Compact star in Tolman–Kuchowicz spacetime in the background of Einstein–Gauss–Bonnet gravity

Abstract The present work is devoted to the study of anisotropic compact matter distributions within the framework of five-dimensional Einstein–Gauss–Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman–Kuchowicz spacetime. The Gauss–Bonnet Lagrangian $$\mathcal {L}_{GB}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>GB</mml:mi></mml:mrow></mml:msub></mml:math> is coupled to the Einstein–Hilbert action through a coupling constant, namely $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> . When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor. These effects are contrasted with the corresponding general relativity results. Besides, we have checked the incidence on an important mechanism: equilibrium by means of a generalized Tolman–Oppenheimer–Volkoff equation and stability through relativistic adiabatic index and Abreu’s criterion. Additionally, the behavior of the subliminal sound speeds of the pressure waves in the principal directions of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing the causality condition and energy conditions, respectively. All these subjects are illuminated by means of physical, mathematical and graphical surveys. The M – I and the M – R graphs imply that the stiffness of the equation of state increases with $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> ; however, it is less stiff than GR.

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