Dependence of the Black-body Force on Spacetime Geometry and Topology

Abstract

In this paper we compute the corrections to the black-body force (BBF) potential due to spacetime geometry and topology. This recently discovered attractive force on neutral atoms is caused by the thermal radiation emitted from black bodies and here we investigate it in relativistic gravitational systems with spherical and cylindrical symmetries. For some astrophysical objects we find that the corrected black-body potential is greater than the flat case, showing that this kind of correction can be quite relevant when curved spaces are considered. Then we consider four cases: The Schwarzschild spacetime, the global monopole, the non-relativistic infinity cylinder and the static cosmic string. For the spherically symmetric case of a massive body, we find that two corrections appear: One due to the gravitational modification of the temperature and the other due to the modification of the solid angle subtended by the atom. We apply the found results to a typical neutron star and to the Sun. For the global monopole, the modification in the black-body potential is of topological nature and it is due to the central solid angle deficit that occurs in the spacetime generated by that object. In the cylindrical case, which is locally flat, no gravitational correction to the temperature exists, as in the global monopole case. However, we find the curious fact that the BBF depends on the topology of the spacetime through the modification of the azimuthal angle and therefore of the solid angle. For the static cosmic string we find that the force is null for the zero thickness case.