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Let's just say you're in a space ship inside this critical radius of the black hole, and you want to get back home. Now, the general rule for determining escape velocity and the critical radius is a matter of conservation of energy. i.e. [tex]\Delta K=-\Delta U[/tex]. I'm going to say for the sake of simplicity that you start off still and get to your destination still, so [tex]\Delta K[/tex] is 0. So now you're left with this following equation: [tex]0=-(U_f-U_i)[/tex]. Part of this potential energy is due to the gravity of the black hole, so splitting that up would give you

[tex]U_i - \frac{{GMm}}{{r_i }} = U_f - \frac{{GMm}}{{r_f }}[/tex]

or

[tex]U_i - U_f = GMm\left( {\frac{1}{{r_i }} - \frac{1}{{r_f }}} \right)[/tex]

And so basically what I am to understand from this simple relationship is that even though the product of the masses may be really large, as long as you have enough potential energy (in the form of chemical potential energy or whatever, such as fuel) then you could get out of a black hole, even if you start out beyond the critical radius of no return.

Maybe when I've heard discussions of black holes only realistic situations are considered where the photons that fall into a black hole don't have some reserve of potential energy lying around, or maybe I'm just not nearly familiar enough with the subject, but at least hypothetically, wouldn't it be possible to get out of a black hole in a space ship?

And if this is correct, would it then be possible for some set of chemical or nuclear reactions to occur in the matter of a black hole to allow matter to escape on its own (however unlikely)?