https://doi.org/10.1140/epjc/s10052-016-4364-6
Regular Article - Theoretical Physics
A family of well-behaved Karmarkar spacetimes describing interior of relativistic stars
1
Department of Physics, National Defence Academy, Khadakwasla, Pune, 411023, India
2
Department of Mathematics, National Defence Academy, Khadakwasla, Pune, 411023, India
* e-mail: neeraj.pant@yahoo.com
Received:
10
July
2016
Accepted:
7
September
2016
Published online:
26
September
2016
We present a family of new exact solutions for relativistic anisotropic stellar objects by considering a four-dimensional spacetime embedded in a 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 the index n. We have discussed the solutions in detail for the neutron star XTE J1739-285 (
km). For this particular star, the solution is well behaved in all respects for 
. However, the solutions with 
possess an increasing trend of the sound speed and the solutions belonging to 
disobey the causality condition. Further, the well-behaved nature of the solutions for PSR J0348+0432 (
km), EXO 1785-248 (1.3
, 8.85 km), and Her X-1 (0.85, 8.1 km) are specified by the index n with limits 
, 
, and 
, respectively.
© The Author(s), 2016
