Massive objects and relativistic effects

[Myslius]

A sphere with the radius of 4 kilometers and a mass of 2 suns moves to observer at the speed of 0.866c. From sphere frame of reference it's mass is 1 sun's mass, radius 4 kilometers and velocity 0. Can light escape from such object? Does escaping is also relative? How about direction of light, does it matter?

 

[clamtrox]

No it's not relative. All observers agree on what kind of paths particles move on. The physical object does not change even if you move with respect to it.

Here you are confusing the simple derived formulas (regarding Schwarzschild radius and all that) with the actual physics (Einstein field equations and geodesic equations). If you started from the beginning, there would be no confusion.