The Cosmological Constant and the Characteristic Development of Trapped Surfaces

TThe cosmological constant is a model of dark energy that is one explanation for the accelerated expansion of the universe. The concept of a trapped surface provides a precise characterization of gravitational collapse that has proceeded beyond the point of no return, resulting in a black hole. Therefore, because of its importance, we examined spherically-symmetric spacetimes with a cosmological constant to determine its impact on the characteristic development of trapped surfaces. The principal result of this study is a relationship between the mass (m) and the cosmological constant (Λ) that is a necessary and sufficient condition for trapped surfaces to develop to the future of a branch of a perfect null hypersurface. For the cosmological constant obtained from the Planck-satellite data, there is a maximum mass for a black hole. We determined the value for the cosmological constant for a Planck-mass black hole and showed that it is 120 orders of magnitude larger than the cosmological constant obtained from the Planck-satellite data. Finally, we argue that that our universe is too massive to be closed and spatially bounded given the value of the cosmological constant obtained from these data.