A ‘naked singularity’ problem that vexed Stephen Hawking takes a step closer to reality
A new theoretical study lends new support to the idea that mathematical patterns of ripples in the space-time geometry could give rise to naked singularities and microscopic black holes. The new discovery advances research on a topic that has puzzled physicists for decades.
in 1997, Stephen Hawking Famously admitted defeat on a bet with fellow theoretical physicists in 1991 kip thorne And John Preskill About the possible existence of naked singularities: black hole-like objects but without an event horizon (a point beyond which light and all other matter cannot escape), which makes them observable. Hawking finally acknowledged that such objects could exist. Thorne and Preskill’s prize? T-shirts to cover their “nudity”.“
Evidence implicating Hawking comes from physicist Matthew Choptuik. In 1993, Choptuik studied a specific set of solutions to Albert Einstein’s general relativity equations. When solved numerically, what was then considered a supercomputer showed how Naked Singularities Can Hypothetically Occur Under very specific circumstances.
Choptuik discovered that by modeling the gravitational collapse of a simple substance such as a sphere and fixing the initial conditions, an unstable state could be created. This theoretical situation later became known as a space-time crystal – a self-organized repeating mathematical pattern of waves in space-time geometry – that consists of a singularity with infinite curvature (a naked singularity). Because such a singularity would not form inside a black hole, it could theoretically be observable.
But like the phase transition from liquid water to ice, this state is also delicate, with the region teetering on the edge between becoming a void or a microsphere. black hole.
However, significant doubt remains about the existence of such a state even in theory.
“Whenever you build a system in numerical code, you always have a problem because you can only represent a limited number of digits on a computer,” said the study’s co-authors. Christian Ackeran astrophysicist at Goethe University in Germany told Live Science. “Historical computer simulations could only go so far before inaccuracies became inevitable.”
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Although recent numerical methods provide much greater accuracy, they are imprecise and can never provide the deep understanding of a phenomenon that traditional analytical methods (such as manipulating equations using algebra and calculus) provide.
In a new study published on May 12 in the journal physical review paperResearchers mathematically accurately described the formation of space-time crystals, naked singularities and microscopic black holes.
An illustration of the space-time “crystal” (left) compared to the natural crystal lattice (right).
(Image credit: TU Wien)
A pen and paper solution
They succeeded using only pen and paper and some mathematical sleight of hand. “Whenever physicists find a small parameter, they are happy because they can first solve the equations when this parameter is zero, then add small improvements to it with standard perturbation theory,” co-authors Daniel Grumilleran astrophysicist at the Institute for Theoretical Physics at the Vienna University of Technology told Live Science. “general relativity There is no small parameter in itself, but if you inject a small parameter [one over the number of dimensions and let this number be huge]…So you can use these trouble-shooting tools and get a handle on otherwise very difficult equations.”
Considering the number of dimensions to be infinite, the team’s exact solution could fit in only a few lines. This solution is unrealistic because we are definitely not living in infinite dimensional universe. However, as they brought the number of dimensions down to more realistic numbers, the solution required additional terms which made the expressions more complex.
“The lowest dimension we can consistently connect to so far is 52, but the numerical data only extend to dimension 14 – so there is a gap,” Grumiller said, referring to the fact that neither pen and paper nor numerical techniques are yet precise enough to cross paths.
“In the future, we plan to extend the numbers to higher dimensions, so we can really connect the two,” Grumiller said.
Doing so would provide a compelling case that space-time crystals, naked singularities and microscopic black holes are mathematically possible in a universe like ours – however, it still would not prove that they actually exist. In the end, Hawking may have provided those T-shirts too soon.
Aaker, C., Aaker, F., and Grumiller, D. (2026). Analytic discrete self-similar solutions of large-scale Einstein–Klein–Gordon. physical review paper, 136(19), 191401. https://doi.org/10.1103/qgl5-5l3t
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