Simulations unveil the electrodynamic nature of black hole mergers and other spacetime collisions

Gravitational waves are energy-carrying waves produced by the acceleration or disturbance of massive objects. These waves, which were first directly observed in 2015, are known to be produced during various cosmological phenomena, including mergers between two black holes that orbit each other (i.e., binary black holes).

Studying gravitational waves can offer valuable insight about gravity, the fundamental force described by Einstein’s general relativity theory. General relativity frames gravity as the curvature of spacetime prompted by mass and energy.

Past research showed that when gravitational effects are particularly pronounced (i.e., in strong-field regimes such as associated with binary black hole mergers) gravity becomes non-linear. Shedding more light on these nonlinear dynamics can help to test and improve existing theories of gravity.

Researchers at California Institute of Technology performed new simulations that frame gravity using Maxwell equations, equations that are typically used to study electromagnetism, instead of conventional general relativity equations.

Their paper, published in Physical Review Letters, introduces a new promising approach to study the gravitational dynamics of binary black hole mergers and other spacetime collisions.

“Our research was inspired by two things,” Elias R. Most, senior author of the paper, told Phys.org.

“In the context of predicting radio transients to merging compact objects, such as neutron stars and black holes, we have done extensive work on regular electric and magnetic fields around black holes, simulated their dynamics, and gained a very good understanding of how they behave.

“At the same time, gravity has always been somewhat mysterious, at least in its common form, lacking the ability for easy visualization, as is common especially for magnetic fields.”

The recent work by Most and his colleagues builds on the idea that gravity can also be expressed in ways that resemble how physics theory describes electric and magnetic fields.

The researchers thus set out to use equations describing electromagnetism, so-called Maxwell equations, to understand gravitational dynamics in strong-field regimes. Their hope was to reach the same level of understanding as that they achieved in earlier studies focusing on radio emission.

“The simulations we ran are based on a common methodology to visualize Einstein’s equations of general relativity on a computer,” explained Most.

“These simulations are intrinsically challenging and were developed by the community over the past 50 years. The main novelty we brought to the table was the ability to completely reinterpret these simulations in ways analogous to electrodynamics. That is, we use the expressions we had derived and reinterpreted the simulations.”

Using their proposed methodology, the researchers were able to compute the electric and magnetic field associated with gravity based on existing simulation data. Interestingly, their simulations showed that general relativity theory can in fact be studied using equations that describe electromagnetism.

“Our work has already taught us how to reinterpret particle trajectories and curved space,” said Most. “It also helped a lot with clarifying the onset of nonlinearity (where strong gravity dominates).”

In the future, the recent study by Most and his colleagues could open new possibilities for research aimed at testing specific aspects of general relativity theory or nonlinear gravitational dynamics. In their next studies, the researchers plan to build on their simulations to explore the turbulence-like aspects of gravitational waves.

“In essence, gravitational waves are unlike regular beams of light,” explained Most.

“When they pass through each other they can (under certain conditions) interact. This interaction can resemble turbulence in the atmosphere, but it is hard to describe mathematically. On the other hand, for some regimes of electrodynamics, it is a well-known and studied phenomenon.

“Using our approach above, we were able to show that the same mathematical formulations underpinning turbulence with regular magnetic fields, apply also to gravitational waves, which is a very nontrivial insight. In the upcoming months, we plan to further investigate gravitational wave nonlinearity.”

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