** Authors:**
M. HORTAÇSU

** Abstract: **
We know that plane waves do not give rise to vacuum fluctuations [1,2].
One may check whether the same result is true also for spherical waves.
A while ago, in the year 1988, Prof. Yavuz Nutku gave me his metric which
was not published yet, and asked me to calculate the vacuum fluctuations
in the background of this metric. He published his metric, in collaboration
with Prof. Roger Penrose much later [3]. The date of my first paper
using this metric [4] shows that this metric was around much before
it was published by Nutku and Penrose.
We applied it to different trial functions [5,6,7,8] and found
no finite fluctuations in the Minkowski case. If we apply the same metric
to the de Sitter universe [9], we got finite vacuum fluctuations given
as T_{vv} proportional to u \delta(v)[f(x,y)] [8,10]. Here
[f(x,y)] depends on the trial function used.
We must stress the fact that in these calculations first order
perturbation theory was used. They gave the null result. This was,
perhaps, the weak point in these calculations. Prof. Alikram Aliev
always insisted that new, non trivial phenomena should be present
in second order calculations, although they may be absent in the first
order. I will report here our results on this problem, performed in
the second order perturbation theory.

** Keywords: **