A flashlight beam travels straight into the dark: that's how we usually think of light. But near a massive body, like a star or a black hole, space is curved, and the beam bends smoothly, as if guided by an invisible hand. The authors of a new study have worked out exactly how gravity alters the familiar laws of electricity and magnetism. They took Maxwell's equations (the very ones that describe light, radio waves, and the behavior of charges) and rewrote them for the curved space around a black hole.
They considered two types of observers. The first hovers in place, resisting the pull. For them, the equations look almost familiar, with only corrections: distances and time stretch, and space itself acts like a lens, altering the field strength. The second observer falls freely into the black hole. In their world, electric and magnetic fields mix like paints in flowing water. A stationary charge appears to them as a flowing current, and the equations link what was once separate. Meanwhile, in the transverse directions, along the angles, everything remains as before. Thus, gravity reshapes the very fabric of electromagnetism. And the flashlight beam we started with, near a black hole, no longer just bends: it follows new rules, where electricity and magnetism are woven together.
as written by the authors arXiv:2606.12630
Classical electrodynamics in curved spacetime is formulated within a tetrad-based framework that preserves the direct physical interpretation of the electromagnetic fields measured by an observer. The formalism is applied to Schwarzschild spacetime for two distinct families of observers described in the same coordinate system: static observers and radially free-falling observers. For static observers, Maxwell equations retain their usual spherical structure, while the gravitational field introduces geometrical corrections in the radial and temporal sectors through the metric function. These corrections are interpreted in terms of proper radial distance, proper time, and the radial variation of the lapse function. For radially free-falling observers, additional kinematical contributions arise from the local radial boost relating the free-falling frame to the static one. As a consequence, charge density mixes with radial current, and the electric and magnetic sectors become intertwined in the temporal-radial projections of Maxwell equations, whereas the angular Amp\`ere-Maxwell and Faraday equations retain the same structure found for the static observer. The weak-field and near-horizon regimes are also examined, and the results are discussed through an effective-medium analogy, in which the Schwarzschild geometry behaves as an inhomogeneous geometrical medium at rest for static observers and as a radially moving effective medium in the temporal-radial sector for free-falling observers.
If you free-fall into a black hole with a flashlight, its beam will change color and direction — for the falling observer, the familiar laws of optics break down near the horizon.
In the movie Interstellar, the bending of light by gravity is shown during the flyby of the black hole Gargantua: there, Maxwell's equations in curved space are working at full tilt.