Analyzing Time near Horizon in Schwarzschild and De-Sitter Space-Time in Particle's Frame of Reference

Here, we calculate the variation of distance due to gravitation in De-Sitter and Schwarzschild space. Then, we calculate motion of the particle in particle’s frame of reference to get the result that the particle can’t reach event horizon [r=2GM for Schwarzschild space and r=√ (3/λ) for De-Sitter space] in any frame of reference.