MOND理论中的引力切伦科夫损失
Gravitational Cherenkov losses in MOND theories
摘要：
高能宇宙射线（HECRs）对抗引力切伦科夫损失的生存被证明不会对与广义相对论（GR）兼容的MOND理论产生强约束：在高加速度极限下与GR重合的理论。的能量损失率，L，被证明是许多订单小于那些在文献中推导的理论没有额外的规模。HECR在其附近产生的重力加速度远高于MOND加速度a0。因此，对GR的修改，它是L的基础，只在粒子的MOND半径之外进入，在此半径内，GR占主导地位：r_M=sqrt（Gp/c a0）。因此，以二次方式进入L的光谱截止值是1/r_M，而不是粒子的德布罗意波数，德布罗意波数要大得多：k_{dB} = p/hbar。因此，L比使用k_{dB}的已发表速率小一个因子（r_M k_{dB}）^2 ~10^{39}（cp/3.10^{11}Gev）^3。以1/r_M为截止值，HECR在没有重大损失的情况下可以行进的距离为q l_M，其中l_M=c^2/a0是MOND长度，q是问题参数的无量纲函数。由于l_M是哈勃距离的2 π倍，HECR的生存并不强烈地约束GR兼容的MOND理论。这样的理论也很容易满足现有的优先框架的限制，因为这些限制是在高加速度系统。我用爱因斯坦-以太理论的MOND改编来解释结果。
英文摘要：
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.
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