Possible Einstein's cluster models in embedding class one spacetime.

For the first time, we present Einstein's cluster model in embedding class one spacetime. This paper shows that for any neutral configurations there is only one Einstein cluster solution in embedding class one. In fact, one can find two solutions where the first solution i.e. g r r = e λ = 1 and g t t = e ν = C is an unphysical one as it has zero density profile as well as violates the Pandey–Sharma condition (i.e. not a class one solution). However, the second solution can describe matter distribution representing Einstein's cluster which is in static and equilibrium as it satisfies the static stability criterion and TOV-equation. The second solution not only satisfies the above conditions, but also satisfies the energy conditions. The equation of state parameter ω t is less than unity signifying that it can represent physical matters. Further, we have also shown that the Einstein's clusters may also exhibit the properties of compact stars. [ABSTRACT FROM AUTHOR]