NOTE Black hole formation by incoming electromagnetic radiation

Abstract. I revisit a known solution of the Einstein field equations to show that it describes the formation of non-spherical black holes by the collapse of pure electromagnetic monochromatic radiation. Both positive and negative masses are feasible without ever violating the dominant energy condition. The solution can also be used to model the destruction of naked singularities and the evaporation of white holes by emission or reception of light. PACS numbers: 04.70.Bw, 04.40.Nr, 04.20.Jb Today there are many models describing the formation, or the evaporation, of black holes in General Relativity, some of them deal with the collapse of matter or fluids, others with out- or in-coming “incoherent radiation”. However, there is no identified case of the formation/evaporation of a black hole by means of electromagnetic radiation solely. The purpose of this sort Note is to call attention to a family of solutions which describe the formation/destruction of black holes (also naked singularities) by reception or emission of pure monochromatic light. Actually, the solution is known since long ago, and has been used to describe the collapse of null dust to non-spherical black holes with negative cosmological constant [13, 14], and to analyze the first example of a dynamical horizon with toroidal topology [5]. However, the fundamental point is that the radiation can be properly identified as monochromatic light —it should not be treated as “incoherent radiation”. The line-element of the solution was first presented —among many other exact solutions — by Robinson and Trautman in their celebrated paper [22], and is given in local coordinates {u, r, x, y} by (see also [24], p.430) ds2 = r2(dx2 + dy2) + 2dvdr