You don't have to go 'faster than the speed of light' to escape a black hole if you're not affected in the usual manner by gravity. And I'm not aware of any suggestion that gravity itself is affected by gravity.
Gravity absolutely is affected by gravity. The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity. All forms of energy, and momentum, and even stress and pressure are combined into the "stress energy tensor" which determines the local curvature of space-time.
> The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity.
Non sequitur? I mean, non-linearity is not the same as feedback. Linear system can exhibit feedback (and still stay linear), and non-linear systems do not have to exhibit feedback.
The equations describing a field theory contain terms which are the product the field, the thing it couples to (could be another field) and the strength of the interaction. When a field couples to itself, there are terms non-linear in the field. So the non-linearity of GR indicates that the gravitational field couples to itself, i.e. that gravity gravitates.
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You don't have to go 'faster than the speed of light' to escape a black hole if you're not affected in the usual manner by gravity. And I'm not aware of any suggestion that gravity itself is affected by gravity.
Gravity absolutely is affected by gravity. The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity. All forms of energy, and momentum, and even stress and pressure are combined into the "stress energy tensor" which determines the local curvature of space-time.
> The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity.
Non sequitur? I mean, non-linearity is not the same as feedback. Linear system can exhibit feedback (and still stay linear), and non-linear systems do not have to exhibit feedback.
The equations describing a field theory contain terms which are the product the field, the thing it couples to (could be another field) and the strength of the interaction. When a field couples to itself, there are terms non-linear in the field. So the non-linearity of GR indicates that the gravitational field couples to itself, i.e. that gravity gravitates.
I knew it was a source of its own much smaller gravity, I guess I was wrong about how strongly coupled that is with the original field.
Still, that's not itself being 'normally' affected by gravity, and I've never seen anything discuss it.