https://doi.org/10.1140/epja/i2018-12510-x
Regular Article - Theoretical Physics
Embedded class solutions compatible for physical compact stars in general relativity
1
Department of Physics, National Defence Academy, 411023, Khadakwasla, Pune, India
2
Department of Mathematics, Jadavpur University, 700032, Kolkata, India
3
Department of Mathematics, National Defence Academy, 411023, Khadakwasla, Pune, India
4
Department of Physics, Lajpat Rai College, 201011, Ghaziabad, India
* e-mail: ntnphy@gmail.com
Received:
7
February
2018
Accepted:
12
April
2018
Published online:
15
May
2018
We have explored a family of new solutions satisfying Einstein’s field equations and Karmarkar condition. We have assumed an anisotropic stress-tensor with no net electric charge. Interestingly, the new solutions yield zero values of all the physical quantities for all even integer 
. However, for all 
(
even numbers) they yield physically possible solutions. We have tuned the solution for neutron star Vela X-1 so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. The solutions yield a stiffer equation of state for larger values of n since the adiabatic index increases and speed of sound approaches the speed of light. It is also found that the solution is physically possible for Vela X-1 if 
(with 
). All the solutions for 
violates the causality condition and all the solutions with 
lead to complex values of transverse sound speed 
. The range of well-behaved n depends on the mass and radius of compact stars.
© SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2018
