# Can a Photon Orbit a Black Hole?

• RobtO
In summary: 's answer is no, because the laser pulse would have to be incredibly intense and have a very short duration in order to produce this effect.
RobtO
In MTW it is derived that a photon can orbit a black hole at a radius r=3M. However, the surface at the Schwartzschild radius r=2M is lightlike, isn't it? So can a photon orbit at both radii? What am I missing?

Circular orbits occur at r=3M. There are plenty of other possible general orbits. The photon "hanging" at r=2M on an outgoing geodesic is just one interesting and somewhat extreme example of a non-circular orbit.

pervect said:
The photon "hanging" at r=2M on an outgoing geodesic is just one interesting and somewhat extreme example of a non-circular orbit.
But these orbits are not stable right? At least I think that is what you claimed a month or two ago.

The circular orbit of a photon at R=3m is not stable, and the photon hanging at r=2m is also not stable. There are a lot of different possible orbits for a photon. If the photon doesn't pass too close to the black hole, most photon orbits will tend to be nearly hyperbolic. Close to R=3m, one will see orbits that either spiral into the black hole, or spiral out. MTW has some pictures of some of the spiral orbits, I believe.

But what about circular orbits at r=2M? Are they possible, too?

does the wavelength of the photon have anything to do with its orbital stibility? like if you have something like bohr orbits only with light waves.

$$n \lambda = 2 \pi r$$

Are there any stable orbits? is there a continuous or discrete spectrum of them if there are any?

Last edited:
RobtO said:
But what about circular orbits at r=2M? Are they possible, too?

The "orbit" of an outgoing photon at R=2m in Schwarzschild coordinates (r, theta, phi, t) is a single point:

r=2M
theta=phi=constant

This is not a circular orbit, because the angles are constant. There are other orbits that start at R=2m and propagate in different directions - all of these orbits wind up at the central singularity. Only the outgoing photon escapes this fate, if the photon starts off at even a small angle away from outgoing, it will get sucked into the black hole.

A circular orbit, by comparison is

r=3M
theta=constant
phi = w t

where w is the angular frequency

Does the wavelength/energy of the photon have anything to do with its orbital stability? What if a photon had the same energy as the black hole itself... hypothetically? could a photon have so much energy that it itself is a black hole?

Stable and unstable photon orbits

Hi, Jonny,

Jonny_trigonometry said:
Does the wavelength/energy of the photon have anything to do with its orbital stability?

A fundamental principle in gtr is that the "path" taken by a monochromatic light beam does NOT depend upon its wavelength. (If this weren't true, gtr would be in serious trouble!) See for example section 15.4 of D'Inverno, Introducting Einstein's Relativity.

Jonny_trigonometry said:
could a photon have so much energy that it itself is a black hole?

Well, the notion of a "photon" belongs to the domain quantum theory, but gtr is a classical field theory, so this question doesn't quite make sense in the context of gtr. So let's modify it: "can a laser pulse have so much mass-energy that it becomes a black hole?" You can probably now figure out what is the answer from gtr :-/

Chris Hillman

## 1. Can a photon orbit a black hole?

Yes, a photon can theoretically orbit a black hole, but not in the same way that a planet or other object would orbit. This is because a photon is a massless particle and does not experience the gravitational pull of a black hole in the same way that a massive object would.

## 2. How close can a photon get to a black hole?

The closest a photon can get to a black hole without being pulled in is known as the photon sphere, which is about 1.5 times the event horizon radius. However, the photon sphere is an unstable orbit and any slight disturbance can cause the photon to either fall into the black hole or escape from its gravitational pull.

## 3. Can a photon escape a black hole's gravitational pull?

No, once a photon crosses the event horizon of a black hole, it cannot escape its gravitational pull. This is because the escape velocity at the event horizon is equal to the speed of light, and a photon travels at the speed of light, so it does not have enough energy to escape.

## 4. How does a black hole affect the path of a photon?

A black hole's strong gravitational pull can bend the path of a photon as it passes by. This can create a phenomenon known as gravitational lensing, where the light from a distant object is bent and distorted as it passes near a black hole.

## 5. Can a photon orbit a rotating black hole?

Yes, a photon can also orbit a rotating black hole, but its orbit will be affected by the black hole's spin. This can cause the photon to experience frame dragging, where its orbit becomes tilted and precesses around the black hole's rotational axis.

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