Black Hole Shrinks in an Expanding Universe express

Original: "Gravitational Field of a Rotating Mass on an Expanding Universe"
· Antonio Peña Peña
arXiv:2605.22895 · 2026-05-21 · CC BY 4.0 · 1 min
A new solution to Einstein's equations combines a rotating black hole with cosmic expansion.

📄 Showing the "Simple" version — "Advanced" is not ready yet. Add it to favorites to help prioritize it.

Imagine an air mattress being stretched, with a whirlpool of water spinning on it. As you stretch, the whirlpool tightens: its size relative to the whole surface shrinks. That's exactly how a rotating black hole behaves in an expanding universe: its event horizon (the boundary of no return) and ergosphere (the twisted region of space) gradually shrink, even though the mass stays the same.

For the first time, physicists have mathematically combined the description of a rotating hole with the expanding cosmos model created by Friedmann and Lemaître. Previously, this was only possible for static holes. A surprising result: dark energy, discovered by Adam Riess, is indifferent to the furious spin: it continues to stretch spacetime without noticing the vortex. It's as if stretching the mattress doesn't care whether water is spinning on it or not.

Original abstract

as written by the authors arXiv:2605.22895

We present a new exact solution to Einstein's field equations that unifies the Kerr black hole with Friedmann-Lema\^itre-Robertson-Walker cosmology. This metric reduces to Kerr-de Sitter in the appropriate limit and accounts for cosmological expansion dynamics both inside and outside the black hole. The model predicts a stationary mass, as well as a contracting ergosphere and event horizon with respect to the expanding cosmic rest frame. This result correctly generalises the McVittie metric to rotating masses or Kerr-de Sitter to arbitrary scale factors $$a(t)$$. Additionally, we find that the ergosphere tends to fade away with respect to the universe's expansion and no further interactions of dark energy with respect to the black hole's rotation.

The shrinking event horizon works like a patch on an air mattress: when the fabric stretches, the patch tightens but the thread stays intact.

Sci-fi writers imagine black holes as portals, but in this work, they are merely obedient objects, shrinking in the swelling cosmos.

Scientists
Roger PenroseStephen HawkingJacob BekensteinJosef LenseVera RubinFritz Zwicky
Concepts
kerr metric kerr black hole rotating black hole de sitter space Einstein field equations schwarzschild metric gravitational field general relativity classical gravity Birkhoff's theorem fr gravity newtonian limit anti de sitter space Wheeler-DeWitt equation horizon area geodesic equation gravitational radius equivalence principle wald entropy charge to mass ratio