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} is coupled to the Einstein–Hilbert action through a coupling constant, namely alpha . 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 ; however, it is less stiff than GR.
Highlights
Maintaining consistency can be a difficult task. Within this branch there are some heuristic methods of determining stability, such as relativistic adiabatic index [54,55], Abreu’s criterion [56], static stability criterion [57,58], and Ponce De Leon’s criterion [59]. This clearly suggests that the study of stability of compact objects can only be carried out in a tentative manner, that is, there is no mechanism to test whether an astrophysical system is stable from a global point of view
From this graph it can be seen that the maximum moment of inertia (Imax) increases with increasing coupling constant α
The obtained solution fulfills the basic and general requirements to be a physically and mathematically admissible model. In this case we have solved the field equations (8)–(10) by imposing the Tolman–Kuchowicz spacetime (Fig. 1). This choice is well motivated for two reasons: (i) this metric is free from physical and geometrical singularities, so it is completely plausible to describe the inner geometry of compact objects, (ii) it yields a well behaved energy density, i.e., a positive definite and monotone decreasing function from the center to the boundary of the star (Fig. 2)
Summary
A recent work on the role played by the anisotropy on the properties mentioned above is [42] (see the references therein) Following this line, in this paper we construct a well behaved anisotropic fluid sphere in the five-dimensional EGB scenario, by using Tolman–Kuchowicz [43,44] spacetime. In this paper we construct a well behaved anisotropic fluid sphere in the five-dimensional EGB scenario, by using Tolman–Kuchowicz [43,44] spacetime This metric has been used by other authors in the study of anisotropic charged/uncharged interior solutions [45,46]. 3 we study the field equations and the mathematical solutions of EGB gravity within Tolman–Kuchowicz spacetime, obtaining the main salient features that characterize the model such as the energy-matter density ρ, the radial pressure pr and the tangential pressure pt and the anisotropy factor.
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