Isotropic compact stars in four-dimensional Einstein-Gauss-Bonnet gravity coupled with scalar field: reconstruction of model

It has been suggested that the Einstein-Gauss- Bonnet theory coupled with a scalar field (EGBS) may allow us to obtain physically viable models of celestial phenomena such that the scalar field effect is active in standard four dimensions. We consider the spherically symmetric and static configuration of the compact star and explain the consequences of the EGBS theory in the frame of stellar modeling. In our formulation, for any given static profile of energy density rho with spherical symmetry and the arbitrary equation of state (EoS) of matter, we can construct a model which reproduces the profile. Because the profile of the energy density determines the mass M and the radius R-s of the compact star, an arbitrary relation between the mass M and the radius R-s of the compact star can be realized by adjusting the potential and the coefficient function of the Gauss-Bonnet term in the action of EGBS theory. This could be regarded as a degeneracy between the EoS and the functions characterizing the model, which indicates that the mass-radius relation alone is insufficient to constrain the model. Here, we investigate a novel class of analytic spherically symmetric interior solutions by the polytropic EoS. We discuss our model in detail and show that it is in agreement with the necessary physical conditions required for any realistic compact star, confirming that EGBS theory is consistent with observations.

Automated summary

It is suggested that the EGBS theory combined with a scalar field can provide physically viable models of celestial phenomena with the scalar field effect active in four dimensions. By considering the spherically symmetric and static configuration of compact stars, the consequences of the EGBS theory in stellar modeling are explained. The mass-radius relation alone is not enough to constrain the model due to the degeneracy between the equation of state (EoS) and the functions characterizing the model, indicating the need for additional considerations.