A rotating universe outside a Schwarzschild black hole where spacetime itself non-uniformly rotates

TL;DR

This paper models a non-uniformly rotating universe outside a Schwarzschild black hole, revealing how time-dependent stresses influence spacetime rotation and violate energy conditions, with implications for understanding spacetime construction.

Contribution

It introduces a novel model of a non-uniformly rotating universe around a black hole using manifolds of revolution, linking stress-energy dynamics to spacetime rotation.

Findings

Time-dependent stress-energy causes spacetime shifts.

Model violates null energy condition.

Coordinate freedom relates to Schwarzschild solutions.

Abstract

We study a non-uniformly rotating universe outside a Schwarzschild black hole by generating a time-dependent manifold of revolution around a straight line. In this simple model where layers of spherical shells of the universe non-uniformly rotate, the Einstein field equations require this phenomenon to be caused by a static mass-energy distribution with time-dependent $T^{\phi\phi}$ (quadratic with time) and $T^{r\phi}=T^{\phi r}$ (linear with time). This indicates that a time-dependent stress along a certain direction results in a spacetime shift in that direction. For this model however, such material violates the null energy condition. Incidentally, the various coordinate systems describing the Schwarzschild solution can be viewed as arising from the freedom in parametrising the straight line and the radial function in the general method of constructing spacetime by generating manifolds of revolution around a given curve.