Stellar structures with constant local adiabatic index under extreme relativistic conditions

Stellar structures with a constant local adiabatic index Γ have been discussed under the extreme relativistic condition (dP/dρ=1, at the center of the configuration). The equation of state,Pαρ^Γ, where ρ _r is the rest-mass density leads to the relations, (i)ρ=AP ^1/Γ?P/(Γ?1) between energy density and pressure, and (ii)e=NP between internal energy density and pressure, where the constantN may be called local polytropic index. The local adiabatic index, Γ, is found to be related to the adiabatic index, γ, through a simple relation, Γ=γ(1+P/ρ). The maximum value of surface redshift comes out to be 0.614 when σ=(P/ρ)₀=0.6. The structure are bound for σ≤0.83 and the maximum value of the binding coefficient is 0.181 at σ=0.4. For bound structures the central redshift z₀≤8.24. The maximum mass of neutron star based upon such a model comes out to be 2.39M _⊙ (for σ=0.4) and the maximum size comes out to be 13.7 km (for σ=0.2).