Rotating, stationary, axially symmetric spacetimes with collisionless matter

TL;DR

This paper proves the existence of axially symmetric, rotating solutions to the Einstein-Vlasov system, providing models for rotating, asymptotically flat spacetimes with non-zero angular momentum.

Contribution

It demonstrates the existence of stationary, rotating solutions with non-zero angular momentum in the Einstein-Vlasov system, handling singularities via a novel recasting method.

Findings

Existence of stationary axially symmetric solutions with angular momentum.

Efficient handling of singular elliptic equations on the rotation axis.

Mathematical models for rotating relativistic spacetimes.

Abstract

The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on $\R^5$.