DPPA, Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev Lett. 2011 Mar 18;106(11):111101. doi: 10.1103/PhysRevLett.106.111101. Epub 2011 Mar 17.
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, is many orders smaller than those derived in the literature for theories with no extra scale. Modification to GR, which underlies E, enters only beyond the MOND radius of the particle: r(M)=(Gp/ca(0))(1/2). The spectral cutoff, entering E quadratically, is thus r(M)(-1), not k(dB)=p/ℏ. Thus, E 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). Losses are important only beyond D(loss)≈qℓ(M), where q is a dimensionless factor, and ℓ(M)=c(2)/a(0) is the MOND length, which is ≈2π times the Hubble distance.
高能宇宙射线（HECRs）在引力切伦科夫损失面前的生存能力并未对与广义相对论（GR）相兼容的修正牛顿动力学（MOND）理论施加强烈约束：对于加速度 ≫a(0)（a(0) 是 MOND 常数）的理论，这些理论与 GR 是一致的。能量损失率 E 比文献中那些没有额外尺度的理论所推导的要小几个数量级。为 E 提供基础的对 GR 的修正仅在粒子的 MOND 半径之外出现：r(M)=(Gp/ca(0))(1/2)。因此，二次方进入 E 的谱截止，即 r(M)(-1)，而不是 k(dB)=p/ℏ。因此，E 比使用 k(dB)的已发表速率小，因子约为 ∼(r(M)k(dB))(2)≈10(39)(cp/3×10(11) Gev)(3)。只有在 D(loss)≈qℓ(M)之外，损失才重要，其中 q 是一个无维因子，而 ℓ(M)=c(2)/a(0) 是 MOND 长度，约为哈勃距离的 2π 倍。
