Thermodynamics and holography of tachyon cosmology

Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter (Farajollahi et al. in Mod Phys Lett A 26(15):1125–1135, 2011; Phys Lett B 711(3–4)15:225–231,2012; Phys Rev D 83:124042, 2011; JCAP 10:014, 20112011; JCAP 05:017, 2011). In particular, for the interacting holographic dark energy (IHDE), the model is studied in Farajollahi et al. (Astrophys Space Sci 336(2):461–467, 2011). In the current work, a significant observational program has been conducted to unveil the model’s thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $\Lambda $ CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event horizon are revisited. From the results, both first and generalized second laws, constrained by the observational data, are satisfied on cosmological apparent horizon.In addition, the total entropy is verified with the observation only if the horizon of the universe is taken as apparent horizon. Then, due to validity of generalized second law, the current cosmic acceleration is also predicted.     

Rainbow black hole thermodynamics and the generalized uncertainty principle

We study the phase transition of rainbow inspired higher dimensional Schwarzschild black hole incorporating the effects of the generalized uncertainty principle. First, we obtain the relation between the mass and Hawking temperature of the rainbow inspired black hole taking into account the effects of the modified dispersion relation and the generalized uncertainty principle. The heat capacity is then computed from this relation which reveals that there are remnants. The entropy of the black hole is next obtained in \(3+1\) and \(4+1\)-dimensions and is found to have logarithmic corrections only in \(3+1\)-dimensions. We further investigate the local temperature, free energy and stability of the black hole in an isothermal cavity. From the analysis of the free energy, we find that there are two Hawking–Page type phase transitions in \(3+1\) and \(4+1\)-dimensions if we take into account the generalized uncertainty principle. However, in the absence of the generalized uncertainty principle, only one Hawking–Page type phase transition exists in spacetime dimensions greater than four.     

Thermodynamics of Viscous Dark Energy in DGP Setup

We investigate thermodynamics of viscous dark energy interacting with dark matter in a DGP braneworld. We show that the Friedmann equation in this setup can be rewritten as the first law of thermodynamics on the apparent horizon. We study the time evolution of the total entropy including the entropy of the matter fields inside the apparent horizon together with the entropy associated with the apparent horizon. Interestingly enough, we find that, in the presence of bulk viscosity, the generalized second law of thermodynamics is always preserved for both branches of the DGP braneworld. When the time varying gravitational constant is taken into account, the generalized second law of thermodynamics can be secured provided $\dot{G}_{4}<0$ , $\frac{\dot{G}_{5}}{G_{5}}>\frac{\dot{G}_{4}}{G_{4}}$ and $\omega_{de}>-1-u+\frac{3H\xi}{\rho_{de}}$ , where ξ and u are, respectively, the bulk viscosity coefficient and the energy densities ratio of the two dark components on the brane.     

Neutrino Tunneling from NUT Kerr Newman de Sitter Black Hole

In this paper, the method of semi-classical is applied to explore the Hawking radiation of a NUT-Kerr-Newman de Sitter Black Hole from tunneling point of view. The Hamilton-Jacobi equation in NUT-Kerr-Newman de Sitter space time is derived by the method presented by Lin and Yang (Chin. Phys. B, 20:110403, 2011). We obtain the Hawking temperatures at the event horizon and cosmological horizon and we also obtain the tunneling probability of neutrino following the semi-classical quantum equation. The results show the common features of NUT-Kerr-Newman de Sitter Black Hole.     

Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree

For the \(q\) -state Potts model on a Cayley tree of order \(k\ge 2\) it is well-known that at sufficiently low temperatures there are at least \(q+1\) translation-invariant Gibbs measures which are also tree-indexed Markov chains. Such measures are called translation-invariant splitting Gibbs measures (TISGMs). In this paper we find all TISGMs, and show in particular that at sufficiently low temperatures their number is \(2^{q}-1\) . We prove that there are \([q/2]\) (where \([a]\) is the integer part of \(a\) ) critical temperatures at which the number of TISGMs changes and give the exact number of TISGMs for each intermediate temperature. For the binary tree we give explicit formulae for the critical temperatures and the possible TISGMs. While we show that these measures are never convex combinations of each other, the question which of these measures are extremals in the set of all Gibbs measures will be treated in future work.     

Spin and mass of the nearest supermassive black hole

Quasi-periodic oscillations (QPOs) of the hot plasma spots or clumps orbiting an accreting black hole contain information on the black hole mass and spin. The promising observational signatures for the measurement of black hole mass and spin are the latitudinal oscillation frequency of the bright spots in the accretion flow and the frequency of black hole event horizon rotation. Both of these frequencies are independent of the accretion model and defined completely by the properties of the black hole gravitational field. Interpretation of the known QPO data by dint of a signal modulation from the hot spots in the accreting plasma reveals the Kerr metric rotation parameter, \(a=0.65\pm 0.05\) , and mass, \(M=(4.2\pm 0.2)10^6M_\odot \) , of the supermassive black hole in the Galactic center. At the same time, the observed 11.5 min QPO period is identified with a period of the black hole event horizon rotation, and, respectively, the 19 min period is identified with a latitudinal oscillation period of hot spots in the accretion flow. The described approach is applicable to black holes with a low accretion rate, when accreting plasma is transparent up to the event horizon region.     

Hawking Radiation of Spin-3/2 Particles from Kerr Black Hole

By using dimensional reduction and consistent anomaly method, we calculate the Hawking flux of the spin- 3/2 field in the Kerr black hole background. The results confirm that the Hawking radiation doesn’t depends on the detail of the fields living near the horizon, at least at the semi-classical level. The Hawking temperature is an universality character of black hole which only depends on the information of the horizon. Our calculation agrees with earlier results obtained by the WKB/tunneling method (Yale and Mann, Phys. Lett. B 673(2), 168–172, 2009).     

A New Regular Black Hole

A spherically symmetric uncharged regular black hole is proposed in this paper. The black hole’s density in proportion to $r^{3n}e^{-r^{3n+3}}$ , and the curvature tensor in the region of r=0 keep finity. When n=0 in our model, this spacetime is no other than Dymnikova regular black hole. What’s more, there are better properties in this spacetime when n>0. We then discuss the temperature and Hawking radiation of the black hole’s horizon.     

Energy loss of a heavy particle near 3D charged rotating hairy black hole

In this paper, we start with a black brane and construct a specific space-time which violates hyperscaling. To obtain the string solution, we apply the Null-Melvin Twist and KK reduction. Using the difference action method, we study the thermodynamics of the system to obtain a Hawking–Page phase transition. To have hyperscaling violation, we need to consider $\theta =\frac{d}{2}.$ In this case, the free energy $F$ is always negative and our solution is thermal radiation without a black hole. Therefore, we find that there is no Hawking–Page transition. Also, we discuss the stability of the system and all thermodynamical quantities.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Stationary scalar configurations around extremal charged black holes

We consider the minimally coupled Klein-Gordon equation for a charged, massive scalar field in the non-extremal Reissner-Nordström background. Performing a frequency domain analysis, using a continued fraction method, we compute the frequencies $\omega $ for quasi-bound states. We observe that, as the extremal limit for both the background and the field is approached, the real part of the quasi-bound states frequencies $\mathcal{R }(\omega )$ tends to the mass of the field and the imaginary part $\mathcal{I }(\omega )$ tends to zero, for any angular momentum quantum number $\ell $ . The limiting frequencies in this double extremal limit are shown to correspond to a distribution of extremal scalar particles, at stationary positions, in no-force equilibrium configurations with the background. Thus, generically, these stationary scalar configurations are regular at the event horizon. If, on the other hand, the distribution contains scalar particles at the horizon, the configuration becomes irregular therein, in agreement with no hair theorems for the corresponding Einstein-Maxwell-scalar field system.     

On the Stability and Thermodynamics of the Dark Energy Based on Generalized Uncertainty Principle

The new agegraphic Dark Energy (NADE) model (based on generalized uncertainty principle) interacting with Dark Matter (DM) is considered in this study via power-law form of the scale factor a(t). The equation of state (EoS) parameter ω _G is observed to have a phantom-like behaviour. The stability of this model is investigated through the squared speed of sound $v_{s}^{2}$ . It is found that $v_{s}^{2}$ always stays at negative level. This indicates instability of the considered model. Moreover, validity of the generalized second law of thermodynamics has been investigated assuming that the apparent horizon is the enveloping horizon. It has been observed that the generalized second law is valid throughout the evolution of the universe.     

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large $r$ go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the $N$ th order Lovelock $\Lambda $ -vacuum solutions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.     

Approximation of the naive black hole degeneracy

In 1996, Rovelli suggested a connection between black hole entropy and the area spectrum. Using this formalism and a theorem we prove in this paper, we briefly show the procedure to calculate the quantum corrections to the Bekenstein–Hawking entropy. One can do this by two steps. First, one can calculate the “naive” black hole degeneracy without the projection constraint (in case of the $U(1)$ symmetry reduced framework) or the $SU(2)$ invariant subspace constraint (in case of the fully $SU(2)$ framework). Second, then one can impose the projection constraint or the $SU(2)$ invariant subspace constraint, obtaining logarithmic corrections to the Bekenstein–Hawking entropy. In this paper, we focus on the first step and show that we obtain infinite relations between the area spectrum and the naive black hole degeneracy. Promoting the naive black hole degeneracy into its approximation, we obtain the full solution to the infinite relations.     

Black hole entropy with minimal length in tunneling formalism

Here we study the effects of the Generalized Uncertainty Principle in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature and entropy for a Schwarzschild black hole. We compare our results with the existing results given by other candidate theories of quantum gravity. In the entropy-area relation we found some new correction terms and in the leading order we found a term which varies as $\sim \sqrt{Area}$ ～ A r e a . We also get the well known logarithmic correction in the sub-leading order. We discuss the significance of this new quantum corrected leading order term.     

Branes as solutions of gauge theories in gravitational field

In this paper we study the behavior of the jet quenching parameter in a background metric with hyperscaling violation at finite temperature. The background metric is covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent \(z\) and hyperscaling exponent \(\theta \) . We have evaluated the jet quenching parameter for a certain range of these parameters which are consistent with the Gubser bound conditions in terms of \(T\) , \(z\) , and \(\theta \) . The results are compared with those of experimental data as well as conformal and the non-conformal cases. Finally, we add a constant electric field to the background and find its effect on the jet quenching parameter.