Einstein's equations reveal how gravity could break, reconnect, and release energy

Physicists Luca Comisso of Columbia University and Felipe A. Asenjo of Universidad Adolfo Ibáñez in Chile have calculated that gravitational fields may break and reconnect under certain conditions, much like the magnetic fields that drive solar flares. They call the process gravitational reconnection and say it would let energy flow from the gravitational field into matter. The work comes more than 100 years after Albert Einstein developed his theory of gravity. Comisso is an associate research scientist in Columbia's Departments of Astronomy and Physics and the Columbia Astrophysics Laboratory. He and Asenjo reexamined Einstein's equations using a mathematical formulation that reveals similarities between gravity and electromagnetism. They then asked what happens when the conditions that keep gravitational field connections intact break down. Under certain circumstances, they found, the fields can reconnect in new configurations.

Comisso stressed that this is not new physics. "We are not modifying general relativity or introducing new physics beyond it," he said. "Rather, we are identifying physical principles that have remained unrecognized for more than a century." On the Sun, magnetic field lines thread through electrically charged gas called plasma. They can be pulled, twisted and stretched. Sometimes they snap and reattach in a different pattern, a process called magnetic reconnection that powers solar flares. Gravity works in four-dimensional spacetime, made of three dimensions of space and one of time. So the researchers describe it with field "sheets" rather than lines. "Adding one dimension to a line gives you a plane," Comisso explained. The sheets are a mathematical picture, not physical surfaces that literally tear. Their reconnection describes a way for the gravitational field to hand energy to matter.

The pair built on an earlier paper written with a third physicist, Maricarmen A. Winkler of Adolfo Ibáñez University. Those calculations showed that gravitational fields can behave as though their connections are frozen in place, preserving links between regions as spacetime evolves. That mirrors magnetic fields in plasma, where field lines stay connected even as the plasma flows. Since magnetic connections can eventually break, the team tested whether gravity's could too. Comisso said the team had suspected some overlap, since Einstein's equations can be rewritten in forms resembling those of electromagnetism. "However, we did not know how far this analogy would extend," he said. The answer came only after working through the calculations "step by step at the blackboard," he said, when they realized how closely gravitational fields could follow the principles that govern magnetic fields in plasmas.

Researchers believe the connection could give new insight into gravity under extreme conditions, including collisions between black holes. In regions where gravity severely distorts spacetime, even the most powerful computer simulations are hard to interpret. The approach could help scientists identify fundamental rules governing gravitational fields in those regions. The study, "Reconnection of Gravitational Fields," was published in the journal Physical Review D. It develops earlier work by Comisso, Asenjo and Winkler in Physical Review Letters, in which the scientists identified mathematical constraints on possible changes in the geometry of spacetime. The alternative mathematical formulation of Einstein's equations is equivalent to the original one, but it resembles equations from plasma physics. This makes it possible to apply approaches developed for studying magnetic fields to identify patterns in the behavior of gravitational fields without necessarily carrying out a full numerical calculation for every system. One possible direction for further work is collisions and mergers of black holes, when spacetime undergoes extreme distortions. Such processes are modeled on supercomputers to predict gravitational waves, which can be detected, among other instruments, by LIGO. The researchers plan to determine whether gravitational reconnection can leave recognizable signatures in gravitational-wave signals and how it affects energy release. For now, gravitational reconnection remains a theoretical result: its operation under astrophysical conditions and the possibility of observing it still need to be established.