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 rs (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
(Score: -1, Offtopic) by Anonymous Coward on Tuesday June 02 2020, @03:16PM
... the US president is planning to put troops on the streets to suppress wide spread anti-government protests; and to designate anti-fascists as terrorists.
Just had to get that one off my chest. Back to Black Holes.
(Score: 2) by Thexalon on Tuesday June 02 2020, @03:44PM (4 children)
Looking this up, this doesn't mean said black hole doesn't move relative to the rest of the universe, because that would be violating every observation ever. What it seems to mean from my quick layman's reading is that the black hole isn't changing significantly over time.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 3, Interesting) by Kitsune008 on Tuesday June 02 2020, @04:44PM (1 child)
I think the intent of the 'stationary black holes' nomenclature is to distinguish between rotating, and non-rotating black holes.
TFA talks about light rings forming at the boundary of a 'photon sphere' around a black hole, then mentions two photon spheres forming around rotating black holes.
The last paragraph in TFS talks about this effect.
Very correct...we have noticed black holes moving around, even merging. And 'Rogue Black Hole Doomsday' scenarios have been proposed as a possible(but very unlikely) end to Earth by many astrophysicists.
Astrophysics is a hobby of mine, and I am not a real astrophysicist, so if I spouted nonsense, hopefully someone more knowledgeable can correct me and enlighten us all. :-)
(Score: 1) by khallow on Tuesday June 02 2020, @08:05PM
I originally thought the same as you, but it appears to be a definition peculiar to the paper. Stationary black holes can rotate.
I think what is meant here is that the properties of the model - things like the axis symmetry, asymptotic flatness, and the Killing horizon (which I think is a mathematical description of the event horizon) - don't change with time. Constant translation motion shouldn't change anything, but it can rotate too, and that does change things somehow.
What's very important about this definition is that it is not dependent on the theory of General Relativity. The "M" above is your spacetime and "g" is a metric on that spacetime which has the property, almost definition, of being positive along space-like directions, negative along time-like directions, and zero along light-like directions. Knowing what directions g is zero along tells you what paths light will take on M. "g" has to have additional special properties in order for it to be a General Relativity spacetime (crudely, its curvature satisfies additional relations). What this paper shows is that one can abandon the structure of relativity (at least between the interior of the black hole and the flat space at infinity) and still make credible deductions about black holes such as what sort of light orbits they have.
(Score: 3, Touché) by takyon on Tuesday June 02 2020, @04:57PM (1 child)
It sounds like this, and other theorems about basic black holes, are describing "spherical cow" black holes.
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(Score: 0) by Anonymous Coward on Wednesday June 03 2020, @06:23AM
Which type of cow would you prefer they be modeled as?