A family of well-behaved Karmarkar spacetime describing interior of relativistic stars

We are presenting a family of new exact solutions for relativistic anisotropic stellar objects by considering four dimensional spacetime embedded in five dimensional Pseudo Euclidean space known as Class I solutions. These solutions are well-behaved in all respects, satisfy all energy conditions and the resulting compactness parameter is also within Buchdahl limit. The well-behaved nature of the solutions for a particular star solely depends on index n. We have discussed the solutions in detail for the neutron star XTE J1739-285 (M = 1.51M$\odot$, R = 10.9 km). For this particular star, the solution is well behaved in all respects for $8 \le n \le 20$. However, the solutions with n < 8 possess increasing trend of sound speed and the solutions belong to n > 20 disobey causality condition. Further, the well-behaved nature of the solutions for PSR J0348+0432 (2.01M$\odot$, 11 km), EXO 1785-248 (1.3M$\odot$, 8.85 km) and Her X-1 (0.85M$\odot$, 8.1 km) are specified by the index n with limits $24 \le n \le 54$, $1.5 \le n \le 4$ and $0.8 \le n \le 2.7$ respectively.Comment: 8 pages, 17 figires, 1 tabl

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

The present work is devoted to the study of anisotropic compact matter distributions within the framework of 5-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 is coupled to Einstein-Hilbert action through a coupling constant. 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.Additionally, the behaviour of the subliminal sound speed of the pressure waves in the principal direction of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing causality condition and energy conditions, respectively. All these subjects are supported by mean of physical, mathematical and graphical surve