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I apologize in advance if this is a stupid or off-topic question. Since Energy can be converted into matter according to $E=mc^2$, how fast does it take for the gravity of that new matter to extend from it and start mutual attraction to other pieces of matter? Is instantaneously? or at the speed of light? or is it that the energy converted in this process already has gravity and that that gravity is only rearranged in this new matter?

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The source of gravity is not mass, but stress-energy-momentum, so you are correct that

the energy converted in this process already has gravity and that that gravity is only rearranged

The change in the gravitational field needs time to propagate, though, and this does indeed happen at the speed of light.

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    $\begingroup$ How was this determined? After all, the only significant nearby change in mass is the sun (which is impossible to get an accurate mass at a specific time). One could use nuclear reactions, but the change in mass is too small to measure. Not only that, there would need to be 2 timers that are synchronized with the accuracy of an atomic clock. I don't think it has ever been determined that gravity moves at the speed of light, it's only theory. $\endgroup$ – LDC3 Oct 19 '14 at 19:33
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    $\begingroup$ @LDC3: it's a theoretical prediction consistent with the orbital decay of binary pulsars, most famously PSR 1913+16 (cf Nobel price 1993, arXiv:1011.0718) $\endgroup$ – Christoph Oct 19 '14 at 19:58

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