This may seem like a strange question - I think it's weird - but if gravity waves travel at the speed of light, how can they escape from a black hole? How can we determine if a black hole has any charge if charge is transmitted by photons?

Or am I just hopelessly confused?

Just confused. It's been asked before, and you may want to do some searching to see if any of the discussions are relevent to your level of understanding.

Here's one thread that is directly what you are asking.

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Numbers are not case sensitive. (me)

That same question was just asked & discussed earlier this month here: Black Holes and Gravity.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

Sorry 'bout that. Hmmm... okay, so the gravitational field is set at the event horizon? Ok, I'll accept that.

In the first thread, alainprice asked about virtual photons which carry charge, but there was no answer. How do they escape the black hole? Is the answer the same, that the electrical field is also set at the event horizon? Or is it just that virtual particles are allowed to break some of the normal rules?

Could a black hole act as a quantum eraser? Would this be a way to empirically test the "black hole information paradox"?

Yep, as Tim said light can't escape black holes, in fact nothing (other than Hawking radiation) can escape, because the required escape velocity is greater than c... perhaps you should do some google searches on event horizon, and hawking radiation.

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The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
It is imperative in science to doubt.
~~~ Richard Feynman ~~~
Common sense is not so common
~~~ Voltaire ~~~