Rindler Trajectories in Cloud of strings in 3rd order Lovelock gravity

This paper studies the Rindler trajectories in the Cloud of strings in 3rd-order Lovelock gravity. According to the generalization of the Letaw-Frenet equations for curved spacetime (ST), the trajectory will continue to accelerate linearly and uniformly throughout its motion. The ST of the Cloud of strings in 3rd-order Lovelock gravity, a boundary is established on the bound of the accelerated magnitude |a| for radially inward traveling trajectories in the expression of the BH mass M which is represented by |a| ≤ 2/(√105 M). For a certain selection of asymptotic initial data h, the linearly uniformly accelerated trajectory always enters the BH for acceleration |a| greater than the bound value. To study the bound value by |a|, the radial linearly uniformly accelerated trajectory can only travel to infinity within a small radius or the distance of the closest approach. However, it is observed that when the bound |a| = 2/(√105M) is saturated, and this distance approaches its lowest value of rb = (b+2)√ 7 √ 5M 4 √ b+1 , r > rs. We also demonstrate that the value of the acceleration has a limited constraint, there is always an extension of the closest approach rb > (b+2) √ 7 √ 5M 6 √ b+1 for |a| ≤ B(M, h), for each set of finite asymptotic initial data h.