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Photon orbits

  1. Oct 31, 2006 #1
    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?
  2. jcsd
  3. Oct 31, 2006 #2


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    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.
  4. Oct 31, 2006 #3
    But these orbits are not stable right? At least I think that is what you claimed a month or two ago.
  5. Nov 1, 2006 #4


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    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.
  6. Nov 1, 2006 #5
    But what about circular orbits at r=2M? Are they possible, too?
  7. Nov 1, 2006 #6
    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.

    [tex] n \lambda = 2 \pi r [/tex]

    Are there any stable orbits? is there a continuous or discrete spectrum of them if there are any?
    Last edited: Nov 1, 2006
  8. Nov 2, 2006 #7


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


    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

    phi = w t

    where w is the angular frequency
  9. Nov 5, 2006 #8
    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?
  10. Nov 19, 2006 #9

    Chris Hillman

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    Stable and unstable photon orbits

    Hi, Jonny,

    Looks like pervect already answered your original question, but you then asked:

    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.

    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
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