Gedanken experiments to destroy a black hole

Abstract

It is widely believed that the complete gravitational collapse of a body always results in a black hole (i.e., “naked singularities” can never be produced) and that all black holes eventually “settled down” to Kerr-Newman solutions. An important feature of the Kerr-Newman black holes is that they satisfy relation m 2 ⩾ a 2 + e 2 where m is the mass of the black hole, e is its charge, a = J m is its angular momentum per unit mass and geometrized units G = c = 1 are used. (For m 2 < a 2 + e 2 the Kerr-Newman solutions describe naked singularities.) In this paper, we test the validity of the above conjectures on gravitational collapse by attempting to create a spacetime with m 2 < a 2 + e 2 starting with a Kerr-Newman black hole with m 2 = a 2 + e 2. Such a spacetime would either have to be a new black hole solution or a “naked singularity,” in violation of the above conjectures. In the first gedanken experiment we attempt to make the black hole capture a test particle having large charge and orbital angular momentum compared with energy. In the second gedanken experiment we attempt to drop into the black hole a spinning test body having large spin to mass ratio. In both cases we find that bodies which would cause violation of m 2 ⩾ a 2 + e 2 will not be captured by the black hole, and, thus, we cannot obtain m 2 < a 2 + e 2, although we can come arbitrarily close in the sense that m 2 = a 2 + e 2 can be maintained in these processes.