SOME ASPECTS OF EXACT STATIC SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN’S FIELD EQUATIONS WITH SPECIFIED EQUATION OF STATE

A. K. Singh

  DOI:  https://doi.org/10.37418/amsj.9.11.15

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In this paper we have obtained some exact static spherical solution of Einstein’s field equation with cosmological constant $\wedge=0$ and equation of state $p=\rho$ (taking suitable choice of $g_{11}$ and $g_{44}$). We have taken $e^{\beta}=lr^{n}, e^{\beta}=lr^{n-1}, ~\text{and}~ e^{\beta}=lr^{7/5}$ (where $l$ is a constant), which help to investigate the value of $e^{\alpha}$. Many previously known solutions are contained here in as a particular case. Various physical and geometrical properties have been studied.

Keywords: Exact solution, Cosmological Model, Equation of state, Static Fluid sphere, Shear tensor, Homogeneous density, Metric space.