Gravitational Cherenkov Losses in Theories Based on Modified Newtonian Dynamics

Survival of high-energy cosmic rays (HECRs) against gravitational Cherenkov losses is shown not to cast strong constraints on modified Newtonian dynamics (MOND) theories that are compatible with general relativity (GR): theories that coincide with GR for accelerations >> a(0) (a(0) is the MOND constant). The energy-loss rate, <(E)over dot>, is many orders smaller than those derived in the literature for theories with no extra scale. Modification to GR, which underlies <(E)over dot>, enters only beyond the MOND radius of the particle: r(M) = (Gp/ca(0))(1/2). The spectral cutoff, entering <(E)over dot> quadratically, is thus r(M)(-1), not k(dB) = p/h. Thus, <(E)over dot> is smaller than published rates, which use kdB, by a factor similar to(r(M)k(dB))(2) approximate to 10(39)(cp/3 x 10(11) Gev)(3). Losses are important only beyond D-loss approximate to ql(M), where q is a dimensionless factor, and l(M) = c(2)/a(0) is the MOND length, which is approximate to 2 pi times the Hubble distance.