# Gravitational potential energy with regards to annihilation

Given particles A, B, C and D, where:

• A and B have an equivalent mass
• C and D have an equivalent mass, both larger than A (or B)
• D is the antiparticle of C.

A and B start close to C, but with velocity, such that they have moved away from C, so their kinetic energy has been converted to GPE. If D then collides with C such that C and D annihilate, what is the fate of the GPE that A and B previously acquired?

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The answer is that the gravitational field of C and D is not generated by their mass, but by their energy density. Energy gravitates in exactly the same way that mass does. The equivalence between the two is just the formula we've all see a hundred times: $E = mc^2$. Life is actually a bit more complicated than this, because the spacetime curvature that creates gravity is actually proportional to an object called the stress-energy tensor. However the mass/energy density is usually the most important part of this object