Spherical symmetric dust collapse in vector-tensor gravity

Abstract

There is a viable vector-tensor gravity (VTG) theory, the vector field of which produces repulsive forces leading to important effects. In the background universe, the effect of these forces is an accelerated expansion identical to that produced by vacuum energy (cosmological constant). Here, we prove that another of these effects arises for great enough collapsing masses which lead to Schwarzschild black holes and singularities in general relativity. For these masses, pressure becomes negligible against gravitational attraction, and the complete collapse cannot be stopped in the context of general relativity; however, in VTG, a strong gravitational repulsion could stop the falling of the shells toward the symmetry center. A certain study of a collapsing dust cloud is then developed, and in order to undertake this task, the VTG equations in comoving coordinates are written. In this sense, as it happens in general relativity for a pressureless dust ball, three different solutions are found. These three situations are analyzed, and the problem of the shell crossings is approached. The apparent horizons and trapped surfaces, the analysis of which will lead to diverse situations, depending on a certain theory characteristic parameter value, are also examined.