Some properties of accelerating observers in the Schwarzschild space

It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is of sense. For the sake of simplicity, we can construct these observers' world lines by comparing with the observers in the Hawking effect and Unruh effect, whose world lines are both hyperbolic curves in the appropriate coordinates. We do it after defining a certain special null hypersurface in the Kruskal coordinates. Our result shows that these accelerating observers defined in our paper can also detect the radiation with the analogy of the Unruh effect, though locally. Furthermore, we conjecture that, for any null hypersurface in any spacetime, the corresponding observers who can at least locally detect the radiation from it can be found.