We obtain a new solution of the Einstein-anti-Maxwell theory with cosmological constant, called anti-Reissner-Nordstrom-(A)de Sitter (anti-RN-(A)dS) solution. The basic properties of this solution is reviewed. Its thermodynamics is consistently established, with the extreme cases and phase transitions, where the analysis is performed through two methods, the usual one and that of Geometrothermodynamics . The Geometrothermodynamics analysis does not provide a result in agreement with the usual method or by the specific heat. We establish local and global thermodynamic stabilities of anti-RN-AdS solution through the specific heat and the canonical and grand-canonical ensembles.

We investigate the effects of quantum particle production on a classical sudden singularity occurring at finite time in a Friedmann universe. We use an exact solution to describe an initially radiation-dominated universe that evolves into a sudden singularity at finite time. We calculate the density of created particles exactly and find that it is generally much smaller than the classical background density and pressure which produce the sudden singularity. We conclude that, in the example studied, the quantum particle production does not lead to the avoidance or modification to the sudden future singularity. We argue that the effects of small residual anisotropies in the expansion will not change these results and show how they can be related to studies of classical particle production using a bulk viscosity. We conclude that we do not expect to see significant observable effects from local sudden singularities on our past light cone.

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Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be p = −ρ − Aρ α , the conformal anomaly can transform the sudden singularity in the singularity of type III for any α > 1/2 and in the singularity of the type I (the big rip) or the big crunch for 1/2 < α < 3/2. Pacs numbers: