by the Ricci scalar curvature. We derive the evolution of the cosmological parameters such as the equation of state and the deceleration parameters as the explicit functions of the redshift parameter z. Then, we plot the evolutions of these cosmological parameters in terms of the redshift parameter during the history of the universe. Interestingly enough, we observe that by choosing L = H ^?1 as the IR cutoff for the HDE with time varying c ²(z) term, the present acceleration of the universe expansion can be achieved, even in the absence of interaction between dark energy and dark matter. This is in contrast to the usual HDE model with constant c ² term, which leads to a wrong equation of state, namely that for dust w _D =0, when the IR cutoff is chosen the Hubble radius.     

Spin and mass of the supermassive black hole in the Galactic Center

A new method for exact determination of the masses and spins of black holes from the observations of quasi-periodic oscillations is discussed. The detected signal from the hot clumps in the accretion plasma must contain modulations with two characteristic frequencies: the frequency of rotation of the black hole event horizon and the frequency of the latitudinal precession of the clump’s orbit. Application of the method of two characteristic frequencies for interpretation of the observed quasi-periodic oscillations from the supermassive black hole in the Galactic center in the X-rays and in the near IR region yields the most exact, for the present, values of the mass and the spin (Kerr parameter) of the Sgr A* black hole: M = (4.2 ± 0.2) × 10⁶ M _⊙ and a = 0.65 ± 0.05. The observed quasi-periodic oscillations with a period of about 11.5 min are identified as the black hole event horizon rotation period and those with a period of about 19 min are identified as the latitudinal oscillation period of the hot spot orbits in the accretion disk.