/ 99 05 32 9 v 2 1 4 Ju n 19 99 Comments on “ Another view on the velocity at the Schwarzschild horizon ”

It is shown that the conclusions reached by Tereno are completely faulty We have recently shown that 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. Although, we have already pointed out 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 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, 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 [ E − ( 1− 2M r )] −1/2 (5)