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Given the following conditions:

  • Two space stations of insignificant mass (compared to what can affect the transmission of a beam of light) are separated by a distance of 100,000 light years.

  • With one exception, there are no other objects of significant mass within a sphere of 1,000,000 light years.

  • The exception is a single black hole, midway between the two stations, and having a mass of 10 solar masses.

  • The sending station is transmitting "S.O.S." in Morse code. A "dot" is 0.5 seconds long. A "dash" is 1.0 seconds long. The time between dots and dashes is 1.0 second. The time between "S.O.S." blocks is 2.0 seconds.

  • The beam's wavelength is 475 nm and its energy at the point of transmission is 1 Petawatt.

  • The beam is as narrowly focused as the technology will allow and no effort is being made to specifically take advantage of the nature of black holes to get the signal past it. Tightly focused beam shot straight at the other station, nothing else. (If necessary, assume the beam is emitted from a 1 meter diameter lens and is well enough focused to hit a 1 meter detector with negligible loss. Yes, that's miraculous. But the question is focusing on what the black hole does to light — and the focusing tech should be (and is) irrelevant.)

  • Ignore all other aspects of physics implied by the conditions of this question. Please don't complain that the existence of space stations or their placement in space has anything to do with this question. It's like telling your college professor that the answer to the question is meaningless because he chose to use a spherical horse.

Conceptually, pretend the two space stations are attached to one another by a string and are so far away from the black hole that the information transmitted along the beam of light string is uncorrupted. Then begin moving the two stations toward the black hole, always keeping the black hole mid-way between the two stations.

Question: How close can the beam of light get to the black hole before the information transmitted through it becomes corrupted?

  • By "corrupted" I mean that the "S.O.S." can no longer be recognized for what it is within a period of ten (10) minutes.
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  • $\begingroup$ Are you wanting the message (say a laser beam) to curve around the black hole in a planned way so as to directly go to the other station (like this youtu.be/89g7sQ7zNqo?t=161)? Or are you sending a wider beam using the black hole as a lense that will focus it in on the other station? $\endgroup$ – chasly - supports Monica Sep 20 '20 at 17:28
  • $\begingroup$ @chasly-reinstateMonica I'll update the question. This is intended to be a narrow beam and no effort is being made to specifically utilize the nature of the black hole. (The video was fun - it's amazing what pool players can do! But I'm not sure a signal can survive around a black hole by putting a little English on it.) $\endgroup$ – JBH Sep 20 '20 at 17:28
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    $\begingroup$ It's not clear what exactly is it that you are afraid might "corrupt" the signal. As described in the question, everything is stationary; it's a steady state, and symmetrical to boot. What non-linear effect is there which might corrupt the signal? $\endgroup$ – AlexP Sep 20 '20 at 17:55
  • $\begingroup$ @AlexP "Then begin moving the two stations toward the black hole...." $\endgroup$ – JBH Sep 20 '20 at 18:29
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    $\begingroup$ @JBH: That's the geometer's "begin to move", it's not physical. The querent want to explain that they are concerned to find out how close to collinearity the three objects may be before the signal becomes "corrupted". What I don't understand it why would it ever become corrupted; either it it received uncorrupted, or it is not received at all (because the black hole will bend it away or block it). $\endgroup$ – AlexP Sep 20 '20 at 18:47
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Your signal integrity might improve!

Chasly notes this possibly in the comment. I was just reading an article about this.

https://www.syfy.com/syfywire/why-is-there-a-normal-galaxy-sitting-at-the-edge-of-the-universe

This exceedingly distant galaxy could be viewed on earth because the lensing effect of a black hole in between pulls the light back together. If it were not for the lens in the middle, this galaxy is so far away that its light would be scattered to invisibility.

gravitational lense

That said, your SOS is not the light from a galaxy. As I understand it, the track of the light between your stations depends on the coherence of the beam and its width at the black hole, the distance between the stations (known) and the gravity of the black hole and consequent strength of the lensing effect.

A lot of numbers. You can adjust these numbers to produce the effect you want for your fiction. I could imagine that at some distance from the hole the path of the light would be bent so it does not reach the far station. But full on to the black hole, if the signal is wide enough it might be bent around the hole (lensed?) on all sides such that it suddenly reaches the far station, extra bright.

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