So I asked a question about what would happen in regards to gravitational potential if I left earth and then vaporized it. The answer I got was that the Mass would still remain the same and even if something is split the total amount of gravity it generates is linearly proportional to mass. But what if I used $E=mc^2$ and turned the entire earth into massless radiant energy? Where would the gravitational potential energy go?
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1Related: https://physics.stackexchange.com/q/22876/2451 , https://physics.stackexchange.com/q/34352/2451 and links therein. – Qmechanic Feb 23 '22 at 18:45
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Short answer - nowhere. Check Kugelblitz,- black holes formed from pure energy- radiation, light, etc. – Agnius Vasiliauskas Feb 23 '22 at 19:04
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Tricky question! That equation, $E=MC^2$, is supposed to represent the equivalence of mass and energy in the theory of general relativity. One of the ways in which they are equivalent is that they both curve spacetime. We should, in principle, be able to say that the gravitational influence of the Earth on the rest of the universe will not change just because you annihilated the Earth.
It could be tricky to measure though, because if there was any change in the gravitational field, that change would propagate outward as a gravitational wave moving at exactly the same speed as the expanding sphere of the light itself. And, as soon as that light sphere encompasses you, then you're going to have to take the shell theorem into account.
Solomon Slow
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The Earth would change in an expanding sphere of photons. The outer photons would radiate away from the inner parts, while the innermost of them follow fast, but, due to a small chance of them scattering with one another, would roam around around in the center. But for a very short time, as the chance for such a second order process to happen (by means of the virtual electron field) is very small. The sphere expands rapidly.
Because pure energy has an effect on the curvature of spacetime, the ball of photons will give rise to the same potential as the massive Earth had. This (negative) potential is gone when the photons have reached faraway regions, and their energy will have decreased a little. Their wavelength will have increased a bit.
Note that you would need quite some anti matter to accomplish this gargantuan feat. Which makes one wonder how a black hole can evaporate into photons completely.
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2@Dale They get redshifted. Which is a decrease in energy. Damned photons... I'll edit. Thanks. – MatterGauge Feb 23 '22 at 20:38