Einstein's Equations May Hide Gravitational Reconnection, a Theoretical Energy-Release Process Akin to Solar Flares

Two physicists, working from an unusual angle on equations that are more than a hundred years old, say they have found something in them that no one had named: a process they call gravitational reconnection. Luca Comisso, an associate research scientist in Columbia University's Departments of Astronomy and Physics and the Columbia Astrophysics Laboratory, and Felipe A. Asenjo of Universidad Adolfo Ibáñez in Chile describe it as a way for structures in a gravitational field to break apart and rejoin, passing energy into matter as they do.

The idea borrows from the Sun. Magnetic reconnection is the process behind solar flares. In a plasma, a gas of electrically charged particles, magnetic field lines get pulled, twisted and stretched. Under the right conditions their connections suddenly change, and the energy stored in the field is released into the surrounding particles. Comisso describes it as field lines that break and reattach in a different configuration, taking energy from the magnetic field and handing it to the particles, which produces explosions and energetic events. It ranks among the most important ways the universe releases energy.

Gravity, the researchers argue, may have an analogue. The catch is geometry. Gravity lives in Einstein's four-dimensional space-time, three dimensions of space plus one of time, so its mathematical structure differs from that of an ordinary magnetic field. Comisso says that extra dimension turns lines into something more like sheets: add a dimension to a line and you get a plane, many lines stacked together. These sheets can rearrange their connections the way magnetic field lines do. They are mathematical representations, not physical surfaces that literally tear.

Getting there required rewriting Einstein's equations. Physicists in recent years developed a formulation that uses different variables but is mathematically equivalent to the original and describes the same physics. Its form resembles the equations used to study plasmas, the material of the Sun, of fusion experiments and of much of the space between stars. Comisso has spent his career on plasma behavior, and he and his colleagues saw that methods built for magnetic fields could expose overlooked properties of gravitational ones. As he puts it, some implications are hidden in the equations, and you have to rewrite them to exploit that behavior.

The new paper, "Reconnection of Gravitational Fields," appeared in Physical Review D. It extends an earlier study in Physical Review Letters by Comisso, Asenjo and Maricarmen A. Winkler, which identified mathematical constraints on which changes in the geometry of space-time are possible. Those restrictions are built into Einstein's theory but had not been recognized in that form. Asenjo says that revealing these hidden properties lets researchers begin to understand the rules governing how gravitational reconnection behaves. In the latest work, Comisso and Asenjo asked what happens when the ideal conditions that normally preserve connections within gravitational structures stop holding. Their answer is that the connections can change.

The practical appeal is for places where gravity is hardest to model. When two black holes merge, space-time is severely distorted, and astrophysicists usually turn to supercomputer simulations: set the initial conditions, calculate the evolution, examine the result. Those simulations help predict the gravitational waves, ripples in space-time, that instruments such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) detect. The new rules could complement that work. Comisso says they help predict patterns of space-time, because even without the full calculation, space-time has to satisfy certain constraints.

For now, this is theory. Scientists have not established how gravitational reconnection operates in real astrophysical settings, or whether its effects can be observed at all. The next step is to study it in specific situations, especially merging black holes. Comisso hopes eventually to estimate how much energy such events release and to learn whether reconnection leaves recognizable signatures in gravitational wave signals. The work was supported by the National Science Foundation and NASA.