First, we construct the Taub-NUT/bolt solutions of (2k+2)-dimensinal Einstein-Maxwell gravity, when all the factor spaces of 2k-dimensional base space B have positive curvature. These solutions depend on two extra parameters, other than the mass and the NUT charge. These are electric charge q and electric potential at infinity V . We investigate the existence of Taub-NUT solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two extra conditions. These two extra conditions come from the regularity of vector potential at r = N and the fact that the horizon at r = N should be the outer horizon of the NUT charged black hole. We find that the NUT solutions in 2k + 2 dimensions have no curvature singularity at r = N , when the 2k-dimensional base space is chosen to be CP 2k . For bolt solutions, there exists an upper limit for the NUT parameter which decreases as the potential parameter increases. Second, we study the thermodynamics of these spacetimes. We compute temperature, entropy, charge, electric potential, action and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We perform a stability analysis by computing the heat capacity, and show that the NUT solutions are not thermally stable for even k's, while there exists a stable phase for odd k's, which becomes increasingly narrow with increasing dimensionality and wide with increasing V .We also study the phase behavior of the 4 and 6 dimensional bolt solutions in canonical ensemble and find that these solutions have a stable phase, which becomes smaller as V increases.
We compute the Euclidean actions of a d-dimensional charged rotating black brane both in the canonical and the grand-canonical ensemble through the use of the counterterms renormalization method, and show that the logarithmic divergencies associated with the Weyl anomalies and matter field vanish. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta, and the electric charge, and show that these quantities satisfy the first law of thermodynamics.Using the conserved quantities and the Euclidean actions, we calculate the thermodynamics potentials of the system in terms of the temperature, angular velocities, and electric potential both in the canonical and grand-canonical ensembles. We also perform a stability analysis in these two ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for a black object with zero curvature horizon. Finally, we obtain the logarithmic correction of the entropy due to the thermal fluctuation around the equilibrium.
Motivated by the holographic principle, it has been suggested that the dark energy density may be inversely proportional to the area A of the event horizon of the universe. However, such a model would have a causality problem. In this work, we consider the entropy-corrected version of the holographic dark energy model in the non-flat FRW universe and we propose to replace the future event horizon area with the inverse of the Ricci scalar curvature. We obtain the equation of state (EoS) parameter ω , the deceleration parameter q and D in the presence of inter-A. Pasqua action between Dark Energy (DE) and Dark Matter (DM). Moreover, we reconstruct the potential and the dynamics of the tachyon, K-essence, dilaton and quintessence scalar field models according to the evolutionary behavior of the interacting entropy-corrected holographic dark energy model.
A new model of dark energy namely "ghost dark energy model" has recently been suggested to interpret the positive acceleration of cosmic expansion. The energy density of ghost dark energy is proportional to the hubble parameter. In this paper we perform the statefinder diagnostic tool for this model both in flat and non-flat universe. We discuss the dependency of the evolutionary trajectories in s − r and q − r planes on the interaction parameter between dark matter and dark energy as well as the spatial curvature parameter of the universe. Eventually, in the light of SNe+BAO+OHD+CMB observational data, we plot the evolutionary trajectories in s − r and q − r planes for the best fit values of the cosmological parameters and compare the interacting ghost model with other dynamical dark energy models. We show that the evolutionary trajectory of ghost dark energy in statefinder diagram is similar to holographic dark energy model. It has been shown that the statefinder location of ΛCDM is in good agreement with observation and therefore the dark energy models whose current statefinder values are far from the ΛCDM point can be ruled out. *
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