Both matter and antimatter have mass and thus gravity, but since energy from annihilation has no mass what happens to the force of gravity that was previously present? What about conservation of energy? Does it include gravity too?
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1$\begingroup$ This question (v1) seems spurred by a confusion between rest/invariant mass and relativistic mass. See e.g. this Phys.SE post, and a couple of paragraphs down on this Wikipedia page. $\endgroup$– Qmechanic ♦Commented Mar 31, 2014 at 22:55
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3 Answers
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The annihilation produces gamma photons, whose total energy sums up to the total energy $E_0=\sqrt{p^2 \,c^2 + m^2\,c^4}$ formerly contained in the matter / antimatter kinetic energy (the $p\,c$ term) and that "frozen" in rest mass (the $m\,c^2$ term). So energy is conserved.
As for gravity, the Einstein field equations "can't tell the difference" between the "matter/anitmatter" and "photons" - they are both pretty much the same and their "effective gravitational mass" is $E_0/c^2$. Look up the Stress Energy Tensor - this is the "source" side of the Einstein field equations that begets the "Curvature" (deviation from Euclid's parallel postulate) of spacetime. There are some subtleties, because the SE Tensor is a tensor, not a scalar, but if you think of all the "Stuff" as a gravitational source of gravitation mass $E_0/c^2$, this is a good mental picture. So, at the time of the collision, nothing much changes as far as gravity is concerned. The change from matter/antimatter to light will change how the SE tensor and thus spacetime curvature evolves with time, because matter / antimatter and light have different propagation equations (the former propagating at some speed less than that of light).
answered Mar 28, 2014 at 23:32
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According to general relativity the source for spacetime curvature/gravity is the stress-energy tensor. Mass contributes rest energy $mc^2$ but it is not the only form of energy that influences gravity. Therefore it's not exactly true to say that mass causes gravity, but energy does. The photons produced during annihilation will carry energy and so they will also affect the gravitational field.
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The idea that gravity is sourced just by mass only hold in the nonrelativistic limit. In a fully relativistic treatment, which is necessary to understand any process involving particle annihilation, you must use the full stress energy tensor. This tensor includes mass, but it also includes, for instance, the energy of any photons created in the annihilation.
