Final Comments on ``Another view on the velocity at the Schwarzschild horizon'' by Tereno

Abstract

We have recently shown that at the Event Horizon of a Schwarzschild BH, the Kruskal derivative assumes a form du/dv = +,- f(r,t)/f(r,t) = +, - 1. Corespondingly, du^2 = dv^2, and the geodesic of a material particle becomes NULL at the EH. Physically this means that the free fall speed measured by the Kruskal observer V=1 at the EH. However, Tereno has difficulty in accepting this limiting value of du/dv=1. We point out that Eq.(4) of his paper shows (1-2M/r) dt/dr =-1, at r=2M, and, indeed, the mod of V=1. However, rather than accepting this, Tereno has obtained and incorrect expression for t=t(r) and has tried to find V graphically. We point out that, instead, if he uses the correct t=t(r) relation by using Eq. (12.2.24) of Shapiro and Teukolsky, he would indeed find V=1. It is simple to understand, physically, why one must have V=1 at the EH. If the free fall speed measured by the static Sch. Observer is Vs and the relative velocity of the other observer is Vso with respect to the Sch. observer, then the velocity of free fall of the test particle, V, can be found by using the Special Relativistic velocity addition formula (locally). Since Vs =1 at r=2M, one would always find, V=1 too. We shall not respond to any further preprint on this line.