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

Abstract

Abstract 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 $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> 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 $$R_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> of the compact star, an arbitrary relation between the mass M and the radius $$R_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> 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.