Dynamics of Anisotropic Collapsing Spheres in Einstein Gauss-Bonnet Gravity

This paper is devoted to investigate the dynamics of the self gravitating adiabatic and anisotropic source in $5D$ Einstein Gauss-Bonnet gravity. To this end, the source has been taken as Tolman-Bondi model which preserve inhomogeneity in nature. The field equations, Misner-Sharp mass and dynamical equations have formulated in Einstein Gauss-Bonnet gravity in $5D$. The junction conditions have been explored between the anisotropic source and vacuum solution in Gauss-Bonnet gravity in detail. The Misner and Sharp approach has been applied to define the proper time and radial derivatives. Further, these helps to formulate general dynamical equations. The equations show that the mass of the collapsing system increases with the same amount as the effective radial pressure increases. The dynamical system preserve retardation which implies that system under-consideration goes to gravitational collapse.

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