Compact stars in the pseudo-complex general relativity

Abstract

The field equations of the pseudo-complex General Relativity (pc-GR) have an extra term, of repulsive character, which may halt the gravitational attractive collapse of matter distributions in the evolution process of compact stars. This additional extra term simulates the presence of dark energy in the Universe. On the first part of this contribution we consider the effect of this additional term of pc-GR on the structure of a white dwarf. Observations of type Ia supernova (SNe Ia) admit white dwarfs with masses as high as 2.3M⊙ − 2.6M⊙, surpassing this way the mass limit established by Chandrasekhar (1.44M⊙). In a more conventional theoretical description of a white dwarf, the electron degeneracy pressure ultimately stabilizes the star against gravitational collapse and establishes this way the Chandrasekhar maximum limit of the stelar mass; this mechanism can not explain however values of masses more expressive like those mentioned above. We investigate here a possible mechanism for carrying out such a hypothesis: the combination of the electron degeneracy and dark energy internal pressures. In this study we use a very simple model for the white dwarf mater which consists of nucleons and degenerate electrons, held together by the presence of the gravitational interaction and superimposed to a repulsive background of dark energy. In the pc-GR formalism, the corresponding modified Tolman-Oppenheimer-Volkoff (TOV) equations are solved and the mass-radius relations as well as the maximum mass of the white dwarf star are determined for different parameter configurations. In the second part of this contribution we explore the presence of this additional term and study the role of dark energy in the structure of neutron stars composed by nucleons, hyperons, mesons, and weakly interacting massive fermion dark matter particles (WIMPs) held together by the presence of the nuclear force and the gravitational interaction, superimposed to the repulsive background of dark energy. To describe the hadron-lepton sector we consider three different effective nuclear models, Zimanyi-Moszkowski, Boguta-Bodmer, and the analytic parametrized coupling model, which we extend to consider, in the baryonic sector, the presence of the whole fundamental baryon octet. By solving the corresponding pc-GR Tolman-Oppenheimer-Volkoff (TOV) equations we estimate the maximum gravitational mass of neutron stars.