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This question already has an answer here:

Some time ago I encouraged by 11 year old son to watch Cosmos: A Spacetime Odyssey with Neil DeGrasse Tyson, and subsequently Cosmos: A personal Voyage with Carl Sagan, as well as other astronomy shows including History Channel's The Universe. One of these such shows inspired a question about black holes and gravity.

Can a black hole be so large that not even the effects of its own gravity can escape?

Perhaps the question rephrased might be: Why are gravitational waves immune to the effects of gravity?

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marked as duplicate by Javier, DilithiumMatrix, Sebastian Riese, ACuriousMind, Gert Dec 15 '15 at 0:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ "Why are gravity waves immune to the effects of gravity?" I think this is a nice question, and Id suggest you to edit your post to use this as your title, and not just "A question about gravity", which might be a bit vague. $\endgroup$ – AccidentalFourierTransform Dec 14 '15 at 19:38
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    $\begingroup$ Gravity waves are not a good rephrasing because gravity is not communicated by waves (and neither is the electromagnetic force communicated by light), especially not classically. Regardless, this question is a duplicate of How does gravity escape a black hole? $\endgroup$ – ACuriousMind Dec 14 '15 at 19:41
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    $\begingroup$ @ACuriousMind The retarded electric field is propagated as a wave, so there is a sense in which the electric force is communicated by a wave. I would presume that gravity has a similar construction, but I don't know enough to say for certain. $\endgroup$ – garyp Dec 14 '15 at 19:58
  • $\begingroup$ @BenitoCiaro: A photon is not an electromagnetic wave (although a classical electromagnetic wave is made up out of many photons), and you should not take virtual particles to be actual particles. $\endgroup$ – ACuriousMind Dec 14 '15 at 20:47
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Gravitational* waves (GW) are not immune to the effects of general relativity (i.e. gravity). If there was a source of GWs inside the event horizon, they would not emanate out of it (e.g. this answer --- which, I think, is much better than the accepted answer on that question).

At the same time, the 'information' about the gravitational field which is experienced/observed outside of an event-horizon has always been outside the event horizon --- and thus does not need to be 'communicated' out.

Consider, for example, if our sun collapsed entirely into a black-hole (e.g. this question). The gravity outside of it wouldn't actually change (assuming the mass of the sun was completely preserved into the black-hole) at all. The 'information' about the black-hole's mass is already (and has always been) outside of the event horizon. If additional matter falls into the black-hole (e.g. this question), the 'information' about it still stays on the outside --- in particular, one can think of it as being imprinted onto the event-horizon.

Regarding your initial question of,

Can a black hole be so large that not even the effects of its own gravity can escape?

The answer is thus, no; but I'd also like to point out that black-holes are 'scale-invariant' --- in that none of the physics changes as the total size/mass increases.

Side-Note:
*'Gravity Waves' are (unfortunately) a term often used for certain types of sound-waves caused by gravity in stars, so the term 'gravitational waves' is preferable. This usage is not universal.

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