<![CDATA[Spherically symmetric static boson stars are solutions of the system of equations of Einstein equation which is coupled to the Klein-Gordon and Proca Equation with complex scalar field with U (1) gauge symmetry. We look for the system of equations of Einstein equation which is coupled to the Klein-Gordon and Proca Equation in the curvature space then we limit the metric to the flat space. The system of equations is assumed to be inhomogeneous so, the pressure in tangential direction is different to the pressure in radialdirection that shows the anisotropic equations of state (EOS). We find numerically solutions to see the equations of state which are formed in boson stars as the consequence of inhomogeneous assumption. We also find the solutions for the case of homogeneous assumption by omitting the derivative terms of that system of equations. The result shows that with the inhomogeneous assumption, the boundary conditions can’t be fulfilled and causes the EOS unstable. For the case of homogeneous assumption, the result can describe the stable EOS of the boson stars. Keywords: boson stars, Klein-Gordon equation, Proca equation, inhomogeneous, homogeneous, EOS.]]>
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