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 \(|a|\le {\frac{ \left( b+1 \right) ^{3/2}}{3 \sqrt{3} m}}\) . 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 \(|a| = {\frac{ \left( b+1 \right) ^{3/2}}{3 \sqrt{3} m}}\) is saturated, and this distance approaches its lowest value of \(r_b = {\frac{3m}{b+1}}\) . We also demonstrate that the value of the acceleration has a limited constraint, there is always an extension of the closest approach \(r_b > {\frac{2m}{b+1}}\) for \(|a|\le B(m, h)\) , for each set of finite asymptotic initial data h.
