Corrections to the Cardy-Verlinde formula at the Planck scale

The possible corrections to the thermodynamic quantities of higher dimensional Schwa-rzschild black hole have been investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole have been calculated based on both the GUP and the MDR analysis. The explicit form of the corrections are worked out up to the sixth power of the Planck length. The impacts of GUP and MDR have been used separately to obtain the quantum gravitational corrections to the Cardy-Verlinde (C-V) formula. It has been shown that the usual C-V entropy formula receives some new corrections. Also the renormalized form of the C-V formula has been introduced by redefining Virasoro operator and central charge within both the GUP and the MDR. Through comparison of the corrections obtained from GUP and MDR approaches it has been found that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients.     

Spacetime dimensionality and logarithmic prefactor in the black hole entropy relation

We study the relation between the existence of the logarithmic prefactor and spacetime dimensionality in black hole entropy relation by a detailed study of a TeV-scale black hole entropy. In a model universe with large extra dimensions and within the Generalized Uncertainty Principle (GUP) framework, we show that probability of black hole production in the Large Hadronic Collider (LHC) decreases for sufficiently large values of the GUP parameter. In this regard, even observation of micro-black holes may be suppressed at TeV energy scale. We determine also the GUP parameter in an extra dimensional scenario by comparing black hole entropy calculated within the GUP and loop quantum gravity frameworks.     

The influence of Coulomb interaction on the equation of state under nuclear statistical equilibrium conditions

In the domain of thermodynamic parameters characteristic of the initial collapse of iron stellar cores, we studied the influence of Coulomb interaction on the thermodynamic functions of a plasma under nuclear statistical equilibrium conditions. Our attention was focused on the nuclear component of the matter. We established that including the interaction shifts the equilibrium toward the nuclei with larger charges. However, this effect and the changes in thermodynamic quantities are noticeable only at high densities (ρ ? 10¹¹ g cm^?3), i.e., at an advanced stage of gravitational collapse. We also showed that the mean ion model is inadequate in regions with a coupling parameter Γ ～ 1. We point out a method for modifying the linear mixing model to properly pass to the Debye limit and discuss other multicomponent plasma models.     

The Generalized Uncertainty Principle and the Friedmann equations

The Generalized Uncertainty Principle (or GUP) affects the dynamics in Plank scale. So the known equations of physics are expected to get modified at that very high energy regime. Very recently authors in Ali et al. (Phys. Lett. B 678:497, 2009) proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this article, the proposed GUP is expressed in a more general form and the effect is studied for the modification of the Friedmann equations of the FRW universe. In the midway the known entropy-area relation get some new correction terms, the leading order term being proportional to \(\sqrt{\mathrm{Area}}\).     

The influence of turbulence pressure on the late stages of evolution of medium and small mass stars (I) Calculation of the turbulence pressure, equation of state and thermodynamic quantities

Using the mixing length theory we give expressions for turbulence pressure and the equation of state and various thermodynamic quantities when turbulence is included. On this basis we examined the size of turbulence in the evolution of two stars of masses 2.8 and 7.0M from the main sequence to the red giant and the AGB stages, Our results show that in the late stages the turbulence pressure near the surface of the star can be as much as 30% of the total pressure.     

On the relation of dynamics to statistical mechanics

A new conceptual framework for the foundations of statistical mechanics starting from dynamics is presented. It is based on the classification and the study of invariants in terms of the concepts of our formulation of non-equilibrium statistical mechanics. A central role is played by thecollision operator. The asymptotic behaviour of a class of states is determined by the collisional invariants independently of the ergodicity of the system. For this class of states we have an approach to thermodynamical equilibrium. We discuss the existence of classes of states which approach equilibrium. The complex microstructure of the phase space, as expressed by the weak stability concept which was introduced by Moser and others, plays here an essential role. The formalism that we develop is meaningful whenever the “dissipativity condition” for the collision operator is satisfied. Assuming the possibility of a weak coupling approximation, this is in fact true whenever Poincaré's theorem on the nonexistence of uniform invariants holds. In this respect, our formalism applies to few body problems and no transition to the thermodynamic limit is required. Our approach leads naturally to a ‘classical theory of measurement’. In particular a precise meaning can now be given to ‘thermodynamic variables’ or to ‘macrovariables’ corresponding to a measurement in classical dynamics.     

On invisible plasma content in radio-loud AGNs: the case of TeV blazar Markarian 421

Invisible plasma content in blazar jets such as protons and/or thermal electron–positron ( e ^±) pairs is explored through combined arguments of dynamical and radiative processes. By comparing physical quantities required by the internal shock model with those obtained through the observed broad-band spectra for Mrk 421, we obtain that the ratio of the Lorentz factors of a pair of cold shells resides in about 2 ∼ 20, which implies that the shocks are at most mildly relativistic. Using the obtained Lorentz factors, the total mass density ρ in the shocked shells is investigated. The upper limit of ρ is obtained from the condition that thermal bremsstrahlung emission should not exceed the observed γ-ray luminosity, whilst the lower limit is constrained from the condition that the energy density of non-thermal electrons is smaller than that of the total plasma. Then, we find ρ is 10²–10³ times heavier than that of non-thermal electrons for pure   e ^±  pairs, while 10²–10⁶ times heavier for pure electron–proton ( e / p ) content, implying the existence of a large amount of invisible plasma. The origin of the continuous blazar sequence is briefly discussed and we speculate that the total mass density and/or the blending ratio of e ^± pairs and e / p plasma could be new key quantities for the origin of the sequence.     

The equal area law of asymptotically AdS black holes in extended phase space

According to Maxwell’s equal area law we study the “real” phase diagram of the charged AdS black hole and the Kerr-AdS black hole. In the extended phase space constructed by treating the cosmological constant as pressure, the two kinds of AdS black hole display themselves like van der Waals system. Under the critical temperature T _c , there exists a regime where the condition of stable equilibrium will be violated. We employ the equal area law to find an isobar which is the real two phase coexistence line. As a byproduct we find a simple method to derive the critical value of the thermodynamic quantities.     

Gaussian states in de Sitter spacetime and the evolution of semiclassical density perturbations.

The evolution of Gaussian quantum states in the de Sitter phase of the early universe is investigated. The potential is approximated by that of an inverted oscillator. We study the origin and magnitude of the density perturbations with special emphasis on the nature of the semiclassical limits     

The generalized second law of thermodynamics for the interacting in f(T) gravity

We study the validity of the generalized second law (GSL) of gravitational thermodynamics in a non-flat FRW universe containing the interacting in f(T) gravity. We consider that the boundary of the universe to be confined by the dynamical apparent horizon in FRW universe. In general, we discuss the effective equation of state, deceleration parameter and GLS in this framewok. Also, we find that the interacting-term Q modifies these quantities and in particular, the evolution of the total entropy, results in an increases on the GLS of thermodynamic, by a factor $4\pi R_{A}^{3} Q/3$ . By using a viable f(T) gravity with an exponential dependence on the torsion, we develop a model where the interaction term is related to the total energy density of matter. Here, we find that a crossing of phantom divide line is possible for the interacting-f(T) model.     

Possible Role of mhd Waves in Heating the Solar Corona

Heating of the solar corona by MHD waves has been investigated. Taking account of dissipation mechanisms self-consistently, a new general dispersion relation has been derived for waves propagating in a homogeneous plasma. Solution of this sixth-order dispersion relation provides information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. Wave quantities with and without dissipation are presented. In particular, we consider one of the most important clues from space observations that viscosity of coronal plasma may be orders of magnitude different from its classical value in heating of the corona by MHD waves.     

Superconducting critical field in cold magnetic white dwarfs and in neutron stars

For an evaluation of the superconducting critical fieldH _c as a function of the mass-density in the external layers of cold magnetic white dwarfs and in the superconducting proton fluid in neutron stars, we use the solution of a differential equation involvingH _c as a function of the pressure. The differential equation and its solution are obtained by pure thermodynamic way.Finally other thermodynamic quantities are calculated for the above superconducting astrophysical systems.     

In-line digital holographic microscopy for terrestrial and exobiological research

We describe here a simple digital in-line holographic microscope (DIHM) that was used to investigate the microbial life forms that exist in perennial springs and glacial melt-water pools on Axel Heiberg Island at near 80°N latitude in the Canadian High Arctic. The instrument determined an upper limit of the density of microbial organisms in the springs and also found an abundance of algae and bacteria in the pools formed from glacial run off. The discovery of life in extra-terrestrial regions of our solar system has been the aim of several space missions. DIHM can capture the dynamics of objects throughout an imaging volume with wavelength limited resolution. The simplicity of DIHM technology furthermore allows the construction of very light-weight and rugged instruments that we believe can be easily adapted for space missions and exobiological studies.     

A General Relativistic Calculation of Boundary Layer and Disc Luminosity for Accreting Non-magnetic Neutron Stars in Rapid Rotation

We calculate the disc and boundary layer luminosities for accreting rapidly rotating neutron stars with low magnetic fields in a fully general relativistic manner. Rotation increases the disc luminosity and decreases the boundary layer luminosity. A rapid rotation of the neutron star substantially modifies these quantities as compared with the static limit. For a neutron star rotating close to the centrifugal mass shed limit, the total luminosity has contribution only from the extended disc. For such maximal rotation rates, we find that well before the maximum stable gravitational mass configuration is reached, there exists a limiting central density, for which particles in the innermost stable orbit will be more tightly bound than those at the surface of the neutron star. We also calculate the angular velocity profiles of particles in Keplerian orbits around the rapidly rotating neutron star. The results are illustrated for a representative set of equation of state models of neutron star matter.