Gravitational Cherenkov losses in MOND theories
  Survival of high-energy cosmic rays (HECRs) against gravitational Cherenkov
losses is shown not to cast strong constraints on MOND theories that are
compatible with general relativity (GR): theories that coincide with GR in the
high-acceleration limit. The energy-loss rate, L, is shown to be many orders
smaller than those derived in the literature for theories with no extra scale.
The gravitational acceleration produced by a HECR in its vicinity is much
higher than the MOND acceleration a0. So, modification to GR, which underlies
L, enters only beyond the MOND radius of the particle, within which GR holds
sway: r_M=sqrt(Gp/c a0). The spectral cutoff, which enters L quadratically, is
thus 1/r_M, not the particle's, much larger, de Broglie wavenumber: k_{dB}=
p/hbar. Thus, L is smaller than published rates, which use k_{dB}, by a factor
(r_M k_{dB})^2~10^{39}(cp/3.10^{11}Gev)^3. With 1/r_M as cutoff, the distance a
HECR can travel without major losses is q l_M, where l_M=c^2/a0 is the MOND
length, and q is a dimensionless function of parameters of the problem. Since
l_M is ~2 pi times the Hubble distance, survival of HECRs does not strongly
constrain GR-compatible, MOND theories. Such theories also easily satisfy
existing preferred-frame limits, inasmuch as these limits are gotten in
high-acceleration systems. I exemplify the results with MOND adaptations of
Einstein-Aether theories.
