Asymptotically Conically Minkowskian spacetimes from self-gravitating dust

Abstract

In this work we investigate some non-Newtonian effects in exact solutions of the Einstein equations, which describe stationary and axisymmetric configurations of self-gravitating dust. A distinctive feature of these solutions is the potential presence of conical singularities along the rotation axis, manifesting as angular deficits. While such singularities can be removed by imposing suitable boundary conditions along the axis, asymptotically far away from it the geometry becomes locally flat, in the sense that the Riemann tensor vanishes, but globally, instead of reducing to Minkowski space, it takes the form of a cone. We refer to these spacetimes as Asymptotically Conically Minkowskian (ACM). We show that such conical structure can originate some interesting effects as seen by asymptotic local observers. These include modifications to the gravitational lensing and the misinterpretation of the vacuum state of a scalar field as a distribution of scalar particles.