Black hole/Hawking radiation thought experiment

[marconius]

Hello everyone! New poster here.
I would first of all like to thank you all, since in these threads i have found answers to many of my questions about astrophysics!

I have a little thought experiment for you guys:

Lets say that because of Hawking radiation, the radius of a black hole's event horizon
is decreasing at the rate of X m/s
Lets imagine that such black hole is large enough to allow for a hypothetical spaceship
to cross the event without being spaghettified/destroyed
Lets also assume that such a spaceship has an abundant amount of fuel and can fire its
powerful engines for an unlimited amount of time, getting as close to traveling at C as
physically possible

If the ship were to cross the black hole, would it manage to resist the pull of the black hole
enough to travel towards the singularity at a rate of only (X-Y)m/s and therefore free itself from its pull? (recall that the black hole is receding at X m/S)?

 

[George Jones]

Unfortunately, there is no escape route. Once inside an evaporating (spherically symmetric) black hole, all (timelike) paths lead to the singularity.