The question whether superluminal particles can exist in the frame work of the general relativistic theory of gravity will be discussed. It seems that the answer to this question is negative. In truth the result may only represent a difficulty to special but not general relativity, the later allowing both Lorentzian and Euclidian metrics. An Euclidian metric does not restrict speed. Although only the Lorentzian metric is stable, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality. The implications of those particles on well-known open questions such as the cosmological homogeneity problem and the dark energy and dark matter problems would be briefly discussed.

Bibliography

[1] ‎ Asher Yahalom "The Geometrical Meaning of Time" [“The Linear Stability of ‎Lorentzian Space-Time” Los-Alamos Archives - gr-qc/0602034, gr-qc/0611124] ‎Foundations of Physics http://dx.doi.org/10.1007/s10701-008-9215-3 Volume 38, ‎Number 6, Pages 489-497 (June 2008).‎

[2] Asher Yahalom "Gravity and Faster than Light Particles" Journal of Modern ‎Physics (JMP), Vol. 4 No. 10 PP. 1412-1416. DOI: 10.4236/jmp.2013.410169.  ‎Pub. Date: October 31, 2013‎.