Escape Velocity from Relativistic Sphere: Derivation & Intuition

[Dilema]

Can you please direct me to ref that shows the derivation of the escape velocity from a spherical object that moves in velocity v~c with respect to rest frame?

I suspect the escape velocity is increasing (intuitively since the mass increases).

Please comment and suggest alternatives.

 

[Nugatory]

I suspect the escape velocity is increasing (intuitively since the mass increases).

No, because relativistic mass doesn't work that way. We have an Insights article that you'll want to read: https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

The escape velocity, as measured by an observer moving along with the object, is exactly what it would be if the object were at rest (as it is in fact at rest relative to that observer).

 

[Ibix]

Also, a frame is just a point of view. You can't change how much energy is needed to escape Earth's gravity just by changing point of view. Otherwise you could have frames where the Voyager probes didn't have enough fuel to generate escape velocity, but leave the solar system anyway.