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In a detailed universe simulation that avoids typical simplifications, galaxy profiles are depicted on a grid illustrating the spacetime fabric influenced by matter distribution. Areas shaded in blue indicate higher matter density, creating stronger gravitational fields, while darker regions with less matter exhibit weaker gravitational effects. Credit: James Mertens
To understand how gravity influences the universe, Einstein's equations from a century ago, detailed in his groundbreaking general theory of relativity, are indispensable. However, these equations are notoriously complex to solve. Consequently, physicists have historically relied on approximations and simplifications. For the first time, researchers have successfully programmed a computer to utilize the complete version of Einstein's theory, enabling more accurate descriptions of the interactions between matter and curved spacetime.
“The complexity of general relativity equations is immense,” says Glenn Starkman, a physicist at Case Western Reserve University in Cleveland, Ohio, in an interview with mental_floss. These equations, referred to as “field equations,” describe the “metric,” which outlines the geometry of spacetime using ten independent functions. Starkman notes, “Typically, solving them manually is impossible.”
Computers were nonexistent during Einstein's era. Even after their invention, applying general relativity to realistic physics and cosmology problems—known as “numerical relativity”—remained challenging. Physicists traditionally employed two approaches: simplifying assumptions about the system (famously joked as “assuming the cow is a sphere”) or using reduced versions of the equations. Both methods, however, only yield approximations of reality.
For specific types of challenges, physicists have also relied on Newton's gravitational equations, which are far simpler than Einstein's. This method was frequently used by researchers examining the development of galaxies and galaxy clusters, Starkman explains. “However, the ultimate goal is to utilize the complete equations of general relativity and solve them computationally without any simplifications. Until recently, this had not been achieved.”
Two separate teams of physicists have now developed computer programs capable of handling “full general relativity.” One team comprises Starkman and James Mertens, a Ph.D. student at Case Western, alongside John Giblin from Kenyon College. Shortly after they published their findings online last autumn, a second, similar study was released by Marco Bruni of the University of Portsmouth in England and Eloisa Bentivegna of the University of Catania in Italy. Both groups' papers were featured in the June 24 edition of Physical Review Letters (here and here), with a follow-up paper by the U.S. team in Physical Review D.
These innovative programs will enable physicists to create models of the universe's evolution, encompassing its overall expansion and the formation of initial structures, both driven by gravitational forces. Additionally, they will assist in simulating how light travels through matter across vast cosmic distances—directly impacting what astronomers can observe through their telescopes.
Both teams plan to make their computer programs accessible online for other researchers to utilize and enhance.
The new computational approaches will act as a “powerful tool,” enabling physicists to apply numerical relativity to cosmology, according to physicist Stuart Shapiro from the University of Illinois at Urbana–Champaign in a statement to mental_floss. (Shapiro was not part of the research.) While earlier approximation methods sufficed for many applications, certain issues, such as the formation of early universe structures and black hole studies, “demand the complete theory of general relativity,” he notes. These advanced tools “could pave the way for groundbreaking discoveries in the future.”
Starkman emphasizes that additional efforts are required. Initially, the programs must undergo further refinement; he currently regards them as a “proof of concept.” Subsequently, physicists will need to employ these tools to simulate specific physical systems and generate predictions that astronomers can validate through observations.
Despite being in its early phases, 2016 has undeniably been a remarkable year for Einstein’s theory. In February, physicists revealed the first detection of gravitational waves, confirming the final unverified prediction of general relativity. Although the timing of these two breakthroughs is coincidental, Starkman notes that it serves as a fitting homage to Einstein’s enduring legacy. “Technological advancements aligned perfectly to make these discoveries possible around the same time—and it’s thrilling that this coincides with the theory’s centennial.”
