Abstract
Modern cosmological models are constructed in the framework of thermodynamic approaches developed within a Van der Waals-Maxwell theory of the first-order phase transitions. In the present work we study a geometrothermodynamics of two-dimensional first-order phase transition with the distribution of relaxation times in a configuration space which describes a spacetime with Newman-Unti-Tamburino-like metric. We utilized the geometrothermodynamical approach to construct the model of a charged generalized-NUT black hole. We reveal following features of the black-hole phase transition: there are series of bifurcations of pitchfork type in dependences of the Gibbs free energy on the Hawking temperature, and although a scalar Berwald curvature of space changes sign in the phase transition, black-hole stability depends on sign of the curvature after the transition.
Highlights
Series of modern cosmological models are constructed in the framework of thermodynamic approaches, which are developed on the grounds of standard thermodynamics of the1-st order phase transitions
The cosmological models which are based on Van der Waals – Maxwell theory of the liquid-gas firstorder phase transitions, should meet a demand of the agreement of different thermodynamic representations (for example, between energy and Gibbs free energy G representations) to provide comprehensive description of the model
To describe a model of the universe filled by barotropic fluid with the Weyl’s canonical coordinates and negative cosmological constant Λ, the static solutions for axially symmetric metric for black holes in vacuum have been acquired [4,5]
Summary
Series of modern cosmological models are constructed in the framework of thermodynamic approaches, which are developed on the grounds of standard thermodynamics of the1-st order phase transitions. The cosmological models which are based on Van der Waals – Maxwell theory of the liquid-gas firstorder phase transitions, should meet a demand of the agreement of different thermodynamic representations (for example, between energy (black-hole mass M) and Gibbs free energy G representations) to provide comprehensive description of the model This demand extremely complicates the calculations because of that a thermodynamic geometry of the cosmological model has been constructed without taking into account a cosmological constant Λ or scalar fields [1]. Symmetric Newman–Unti–Tamburino (NUT) metrics pretend to play role of such metrics Some their thermodynamic properties have been studied in f(R) gravity [6] and within Rastall theory of gravity [7], due to a complexity of the NUT-models a thermodynamic geometry has not been constructed yet.
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