# Talk:Photon sphere

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## Some corrections

First, the phrase extremely massive objects such as black holes is misleading. Anything small enough to have a surface radius less than ${\displaystyle {\frac {3}{2}}\,R_{\rm {Schwarz}}}$ is likely to be a black hole, not because it is so massive, but because it is so compact.

Second, the numerical relations quoted hold only for a non-rotating black hole, which is modeled in gtr by the Schwarzschild vacuum solution (compare Kerr solution).

Third, within the photon sphere constant acceleration will allow a spacecraft or probe to hover above the event horizon is misleading in the context of reference to "spaceprobes" (compute the magnitude of acceleration required for a stellar mass black hole).

Fourth, the orbits (null world lines) in question are unstable (to see this, plot the effective potential, as in any standard textbook on gtr). This means that contrary to what the article implies, photons or radio pips cannot really be "injected" into such an orbit the way that a spaceprobe can be "injected" into a desired orbit around Venus, say.---CH 15:18, 14 April 2006 (UTC)

Maybe messive is ment to mean "Lots of mass" (as in weight) as opposed to "Lots of size"? Alan2here 15:13, 20 November 2006 (UTC)
Alan2here, the short answer is "no". For black holes, mass is size.
I've added a disputed tag to the article, CH is completely corect; this article has numerous faults. linas 00:57, 27 January 2007 (UTC)
I changed "small and massive" to "extremely compact". Thought that was better; micro black holes aren't massive, and galactic black holes aren't small. --Alvestrand 13:01, 2 December 2007 (UTC)

A bit of a conflict between information here and other sources (including other Wikipedia pages). It says "The photon sphere is located further from the center of a black hole than the event horizon and ergosphere."

For a non-rotating black hole, the photon sphere extends from the event horizon to a distance of 0.5 Schwarzschild radius from it, that is, the outer boundary of the photon sphere is at 1.5 Schwarzsfield radii from the singularity.

However, the Wikipedia page on the Ergosphere says "The ergosphere is ellipsoidal in shape and is situated so that at the poles of rotating black hole it touches the event horizon and stretches out to a distance that is equal to the radius of the event horizon." This page can be found here:

[[1]]

So according to this, the "equatorial bulge" of the ergosphere reaches to 2 Schwarzschild radii from the singularity, while the photon sphere only extends to 1.5 Schwarzschild radii. Obviously, the ergosphere extends farther than the photon sphere, contradicting the first statement, namely "The photon sphere is located further from the center of a black hole than the event horizon and ergosphere."

The situation is not clear cut, since the 1.5 Schwarzschild radius size of the photon sphere is for a non-rotating black hole, whereas the ergosphere is a feature of rotating black holes. So this needs some clarification. Is the photon sphere larger for rotating black holes? What is the nature of the photon sphere in rotating black holes that justifies the statement "The photon sphere is located further from the center of a black hole than the event horizon and ergosphere". —Preceding unsigned comment added by 67.176.200.23 (talk) 18:02, 20 June 2009 (UTC)

## Who thought of this first?

Was it me http://www.scienceforums.net/showthread.php?t=22400 I made that post quite some time ago, having not read this article. Alan2here 10:54, 30 September 2006 (UTC)

The idea of photons orbiting a black hole must be nearly a century old. Its a standard treatment in standard textbooks on GR. linas 00:59, 27 January 2007 (UTC)
TY for info :¬(

## Erratic orbits of photons

If there is a plenitude of black holes in a given volume of space, wouldn't a photon follow an erratic course around them, or between them?

Similarly, why is it assumed that the event horizon of a single black hole will be perfectly circular? It was my understanding that the event horizon was anything but perfectly circular, but rather vibrating and turbulent due to quantum effects.198.177.27.21 (talk) 07:17, 1 August 2008 (UTC)

## Purely GR approach

I believe that if we are going to describe such object as black hole we shall use only GR as mathematical argument for our deductions. Unfortunately there is still "classical gravity" step in derivation of photon sphere radius, where it is found "speed of light on it's orbit". So I'm going to edit it in purely GR way. —Preceding unsigned comment added by Goykhman (talkcontribs) 09:47, 11 May 2009 (UTC)

## Broken Sentence

"In the standard electromagnetic and gravitational resonator approach used the following photon radius:"

Someone know what this is supposed to say? LokiClock (talk) 17:45, 14 September 2009 (UTC)

## D-theta should not be zero

... a general circular orbit can have a varying theta, as long as r remains constant. Right?

Suggest merging with the article on gravitational lensing; the photon sphere is really a special case of the general light-bending behaviour around a spherically symmetric mass. 130.56.71.50 (talk) 16:00, 23 September 2009 (UTC)

## Singularity

Isn't it true that, from the point of view of a photon, the entire universe looks like a singularity? A photon travels EVERYWHERE in the universe in ZERO time from its own point of view. So doesn't that mean that from a photon's point of view, the universe is a singularity? 68.200.98.166 (talk) 01:33, 25 December 2009 (UTC)

Well according to Relativity, the photon would not experience time, nor distance (remember that time and distance are connected and is especially apparent when upping velocity). I'm not sure if it can travel everywhere at once because where is it going to travel? How can it when there is no time to do it in? From what I can tell, that is still a great conundrum of physics. You tell clearly, from our perspective of close to 0c that light travels and takes time to do it in. I'm not quite sure, but both are true, the photon is instantaneously created and destroyed at perspective from c but yet travels from stars millions of ly away and hits our telescopes from perspective 0c. Maybe someone more experienced in SR/GR could help us out on getting our heads around both being true? Cody-7 (talk) 03:26, 24 February 2016 (UTC)

## Rotating black hole

Because 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.
1. So, how many photon spheres does a rotating black hole have? Two (and the polar direction is where they intersect) - or infinitely many, one for each angle of approach? I gues it's the former.
2. Intuitively, it makes no sense that it's supposed for it to matter whether the photon travels in the direction of the hole's rotation rotation or against it if it goes parallel to the equator, but not if it deviates from that direction by a fraction of a degree. I'd say that there are two photon spheres (or - better said - that the two photon spheres differ) for every angle, with the exception of the polar one.

Mike Rosoft (talk) 09:47, 24 August 2010 (UTC)

See this webpage: http://www.physics.nus.edu.sg/~phyteoe/kerr/ and the corresponding paper: http://www.springerlink.com/content/l20m7u60l6011134/ . To summarize how they answer your questions:
1. If we define a "photon sphere" as a sphere containing a photon orbit with a constant coordinate radius, then there are indeed infinitely many photon spheres. Every radius between r1 (the radius of the inner, prograde circular orbit) and r2 (the radius of the outer, retrograde circular orbit) has a corresponding constant-radius orbit, but only the two extreme values r1 and r2 correspond to circular orbits. All the intermediate radii correspond to complicated paths that oscillate in latitude about the equator as they orbit, and almost all of them are aperiodic orbits, which means they never come back to exactly the same point twice, and instead densely cover a finite area of the photon sphere (rather than just a closed curve like a circle).
2. The only possible circular orbits are in the equatorial plane, so the situation seems to be quite different from what you imagined. However, there is a grain of truth to what you guess about there being two possible orbits for each "angle" with the exception of the polar one: For every value of the constant of motion Q, there are two orbits, one "prograde" and one "retrograde", except for the maximum value of Q, which corresponds to a single orbit - the only one that actually reaches the poles (which is the first example shown). (I use scare quotes around "prograde" and "retrograde" because a particular orbit can be sometimes prograde and sometimes retrograde due to the Lense-Thirring effect.) —Keenan Pepper 17:44, 24 August 2010 (UTC)

## Layman question

From the statement: "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 permanently. "

How can you cross the orbit from the inside? That would require escaping from the event horizon.

Silenceisgod (talk) 23:52, 3 October 2015 (UTC)

The photon sphere is outside the event horizon. A rocket above the event horizon but below the photon sphere could get an impulsive boost and then coast through the photon sphere on an escape orbit. Cloudswrest (talk) 04:42, 4 October 2015 (UTC)
Wouldn't that require the rocket to travel faster than the trapped light? --Ayeroxor (talk) 14:19, 16 November 2016 (UTC)
No, as this is only necessary inside the event horizon, which is inside the photon sphere. Absolutelypuremilk (talk) 14:41, 16 November 2016 (UTC)

## "Long Term"

The article currently states that photon orbits "are rarely stable in the long term." Well, no orbit goes on forever, and "long term" can mean different things in different contexts. I think the average term or term range, and aspects such as how the mass of the black hole affects these calculations, should be more precise. --Ayeroxor (talk) 14:18, 16 November 2016 (UTC)