Constraining the dynamics of rotating black holes via the principle of gauge symmetry

In 2015, the LIGO/Virgo experiment, a large-scale research effort based at two observatories in the United States, led to the first direct observation of gravitational waves. This milestone has since prompted physicists around the world to devise new theoretical descriptions of black hole dynamics, drawing on data collected by the LIGO/Virgo collaboration.

Researchers from Uppsala University, the University of Oxford and the University of Mons recently set out to explain the dynamics of Kerr black holes, theoretically predicted black holes that rotate at a constant speed, using the theory of high-spin massive particles. Their article, published in Physical Examination Lettersspecifically proposes that the dynamics of these rotating black holes are constrained by the principle of gauge symmetry, suggesting that certain changes in parameters of a physical system would have no measurable effect.

“We looked for a link between rotating Kerr black holes and massive higher-spin particles,” Henrik Johansson, co-author of the paper, told Phys.org. “In other words, we modeled the black hole as a rotating fundamental particle, in the same way that the electron is treated in quantum electrodynamics.”

The connection between Kerr black holes and higher spin theory was first explored in two separate papers published in 2019. The first of these studies was carried out by Alfredo Guevara of the Perimeter Institute for Theoretical Physics and his collaborators in Europe, while the second by Ming-Zhi Chung of National Taiwan University and colleagues at Seoul National University.

These two previous works showed that the well-known Kerr metric can be adapted to an infinite family of higher spin scattering amplitudes. These amplitudes were first obtained by physicists Nima Arkani-Hamed, Tzu-Chen Huang and Yu-tin Huang, in a previous study.

“While these previous results are remarkable, they are not yet sufficient to accurately describe the dynamics of Kerr black holes for future experiments, such as the Einstein Telescope, LISA and Cosmic Explorer,” Johansson said. “Some important missing information is contained in the Compton scattering amplitude of the black hole, which is currently unknown for general spin.”

In their paper, Johansson and colleagues suggest that the principle of gauge symmetry could be used to successfully constrain the dynamics of rotating black holes. The researchers showed that massive higher-spin gauge symmetry, informed by a mechanism first described by Ernst Stueckelberg and then formalized by Yurii Zinoviev, can be used to reproduce the Kerr scattering amplitudes reported in previous papers.

“We also showed that unknown Compton scattering amplitudes are severely constrained, although achieving uniqueness requires additional information,” Johansson said.

“High-spin quantum field theories (QFTs) are known for their complexity. Even low-spin QFTs, like the spin-1 case of the Standard Model and the spin-2 case of general relativity, are of course complicated, and their formulations are fundamentally based on gauge symmetry and diffeomorphism (general covariance) symmetry. These two symmetries can be considered as the two lowest rungs of an infinite scale called higher spin gauge symmetry.

Although gauge symmetry is not necessary to describe the dynamics of massive particles, it has proven to be a valuable tool for describing coherent interactions. One realization of this massive gauge symmetry is the so-called Higgs mechanism.

“By using massive higher spin gauge symmetry for black holes, we could ensure that the spin degrees of freedom are treated consistently and write an efficient Lagrangian,” Johansson explained. “The Lagrangian both gives the correct description of a higher spin of a Kerr black hole and has reasonably good behavior at high energies. Good behavior at high energies is not important for classical black holes , but it gives some confidence that the effective theory could also describe some quantum processes.

Johansson and his colleagues were the first to apply higher spin gauge symmetry to black holes. The results of their first calculations are promising and could soon pave the way for other studies exploring this link.

“Although we anticipate that it will be some time before the fully effective theory of black hole rotation is understood, we believe that higher-spin gauge symmetry will be an essential element in its formulation, in the same way that “Gauge symmetry and diffeomorphism symmetry guided the theoretical framework of 20th century physics,” Johansson said. “The full Compton scattering amplitude for a Kerr black hole remains enigmatic, but we have high hopes of being able to fully constrain it in the future. This involves both understanding it for arbitrary spin orders and for higher orders in Newton’s constant.”

Fully constraining the diffusion amplitude of Kerr black holes will ultimately require close collaboration between theoretical physicists studying massive, high-spin particles and those trying to solve the so-called Teukolsky equation, rooted in the theory of general relativity. . Recent collaborations between these distinct research communities suggest that progress may soon be made in this direction.

“In our next work, we would also like to deepen the connection between black holes and their quantum properties, which are reminiscent of elementary particles,” added Johansson.

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