Researchers Gabriele Benomio and Rita Teixeira da Costa, affiliated with the University of Cambridge and the University of Lisbon respectively, have delved into the complex world of black hole physics to study the behavior of electromagnetic fields around Kerr black holes. Their work, published in the journal “Classical and Quantum Gravity,” focuses on the Maxwell equations, which describe how electric and magnetic fields behave in the presence of charges and currents.
In their study, Benomio and da Costa examined the Cauchy problem for the Maxwell equations in the region outside Kerr black holes. They formulated the equations using a specific frame of reference, treating the unknowns as tensorial quantities associated with a non-integrable horizontal distribution. This approach allowed them to decouple the equations into two main parts: the extremal components, which follow the Teukolsky equations, and the middle components, which form a coupled system of transport and elliptic equations.
The researchers found that, assuming control over the extremal components, they could prove uniform boundedness and decay estimates for the middle components across the full range of spacetime parameters, from sub-extremal to extremal Kerr black holes. This was achieved by deriving a decoupled system of transport and elliptic equations for two modified middle Maxwell components and decomposing general solutions into a dynamical and stationary part. The stationary part is determined by two real charges, electric and magnetic, which are derived from the initial data at the event horizon.
For sub-extremal black holes, where the angular momentum is less than the mass, previous works by Shlapentokh-Rothman and da Costa provided the necessary control over the extremal components. This led to unconditional boundedness and decay results for all the unknowns in the equations. However, for extremal black holes, where the angular momentum equals the mass, the researchers formulated a conjectural boundedness and decay statement for the extremal components, motivated by work of Casals, Gralla and Zimmerman. Their boundedness and decay results for all the unknowns in the equations remain, therefore, conditional.
The study also revealed that the complicated dynamics of the extremal components at the event horizon is inherited by the middle components. In particular, the researchers uncovered novel conservation laws for the middle components of axisymmetric solutions.
While this research is primarily theoretical and focused on the fundamental physics of black holes, it has potential implications for the energy sector, particularly in the field of plasma physics and magnetic confinement fusion. Understanding the behavior of electromagnetic fields in extreme environments can provide insights into the development of more efficient and stable fusion reactors, which could potentially revolutionize the energy industry by providing a clean, abundant, and sustainable source of power.
Source: Benomio, Gabriele, and Rita Teixeira da Costa. “The Maxwell equations on full sub-extremal and extremal Kerr spacetimes.” Classical and Quantum Gravity (2023).
This article is based on research available at arXiv.