How would this experiment play out? Length contraction / black hole

[mrspeedybob]

Bob, Ed, and Sussie are all observers, each in their own space-ship. Ed and Sussie accelerate on parallel paths to very near the speed of light. Bob sees both length contraction and an increase in mass of both Eds and Sussies ships. These effects are great enough that each ship achieves the mass and density required to form an event horizon. Bob sees them fall together and become a single black hole moving at high speed.

Ed and Sussie accelerate simultaneously and remain at rest relative to each other. There is no reason that they should feel any irresistible attractive force (Unless Sussie is hot). After a period of time they slow down and are once again at rest relative to Bob.

How is the experience of Ed and Sussie reconcilable with the observation of Bob?
What does Bob see as Ed and Sussie slow down?

 

[Dale]

each ship achieves the mass and density required to form an event horizon

This is an incorrect premise:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

Remember, in GR the source of gravity is not a scalar mass (energy), but the entire stress-energy tensor of which energy is only a single component.

 

[yuiop]

If you look up the term "relativistic mass" you will see this concept is largely discontinued in modern texts and one reason is precisely the sort of paradox you are talking about. While there is a sense that inertial mass increases and objects appear to become more difficult to accelerate, it is certain that gravitational mass does not increase in the same way and fast moving objects do not become black holes. In fact Ed and Sussie accelerate towards each slower when they are moving fast relative to Bob, than when they are moving slow. Gravitational interactions are fairly complicated for moving objects and are dependent upon the relative speeds and directions of the objects.

To put some numbers to this, if the gravitational acceleration of Sussie towards Ed is (a) when they are floating in otherwise free space and approximately at rest with Bob, then when they are moving at some some velocity (v) relative to Bob, that is a large fraction of the speed of light , the acceleration of Sussie towards Ed is a*(1-v^2/c^2). As v approaches c the acceleration tends towards zero. In fact two photons traveling parallel to each other and in the same direction have zero mutual gravitational acceleration towards each other and this is not just because photons have zero rest mass. Two photons traveling parallel to each other but in opposite directions would experience mutual gravitational attraction, because while they have zero rest mass they have energy which contributes to their "effective active gravitational mass".