Modern Physics Letters A

In this paper we discuss the question of whether the entropy of cosmological horizon in topological Reissner–Nordström–de Sitter spaces can be described by the Cardy–Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy–Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Our result is in favour of the dS/CFT correspondence.

It is shown that an action inspired from a BF and Chern–Simons model, based on the AdS₄ isometry group SO(3,2), with the inclusion of a Higgs potential term, furnishes the MacDowell–Mansouri–Chamseddine–West action for gravity, with a Gauss–Bonnet and cosmological constant term. The AdS₄ space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in AdS₄ space representing the higher spin extension of this model. Brief remarks on noncommutative gravity are made.

We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various *-products which generalize the κ-Minkowski commutation relation.

Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure also exists between a class of non-central potentials. As an illustrative example, we discuss the inter-relation between the generalized Coulomb and oscillator systems.

We consider the scalar gravity theory in (2 + 1) dimensions and find an electrically charged and a rotating black hole solutions. The first solution was obtained by combining the scalar gravity and Maxwell equations and the second one by applying the method of complex coordinate transformation to the nonrotating counterpart solution.

It is shown that electron gas in dense stellar matter exhibit super-fluid (frictionless) like property if the magnetic field strength is high enough to populate only the zeroth Landau levels, i.e. it is possible that at the core of a magnetar, the proton matter behaves like a superconductor, neutron matter behaves like a super-fluid and electron gas shows super-fluidity without superconductivity. Therefore, the core region as a whole of a magnetar may behave like a frictionless matter which is quite surprising.