Final Comments on “Another view on the velocity at the Schwarzschild horizon” by Tereno

It is shown that the conclusions reached by Tereno are completely incorrect. We have recently shown that at the Event Horizon (EH) of a Sch. Black Hole (BH), the Kruskal derivative assumes a form [1] du dv → f(r, t, dr/dt) ±f(r, t, dr/dt) (1) because u → ±v as r → 2M . Although this limit attains a value of ±1 irrespective of f → 0,∞, or anything, Tereno [2] refuses to accept this. We have already pointed out that that one should work out the limiting values of the relevant fractions appropriately[3], Tereno has decided to adopt another view point on this issue[4]. In his new note[4], he has correctly reexpressed our result in terms of the physical speed V , as seen by the Kruskal observer, and more explicit Sch. relationships: For r > 2m, the expression is, V = 1 + tanh(t/4M) dt dr (1− 2M/r) tanh(t/4M) + dt dr (1− 2M/r) , (2) Now since as the r → 2M , t → ∞ and tanh(t/4M) → 1, the above equation approaches a form: V = f(r, t, dt/dr) f(r, t, dt/dr) ; r → 2M (3) Clearly, the foregoing limit assumes a value of 1 irrespective of whether f → 0,∞ or anything. But Tereno thinks it is less than unity! He, on the other hand, invokes (correctly) the expression for dt/dr for a radial geodesic: dt dr = −E ( 1− 2M r ) −1 [ E − ( 1− 2M r )] −1/2 . (4) where E is the conserved energy per unit rest mass. It follows from this equation that (1− 2M/r) dt dr = −E [