In a simulation of the universe without commonly made simplifications, galaxy profiles float atop a grid representing the spacetime background shaped by the distribution of matter. Regions of blue color contain more matter, which generates a deeper gravitational potential. Regions devoid of matter, darker in color, have a shallower potential. Image credit: James Mertens

If you want to calculate how gravity shapes the universe, then Einstein’s got the equations for you—he set them down 100 years ago in his masterpiece, the general theory of relativity. But there’s a catch: Those equations are notoriously difficult to solve. And so, over the last century, physicists have had to rely on various approximations and simplifications when applying the theory to specific problems. Now, for the first time, physicists have been able to program a computer to use the “full” version of Einstein’s theory. The programs will be able to describe how matter and curved space-time interact more precisely than ever before.

“The problem with the general relativity equations is that they’re incredibly complicated,” Glenn Starkman, a physicist at Case Western Reserve University in Cleveland, Ohio, tells mental_floss. Those equations, known as “field equations,” model something called the “metric,” which describes the geometry of space-time through a set of 10 independent functions, Starkman explains. “In general, you can’t solve them with paper and pencil.”

Of course, computers didn’t exist in Einstein’s day. But even after the advent of the electronic computer, it was a challenge to model realistic problems in physics and cosmology using general relativity (a technique called “numerical relativity”). Traditionally, physicists found two strategies for working around the problem: They could make simplifying assumptions about the system being studied (as an old physics joke puts it, “assume the cow is a sphere”)—or they could use simplified versions of the equations. Either way, the results will only be an approximation of reality.

For certain kinds of problems, physicists could also reach back to Newton’s equations for gravity, which are much simpler than those of Einstein. This was the approach often taken by those studying the evolution of galaxies and clusters of galaxies, Starkman says, “But what you really want to do is to take the full equations [of general relativity], and use a computer to solve them, without simplifying assumptions. Until now, no one has been able to do that.”

Now two teams of physicists, working independently, have written computer programs that can handle “full general relativity.” One team includes Starkman and James Mertens, a Ph.D student at Case Western, along with John Giblin of Kenyon College. Soon after they posted their work online last fall, a second, similar paper was posted by Marco Bruni of the University of Portsmouth in England and Eloisa Bentivegna of the University of Catania in Italy. Papers from the two groups appear in the June 24 issue of Physical Review Letters (here and here), with a second paper by the U.S. group in Physical Review D.

These new programs will help physicists develop models of the universe’s evolution, including its overall expansion and the formation of the first structures, both of which are governed by the force of gravity. The programs will also help to model how light propagates through matter over cosmological distances—which bears directly on what astronomers will be able to observe though their telescopes.

Both teams’ computer programs will be made available online for other researchers to work with, and to improve.

The new computer methods will serve as a “powerful tool” that will allow physicists to apply numerical relativity to cosmology, physicist Stuart Shapiro of the University of Illinois at Urbana–Champaign said in a statement to mental_floss. (Shapiro was not involved in the research.) Although the earlier, approximate methods were adequate for many applications, there are certain problems “which do require the full theory of general relativity,” he says, including the formation of structure in the early universe and the study of black holes. These new computational tools “may lead to significant new results in the future.”

There’s still more work that needs to be done, says Starkman. First, the programs need to be further developed; he describes them as a “proof of concept” at this stage. Second, physicists will have to use the new programs to model specific physical systems, and make predictions that astronomers can actually test against observation.

Even at this early stage, however, it’s clear that 2016 has been a very good year for Einstein’s theory. In February, physicists announced they'd observed gravitational waves for the first time, verifying the last outstanding prediction of general relativity. While it’s a coincidence that the two breakthroughs happened within a few months of each other, it’s a fitting tribute to Einstein’s legacy, Starkman says. “Everything seemed to come together to make these things possible, technologically, at about the same time—and it’s exciting that it coincides with the centenary.”