What did current experiments find about the question of antimatter being repulsive for gravitation, that is to create an opposite curvature of spacetime compared to matter?
Antimatter and matter respond to gravity in the same way, experiment reveals – Physics World
https://physicsworld.com/a/antimatter-and-matter-respond-to-gravity-in-the-same-way-experiment-reveals/
No, it may not, as long as gravity is described by general relativity, or scalar-tensor generalizations thereof.
Gravity, in general relativity, is attractive, because it is mediated by gravitons, particles that carry spin 2 and even spin particles mediate only attractive interactions.
Matter differs from antimatter by the internal charges, not, however, by the value of the energy-momentum tensor.
So, if gravity is described only by general relativity, then matter and antimatter can’t be distinguished. The reason for doing the experiment would be to check, whether gravity requires fields beyond the metric tensor, in order to describe spacetime geometry-and the additional fields will be sensitive to the internal charges. Scalar fields, however, would, also, describe attractive forces, since they describe the exchange of spin 0 particles; vector fields, though, would describe repulsive forces, since they describe the exchange of spin 1 particles. Such particles are predicted in generalizations of general relativity, like scalar-tensor theories (for spin-0 particles) or supergravity (for spin-1 particles).
In the 1970s this was pointed out here: https://inspirehep.net/literature/142417
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