A new exact solution of Einstein's equations is presented, unifying the Kerr metric of a rotating black hole with the Friedmann–Lemaître–Robertson–Walker cosmological model. In the appropriate limit, this metric reduces to the Kerr–de Sitter solution and describes the dynamics of cosmological expansion both inside and outside the black hole. The model predicts a stationary mass, as well as the contraction of the ergosphere and event horizon relative to the expanding cosmological rest frame. The constructed solution generalizes the McVittie metric to the case of rotating masses, or the Kerr–de Sitter metric to an arbitrary scale factor a(t). It is found that the ergosphere tends to disappear as the universe expands, without any additional interaction between dark energy and the black hole's rotation occurring.
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.
🎯 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.