Matter-Spacetime Coupling: New Ways To Understand Fundamental Physics Emerge

The interplay between gravity, electromagnetism, and the intrinsic angular momentum of matter remains a central challenge in theoretical physics. Recent research explores a specific geometric framework, Riemann-Cartan geometry, which extends general relativity by incorporating torsion, a measure of spacetime’s twisting, and investigates its consequences for black hole solutions. Sebastian Bahamonde, from the Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, and Jorge Maggiolo, from Pontificia Universidad Católica de Valparaíso, alongside Christian Pfeifer and colleagues from ZARM, University of Bremen, present their findings in the article, “Coupling Electromagnetism to Torsion: Black Holes and Spin-Charge Interactions”. Their work details how coupling the electromagnetic field to spacetime torsion modifies the characteristics of black holes, potentially allowing for effective charges that are not strictly positive and revealing novel interactions between electric charge and intrinsic spin.

Researchers are investigating modifications to general relativity by incorporating torsion, a geometric property stemming from the antisymmetric component of the affine connection, and its potential interaction with electromagnetism. This pursuit arises from theoretical inconsistencies within the standard model and a desire for a more complete description of gravity, particularly in extreme gravitational environments such as those surrounding black holes. By examining non-minimal couplings between the electromagnetic field and spacetime geometry, scientists aim to uncover novel interactions that could fundamentally alter our understanding of these objects and their influence on the universe. This work centres on Riemann-Cartan geometry, which permits the inclusion of torsion while remaining compatible with the metric tensor, providing a natural framework for exploring these interactions.

The study establishes a connection between Riemann-Cartan geometry and solutions to the Einstein-Maxwell field equations, a set of equations describing the interplay between gravity and electromagnetism. Researchers derive a generalized Reissner-Nordström black hole solution—representing a charged, non-rotating black hole—by allowing a non-minimal coupling between the electromagnetic field strength tensor and the antisymmetric part of the Ricci tensor. The Ricci tensor, a key component of the Einstein field equations, describes the curvature of spacetime. This coupling introduces new terms into the field equations, modifying the gravitational interaction experienced by charged particles and altering the spacetime geometry around the black hole.

This generalized solution reveals that the effective charge of the black hole is not necessarily positive, a significant departure from the standard Reissner-Nordström solution where charge is always positive. Researchers demonstrate that the sign of the electric charge influences its gravitational effects, meaning a negatively charged black hole would exhibit different gravitational behaviour compared to a positively charged one. This finding has profound implications for our understanding of black hole formation, evolution, and their interactions with surrounding matter and energy. The study further explores the physical implications of this modified charge behaviour, investigating how it affects the event horizon—the boundary beyond which nothing can escape—ergospheres—regions surrounding rotating black holes where spacetime is dragged along—and accretion disks—structures formed by matter spiralling into the black hole, offering new insights into the complex processes occurring in these extreme environments.

Researchers employ advanced mathematical techniques, including differential geometry and tensor calculus, to solve the Einstein-Maxwell field equations with the specified non-minimal coupling. This requires a thorough understanding of the underlying mathematical framework and the ability to manipulate complex equations with precision. The resulting solutions are then analysed to determine their physical properties, such as the event horizon and gravitational effects. To explore these solutions further, researchers also derive a modified solution for rotating black holes and investigate the thermodynamic properties of these modified black holes, such as their entropy—a measure of disorder—and temperature. This involves applying the laws of thermodynamics to the derived solutions and determining how the inclusion of torsion affects these fundamental quantities.

Researchers intend to investigate the stability of these solutions under perturbations, crucial for determining their physical relevance. This will involve performing a detailed analysis of the black hole’s response to external perturbations, such as gravitational waves or the infall of matter. The implications of these findings extend beyond theoretical physics, potentially impacting our understanding of cosmology, astrophysics, and the fundamental nature of spacetime. By challenging the assumptions of standard general relativity and exploring the role of torsion and non-minimal couplings, researchers are paving the way for a more complete and accurate description of the universe. This research opens up new avenues for investigating the origin of cosmic magnetic fields, the evolution of black holes, and the dynamics of the early universe. Furthermore, scientists plan to explore the implications of these findings for the dynamics of accretion disks around black holes and investigate the potential connection between torsion and dark matter.