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What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?

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  • $\begingroup$ Equal mass doesn't mean that the generate the same gravity, their radius is important too. $\endgroup$ – iharob Jul 2 '15 at 16:32
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    $\begingroup$ @iharob for Schwarzschild black holes, same mass <-> same radius (and same all other properties as well). $\endgroup$ – Kyle Oman Jul 2 '15 at 16:59
  • $\begingroup$ An important feature of general relativity is that if the situation is non-realistic, there will necessarily be some pathologies in the corresponding space-time. For instance, if you consider a set of two static black holes (which would in fact immediately collapse onto each other), there will be a so called "conical singularity" in the space between them and the path of a light-ray going through the conical singularity will be ill-defined. So if you want a precise answer, you have to first specify what exactly is the situation as to staticity, the exact position of the lightray etc. $\endgroup$ – Void Jul 2 '15 at 21:17
  • $\begingroup$ @Void you mean that if the two black holes are far enough not to collapse they will not deflect the light ray at all because the gravitational effect will be negligible in the region the light ray passes through? If so, wouldn't there be a limit where the ray will be deflected to one of the black holes if it doesn't pass exactly through the middle? I am sorry for this question, I don't know much about general relativity, but I know that the symmetry involved in this layout would imply that there will be no deviation. $\endgroup$ – iharob Jul 2 '15 at 21:34
  • $\begingroup$ what i meant was that there are two black holes, having equal mass and radius spaced very closed to each other, and a ray of light passes through center of the line joining the center of the two blackholes perpendicularly, i hope you get the picture now @void $\endgroup$ – aparajita Jul 3 '15 at 10:36
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What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?

Like iharob and JohnnyMo1 said, the light goes straight. But something else happens to it. See this screenshot of Irwin Shapiro's seminal paper:

enter image description here

See where he said the speed of light depends on gravitational potential? The light goes straight, but it also goes slower. Also see Professor Ned Wright's Deflection and Delay of Light, where you can read this: "In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light".

enter image description here

Einstein said much the same here: "the curvature of light rays occurs only in spaces where the speed of light is spatially variable". Also see Baez. It's like light veers, like a car veers when it encounters mud at the side of the road. However when light passes between two massive objects, it isn't slowed down more on one side than the other, so the net deflection is zero.

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  • $\begingroup$ I think that the evaluation that" light goes slower " is a misrepresentation of the calculations, where he assumes as c the velocity of light and uses the GR equations to get the delay. "he effect may be considered as a special case of gravitational time dilation."en.wikipedia.org/wiki/Shapiro_delay . Light follows the geodesics of general relativity with velocity c , it is space time that changes en.wikipedia.org/wiki/Geodesics_in_general_relativity $\endgroup$ – anna v Jan 7 '16 at 17:29
  • $\begingroup$ @anna v : I'm sorry, but that's incorrect. See the GR section of this Baez article or look at the Einstein digital papers: "However, the writer of these lines is of the opinion that the theory of relativity is still in need of a generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned". NB: the word velocity ought to be speed. $\endgroup$ – John Duffield Jan 7 '16 at 17:40
  • $\begingroup$ I think you are misunderstanding the GR section of Baez. Light follows geodesics with the speed of light. in GR these can be curved. $\endgroup$ – anna v Jan 7 '16 at 18:07
  • $\begingroup$ @anna v : I'm not. The Baez article doesn't even mention geodesics. Light doesn't curve because it "follows a geodesic". See Wikipedia and note that the geodesic is a worldline in spacetime. But like Ben Crowell said, objects don't move through spacetime. Instead light curves because the speed of light is spatially variable. See Ned Wright's article: "in a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light". $\endgroup$ – John Duffield Jan 7 '16 at 19:35
  • $\begingroup$ Look , a "worldline" in Baez is the geodesic . In Newtonian physics, measuring particle with velocity v at the beginning of a line and at the end and dividing by time will give a smaller velocity if assumed straight, if the real line is curved, as it travels a larger distance. In GR space itself is curved so one HAS to measure the velocity along the curve. Going outside the curve changes the frame of reference and has no meaning, as the light is following the curve in space with velocity c. everything else seems like a contradiction but is just a mixup of inertial frames reference. $\endgroup$ – anna v Jan 8 '16 at 6:42
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I think the answer is very simple if you ask another question, you are implying that both black holes generate the same gravity and that the light passes exactly through the middle between them, so the question is

  • If the light deviates, where will it deviate to?

Since given the conditions it's not possible to give an answer to this question, it means that it will not deviate.

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  • $\begingroup$ but then will the light follow a straight path? @iharob $\endgroup$ – aparajita Jul 2 '15 at 16:44
  • $\begingroup$ Yes, why wouldn't it. If it can't decide which hole to go to, there is no other option but a straight line. $\endgroup$ – iharob Jul 2 '15 at 16:45
  • $\begingroup$ then what about the effects of the gravity on light? $\endgroup$ – aparajita Jul 2 '15 at 16:47
  • $\begingroup$ They are cancelled out by the gravity of the another black hole, this is not related to the effect but, I don't really know the spelling in english simetry? -> simetría in spanish. $\endgroup$ – iharob Jul 2 '15 at 16:48
  • $\begingroup$ The English spelling is "symmetry." $\endgroup$ – JohnnyMo1 Jul 2 '15 at 16:52
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I'm going to assume you mean that the light travels on the precise center line between the holes, as iharob did.

This sort of symmetry question is very common in physics. Here's a similar question in classical electrodynamics. "If I place a positive charge at the center of a perfect equilateral triangle of equal negative charges, will it move?" Let's say it does move, then we can draw a vector for the direction the force on the center charge points. But if we rotate our heads by 120 degrees and look at the situation from a different angle, all the charges are in the exact same configuration, but the force now points in a different direction. How can that be? We're forced to conclude that the force does not really exist. There is no consistent direction it could point in! Similar arguments apply for a square of charges, or a pentagon, etc.

In the black hole situation, say the light beam curves toward one of black holes. Now stand on your head, or look at the situation in a mirror. Since the black holes have equal masses, the physical situation is identical, but now the light appears to curve toward the other black hole. So why didn't it do that to begin with? We're forced to conclude once again that the path of the light does not curve toward either black hole.

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