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martyb writes:

A new theorem predicts that stationary black holes must have at least one light ring:

Researchers at the Max Planck Institute for Gravitational Physics in Germany and Universidade de Aveiro in Portugal have recently introduced a theorem that makes predictions about the light rings around stationary black holes. Their theorem, presented in a paper published in Physical Review Letters, suggests that equilibrium black holes must, as a general rule, have at least one light ring in each of their sense of rotation.

"Remarkably, the properties of light rings can encode much relevant black hole information," Pedro Cunha and Carlos Herdeiro, the two researchers who carried out the study, told Phys.org via email. "Measuring these properties grants a direct window into the elusive and yet fairly uncharted regime of very strong gravity close to a black hole. At this moment it is still unclear whether Einstein's theory of general relativity remains a good description of the laws of gravity under such extreme conditions. Therefore, a key question is: does any black hole model, in any theory of gravity, need to have a light ring?"

[...] "In our paper, we introduce a generic and mathematically innovative argument that establishes that an equilibrium black hole must indeed have, as a rule, at least one standard light ring in each rotational sense," Cunha and Herdeiro said. "To analyze light rings, typically, one considers families of solutions of a given theory of gravity, like general relativity, or some particular model of modified gravity. Here, however, the argument is of a topological nature."

[...] "The prediction that black holes always have light rings and they are always outside the horizon has important consequences," Cunha and Herdeiro say. "For instance, it implies that the silhouette of a black hole, known as the black hole shadow, is generically different and usually larger than what one would expect the size of the black hole itself to be. So the shadow should always be a magnification of the black hole."

[...] "One key assumption of our theorem is that far away from the black hole there is no gravitational field," Cunha and Herdeiro said. "However, in the Universe there is a cosmological constant that drives the expansion of the Cosmos. This creates a tiny gravitational field no matter how far away from the black hole one is. It would be very interesting to understand if this slight change in assumption would change our theorem's conclusions."

Journal Reference:
Pedro V. P. Cunha, Carlos A. R. Herdeiro. Stationary Black Holes and Light Rings, Physical Review Letters (DOI: 10.1103/PhysRevLett.124.181101)

A light ring is a subset of a photon sphere, which has some interesting properties:

The photon sphere is located farther from the center of a black hole than the event horizon. Within a photon sphere, it is possible to imagine a photon that's emitted from the back of one's head, orbiting the black hole, only then to be intercepted by the person's eyes, allowing one to see the back of the head. For non-rotating black holes, the photon sphere is a sphere of radius 3/2 r_s (the Schwarzschild radius). There are no stable free fall orbits that exist within or cross the photon sphere. Any free fall orbit that crosses it from the outside spirals into the black hole. Any orbit that crosses it from the inside escapes to infinity or falls back in and spirals into the black hole. No unaccelerated orbit with a semi-major axis less than this distance is possible, but within the photon sphere, a constant acceleration will allow a spacecraft or probe to hover above the event horizon.

Another property of the photon sphere is centrifugal force (nb: not centripetal) reversal. Outside the photon sphere, the faster one orbits the greater the outward force one feels. Centrifugal force falls to zero at the photon sphere, including non-freefall orbits at any speed, i.e. you weigh the same no matter how fast you orbit, and becomes negative inside it. Inside the photon sphere the faster you orbit the greater your felt weight or inward force. This has serious ramifications for the fluid dynamics of inward fluid flow.

A rotating black hole has two photon spheres. As a black hole rotates, it drags space with it. The photon sphere that is closer to the black hole is moving in the same direction as the rotation, whereas the photon sphere further away is moving against it. The greater the angular velocity of the rotation of a black hole, the greater the distance between the two photon spheres. Since the black hole has an axis of rotation, this only holds true if approaching the black hole in the direction of the equator. If approaching at a different angle, such as one from the poles of the black hole to the equator, there is only one photon sphere. This is because approaching at this angle the possibility of traveling with or against the rotation does not exist.

See also: Max-Planck-Instituts für Gravitationsphysik

Original Submission