Does E in E=mc^2 Include Gravity?

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Does the E in E=MC^2 include the gravitons?
 
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Assuming gravitons exist, they would be massless and would fall under the equation E2 = M2C4 + P2C2, where the M2C4 portion is zero (because m is zero) but the P2C2 portion is non-zero, as gravitons would have momentum.
 

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