Relativity and c/sqrt{3}

We define the critical coordinate velocity v_c. A particle moving radially in Schwarzschild background with this velocity, v_c= c/sqrt 3, is neither accelerated, nor decelerated if gravitational field is weak, r_g << r, where r_g is the gravitational radius, while r is the current one. We find that the numerical coincidence of v_c with velocity of sound in ultrarelativistic plasma, u_s, is accidental, since two velocities are different if the number of spatial dimensions is not equal to 3