Turkish Journal of Physics

Vacuum Fluctuations in the Presence of Spherical Gravitational Impulsive Waves






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.

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