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.