Isoperimetric inequalities for sectors in the Minkowski 2-spacetime

Abstract

In the Minkowski 2-spacetime $$\mathbb{L}^2 $$ the hyperbolic angle is defined by the hyperbolic parametrization of the plane. With this notion of hyperbolic angle Helzer obtained a relativistic version of Gauss-Bonnet formula (cf. [3]). In this paper, we derive an isoperimetric inequality for timelike sectors in $$\mathbb{L}^2 $$ bounded by an achronal spacelike curve and two timelike rays from a point using this Gauss-Bonnet formula.