Black Hole Singularities Might Not Exist

New research suggests a black hole doesn’t have a point of infinite density.

Roy Kerr is a legend. Back in 1963, the highly decorated mathematician from New Zealand found an exact solution to the field equations for Einstein’s General Relativity. This solution was the first to model a realistic, rotating black hole accurately. The importance of this cannot be understated. The General Relativity field equations are notoriously complex, and exact solutions that work in the real world and not just on paper are exceedingly difficult to find.

In 2023, Kerr built on his groundbreaking work and challenged physics titans like Stephen Hawking and Roger Penrose. His new idea was that black holes do not contain singularities, the points of infinite density in their centers. This flies in modern cosmology’s face and leads to profound consequences.

From Einstein to Schwarzchild

Einstein completed General Relativity in 1915. Though controversial at first, General Relativity is humanity’s best gravitational theory. Put simply, it states that matter and energy warp spacetime, the four-dimensional fabric of the universe. The more matter or energy there is, the more spacetime is warped. Gravity, then, should not be considered a fundamental force like electromagnetism. Rather, matter and energy follow a path through curved spacetime, creating the appearance of a force. For example, Earth orbits the Sun because it follows a straight line path through the spacetime depression caused by the Sun’s mass.

Because time, of course, is a part of spacetime, it warps as well. For an observer in one reference frame, the measurement of time will be accurate but will differ from those in other reference frames. For example, if two people synchronize their clocks, and then one flies away in a rocket at half the speed of light, when this person returns to Earth, each will have measured different amounts of time. Time is not constant due to relativistic time dilation.

Within only a few months after Einstein published General Relativity, Karl Schwarzchild found the first exact solution to the field equations while fighting for the Germans on the Russian front during World War 1. He used a perfectly spherical, non-rotating, massive body and a static spacetime to accurately describe how spacetime warped around it. Though it uses unrealistic conditions, the Schwarzchild solution is still used today because of its simplicity.

An important consequence of the Schwarzchild solution is the Schwarzchild radius. This radius marks the event horizon of a black hole. With enough mass in a small enough area, spacetime will warp to the point that not even light can escape. For example, if the Sun were condensed into a point, it would have a Schwarzchild radius of 3 km. Inside this radius, it is impossible for anything to escape, as it would require traveling faster than the speed of light.

From Penrose to Hawking

In 1965, two years after Kerr found his exact solution to Einstein’s field equations with rotating bodies, British physicist and mathematician Roger Penrose published his paper “Gravitational Collapse and Space-Time Singularities.” In this paper, he demonstrated geometrically that singularities must exist in the center of a black hole. His reasoning was that “trapped surfaces inevitably lead to light rays of finite affine length.” In other words, light trapped behind a black hole’s event horizon must follow the geometry caused by ever-collapsing spacetime.

Stephen Hawking jumped on board in 1972. In his paper “Black Holes in General Relativity,” he echoed and built on Penrose’s ideas. He said, “the existence of a closed trapped surface implies the occurrence of a singularity under these conditions.”

Since then, both Penrose and Hawking, as well as numerous other physicists, developed an array of singularity proofs. These are lumped together under the Penrose–Hawking singularity theorems umbrella.

The Universe Hates Infinities

Infinity pops up frequently in math, but physicists struggle with it. Infinity doesn’t describe the real world, so physicists need to find clever methods of getting rid of it. For example, in quantum field theory, physicists regularly divide or subtract infinities of the same order to cancel them out. Though infinities appear as a natural consequence of the mathematics that describes the universe, physicists find it difficult to actually use them, as they don’t match observations.

So when infinities are used in physical descriptions of the universe, this should be a red flag. Kerr himself pointed this out in his criticism of black hole singularities. “The problem is that there is an infinity of possible solutions but their Einstein tensors do not necessarily satisfy appropriate physical conditions.” So yes, it works on paper, but it does not match reality.

In 2023, Kerr published “Do Black Holes Have Singularities?” In this paper, he takes direct aim at Penrose and Hawking. He criticized their assumption that spacetime geometry inside an event horizon inevitably results in a singularity. Rather, a singularity is only one of many possible solutions. “It has not been proved that a singularity, not just a FALL, is inevitable when an event horizon forms around a collapsing star.” FALL, or finite affine length light, refers to the idea that light rays within an event horizon are not infinite and must terminate.

He further claimed that rotating black holes might create layers. Outside the event horizon, the rotation contorts spacetime through frame dragging, creating the outer ergosphere, a dynamic region in which the laws of physics behave strangely. Below the ergosphere is the outer horizon, which corresponds to the event horizon or Shwartzchild radius. Inside the event horizon, are the inner horizon, outer ergosphere, and the ring singularity. Light rays, therefore, can exist in one or more of these layers, meaning they do not necessarily terminate. Kerr claimed that “The singularity believers need to show why it is true, not just quote the Penrose assumption.”

Black Holes and the Theory of Everything

In this model, there is no point singularity, eliminating problematic infinities. Without point-like black hole singularities, it might be easier to unite General Relativity and Quantum Mechanics. This is the fabled theory of everything,” aka the unified field theory. General Relativity explains gravity on a cosmic scale, while Quantum Mechanics explains the other three fundamental forces (the weak force, the strong nuclear force, and the electromagnetic force) on tiny scales. Both are wildly successful, yet they don’t work together, especially when it comes to black hole singularities. If Kerr is right and these singularities are not point-like, then problematic infinities might finally be removed from our models, perhaps paving the way for the theory of everything.