Here’s what you’ll learn when you read this story:

• Scientists have used math to show how neutron stars have a backward “time’s arrow.”
• This is likely because their incredibly strong gravity leads to gravitational entropy.
• Regular entropy pulls things apart, but gravitational entropy causes things to clump together.

Scientists in South Africa recently broke down the math of neutron stars and compared it to our existing paradigm for the forward-moving “arrow of time”—the idea that time moves consistently ahead, rather than backward or in any kind of looping or changing way. They found that in certain conditions, a neutron star’s specific, extremely high gravity turns this math inside out, creating a separate arrow of time traveling the opposite of its usual direction. When it comes to the math, at least, these neutron stars are collapsing backward in time. The researchers’ work appears now in the journal European Physical Journal C.

Their investigation focuses on what are known as epoch functions, which account for key aspects of spacetime. These functions also help to form our current understanding of time’s arrow by quantifying entropy, the breakdown of order over time. The scientists call out three parameters (well, one with two subtypes) in particular that make up these math problems:

The Ricci curvature scalar measures how local spacetime curvature differs from flat space and is an indication of the matter-energy content. The Ricci square helps describe how volumes deform and expand or contract along geodesics. The Kretschmann scalar allows for the detection of true singularities which are invariant to coordinate change. The Weyl tensor allows us to measure the distortion of spacetime due to tidal effects.

All that to say: These parameters help define how spacetime curves, contracts, deforms, and distorts in different contexts.

Cosmologists who study the tiny period of time directly after the Big Bang have long tried to reconcile the high entropy of the early universe with the fact that we still appear to be on the “later” end of time’s arrow today. Could the answer be that some pockets or processes have always been winding the clock back, so to speak?

To investigate, the researchers basically chose to set two different ends of math equations opposite each other: epoch functions of gravitational collapse, and epoch functions of spacetime curvature and structure. The researchers loosely modeled these functions on recent work where other scientists used spacetime curvature “as a probe to study exotic phases in neutron stars.”

Neutron stars are unusual compared to the bulk of the observed universe. In fact, in many ways, they behave more like black holes than what they actually are: the cores of dead stars. You could walk across a neutron star’s width in a couple of hours, but it would still have a larger mass than the Sun.

When actively collapsing, neutron stars are called “unstable,” referring to their energy state. In this study, the scientists set up a model spacetime and (mathematically) placed an unstable neutron star inside in order to calculate out the Ricci, Ricci squared, Kretschmann, and Weyl values over time. They found that the epoch functions that included these values “clearly decrease monotonically as the collapse progresses,” indicating that entropy is decreasing locally.

That may not sound like much on the surface, but decreasing entropy is one way to say that time, as we conceive of it, is moving backward. It’s like the collapsing neutron star is neatly sucking toothpaste back into the tube, to use one famous example.

The researchers wrote that this result was expected intuitively, because “[g]ravitational entropy favors clumping of matter, whereas the usual matter entropy favors dispersion.” Gravitational entropy is a newer idea that gravity—instead of being a predictable fundamental force—results from entropy slowly throwing everything in the universe into more and more disorder. The two types of entropy (one which clumps and one which disperses), then, are in a tension that changes when the gravity is stronger or weaker.

The scientists concluded their paper by noting that their work is meant as a continuation and stepping stone in cosmology’s ongoing quest to quantify different gravities and curvatures. Each new setup that we study helps to unlock some broader idea that can hopefully be applied to future research and keep the process moving forward—a proverbial time’s arrow in itself.