A phenomenon of "asymptotic freedom" arises in Schwarzschild spacetime based on a special Lorentz violation model

In our previous work, we proposed a special Lorentz violation model characterized by the fact that the maximum energy of a particle with mass is finite and proportional to its rest mass, rather than infinite as predicted by the Lorentz model. In this paper, we continue to investigate the impact of the Lorentz violation model on the curved spacetime. Firstly, we proposed a method to obtain the spacetime metric corresponding to this Lorentz violation model. Secondly, we used this new metric to analyze the proper acceleration of particles fixed in the Schwarzschild spacetime. To our surprise, we find that when the distance between particles and the event horizon of the Schwarzschild black hole is less than a certain distance, the smaller the distance, the smaller the proper acceleration, and the proper acceleration tends to 0 when the particle is fixed at the event horizon. By analogy with the quark model in particle physics, we can also call this phenomenon the "asymptotic freedom" in Schwarzschild spacetime, which shows us a different black hole.