Cerenkov Emission by Neutral Particles in Gravitoelectro- Magnetic Fields

It is shown that under the post-Newtonian approximation the Einstein equations can be reduced to the standard Maxwell-type field equations in a medium; in such a context the Cerenkov emission by a neutral particle gives large energy loss while the particle moves at faster than the phase speed of waves in the medium. It has often been noted that magnetism can be understood as the consequence of electrostatics plus Lorentz invariance. Similarly, Newtonian gravity together with Lorentz invariance in a consistent way must include a gravitomagnetic field. This is the case of gravitoelectromagnetic (GEM) form of the Einstein equations in a medium [1-5]. In such a framework, the refractive index n ≡ √ ε t of a medium is often is more than one [see (27), below]; note that the statement that only accelerated particles radiate is not correct when there are waves with n > 1 [6]. Hence the Cerenkov emission by neutral particles in constant rectilinear motion is unavoidable. It is well known that in the slow-motion limit of general relativity, accurate to post-Newtonian (PN) order, where the field equations can be reduced as [7]: ∇ 2 φ = 4πGρ, (1) ∇ 2 A = 16πGρv/c; (2)