We Understand Rotating Black Holes Even Less Than We Thought

Black holes are real. We see them throughout the cosmos, and have even directly imaged the supermassive black hole in M87 and our own Milky Way. We understand black holes quite well, but the theoretical descriptions of these cosmic creatures still have nagging issues. Perhaps the most famous issue is that of the singularity. According to the classical model of general relativity, all the matter that forms a black hole must be compressed into an infinite density, enclosed within a sphere of zero volume. We assume that somehow quantum physics will avert this problem, though without a theory of quantum gravity, we aren’t sure how. But the singularity isn’t the only infinite problem. Take, for example, the strange boundary known as the Cauchy horizon.

When you get down to it, general relativity is a set of complex differential equations. To understand black holes, you must solve these equations subject to a set of conditions such as the amount of mass, rotation, and electromagnetic charge. The equations are so complex that physicists often focus on connecting solutions to certain mathematical boundaries, or horizons. For example, the event horizon is a boundary between the inside and outside of a black hole. It’s one of the easier horizons to explain because if you happen to cross the event horizon of a black hole, you are forever trapped within it. The event horizon is like a cosmic Hotel California.

For a simple, non-rotating black hole, the event horizon is the only one that really matters. But for rotating black holes, things get really weird. To begin with, the singularity becomes a ring, not a point. And rather than a single event horizon, there is an outer and an inner horizon. The outer one still acts as an event horizon, forever trapping what dares to cross its boundary. The inner one is what’s often called the Cauchy horizon. If you cross the inner horizon, you are still trapped within, but you aren’t necessarily doomed to fall ever closer toward the singularity. Within the Cauchy horizon, spacetime can behave somewhat normally, though it is bounded.

The Cauchy horizon can cause all sorts of strange things, but one of them is that the horizon is unstable. If you try to determine perturbations of the horizon, the calculated mass within the horizon diverges, an effect known as mass inflation. It’s somewhat similar to the way the singularity approaches infinite density in the classical model. While this is frustrating, physicists can sweep it under the rug by invoking the principle of cosmic censorship. It basically says that as long as some basic conditions hold, all the strange behaviors like singularities and mass inflation are always bounded by an event horizon. There may be an infinity of mathematical demons in a black hole, but they can never escape, so we don’t really need to worry about them.

But a new paper may have handed those demons a key. The paper shows that mass inflation can occur even without a Cauchy horizon. Without an explicit Cauchy horizon, those basic conditions for cosmic censorship don’t necessarily apply. This suggests that the black hole solutions we get from general relativity are flawed. They can describe black holes that exist for a limited time, but not the long-lasting black holes that actually exist.

What this means isn’t entirely clear. It might be that this impermanent loophole is just general relativity’s way of pointing us toward a quantum theory of gravity. After all, if Hawking radiation is real, all black holes are impermanent and eventually evaporate. But the result could also suggest that general relativity is only partially correct, and what we need is an extension of Einstein’s model the way GR extended Newtonian gravity. What is clear is that our understanding of black holes is incomplete.

Reference: Carballo-Rubio, Raúl, et al. “Mass inflation without Cauchy horizons.” Physical Review Letters 133.18 (2024): 181402.

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