On the Bergqvist Approach to the Penrose Inequality

Abstract

The Penrose inequality in terms of the Bondi mass at past null infinity can be approached with a method due to Ludvigsen and Vickers and clarified later on by Bergqvist (Ludvigsen and Vickers, J. Phys. A: Math. Gen. 16:3349–3353, 1983; Bergqvist, Class. Quantum Grav. 14:2577–2583, 1997). In this work, we apply the method to the special case of null shells of dust collapsing in a four-dimensional Minkowski background (Penrose construction, 1973). Our main conclusion is that the class of surfaces covered by the method is severely restricted. We provide afterwards a wide family of surfaces satisfying the Penrose inequality which includes the ones determined by the Bergqvist method.