GRG Editor's Choice: A toy Penrose inequality and its proof

© SpringerBengtsson, I. & Jakobsson, E., A toy Penrose inequality and its proof, Gen Relativ Gravit (2016) 48: 156. doi:10.1007/s10714-016-2155-x

Open Access | Editor's Choice (Research Article)

First Online: 07 November 2016

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.


We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: a shell of null dust collapses in Minkowski space and a marginally trapped surface forms on it. Through a series of arguments relying on established assumptions, an inequality relating the area of this surface to the total energy of the shell is formulated. Then a further reformulation turns the inequality into a statement relating the area and the outer null expansion of a class of surfaces in Minkowski space itself. The inequality has been proven to hold true in many special cases, but there is no proof in general. In the toy version here presented, an analogous inequality in (2 + 1)-dimensional anti-de Sitter space turns out to hold true.