Expansion and collapse of spherical source with cosmological constant

In this research paper, we address the issues of expansion and gravitational collapse of anisotropic spherical source in the presence of cosmological constant. For this purpose, we have solved the Einstein field equations with gravitating source and cosmological constant. The absence of radial heat flux in the gravitating source provide the parametric form of two-metric functions in terms of a single-metric function. The expansion scalar and the mass function of the gravitating source is evaluated for the given metric. The trapping condition is applied to mass function which implies the existence of horizons, like the horizons of Schwarzschild de-Sitter black holes. The trapping condition provides the parametric form of the unknown metric function. The value of expansion scalar has been analyzed in detail to see its positivity and negativity, which correspond to expansion and collapse, respectively. So, the values of parameter [Formula: see text] for which expansion scalar is positive have been used to analyze the other physical variables including density, pressures and anisotropy. The same quantities have been evaluated for the values of [Formula: see text] that result in the negative values of expansion scalar leading to collapse. The effects of positive cosmological constant have been noted in both expansion and collapse solutions. Due to the presence of cosmological constant after collapse, there would occur inner and outer horizons or a unique horizon depending on the value of mass of the gravitating source.

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