According to the Dirac equation, antimatter is the negative energy solution to the following relation:
$$E^2 = p^2 c^2 + m^2 c^4.$$
And according to general relativity, the Einstein tensor (which roughly represents the curvature of spacetime) is linearly dependent on (and I assume would then have the same mathematical sign as) the stress-energy tensor:
$$G_{\mu \nu} = \frac{8 \pi G}{c^4}T_{\mu \nu}.$$
For antimatter, the sign of the stress-energy tensor would change, as the sign of the energy changes. Would this change the sign of the Einstein tensor, causing spacetime to be curved in the opposite direction as it would be curved if normal matter with positive energy were in its place? Or does adding in the cosmological constant change things here?
Answer
Antimatter has the same mass as normal matter, and its interaction with gravity should be the same according to GR and QM.
That said, antimatter has only been created in tiny amounts so far and only few experiments have been performed to confirm there is no new physics involved.
The gravitational interaction of antimatter with matter or antimatter has not been conclusively observed by physicists. While the overwhelming consensus among physicists is that antimatter will attract both matter and antimatter at the same rate that matter attracts matter, there is a strong desire to confirm this experimentally, since the hypothesis is still open to falsification.
https://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter
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