Interaction of the Fulling-Davies-Unruh thermal bath of the Proca field with a source static in the Rindler spacetime

Full text. We compute the total response of a static source with some fixed proper acceleration a0 in Rindler spacetime interacting with the zero energy massive vector particle of the Fulling-Davies-Unruh (FDU) thermal bath. According to the FDU effect, the inertial vacuum of a field in Minkowski spacetime corresponds to an FDU thermal state as seen by uniformly accelerated observers confined to the Rindler wedge and our computed response should be exactly the same as the response of such a source when it is uniformly accelerated in the inertial vacuum of Minkowski spacetime. This response of a static source in Rindler spacetime is computed in order to compare the result with the response of a static source with the same proper acceleration outside a Schwarzschild black hole interacting with the massive vector particles of the Hawking thermal radiation. Surprisingly, as it was already shown, these responses would be identical if a massless scalar field is consider instead of the Proca field, the field outside the Schwarzschild black hole is supposed to be in the Unruh vacuum and the source proper acceleration a0 is the same in both cases. This came as a surprise because structureless, static sources can only interact with zero-frequency field modes. Such modes can probe the global geometry of spacetime and are accordingly quite different in Schwarzschild spacetime and in the Rindler wedge. (author)