Building a linear equation-of-state for trapped gravitons from finite size effects and the Schwarzschild black hole case

摘要

In this paper, we continue the investigations present in [S. Viaggiu, Physica A 473 (2017) 412; 488 (2017) 72.] concerning the spectrum of trapped gravitons in a spherical box, and in particular, inside a Schwarzschild black hole (BH). We explore the possibility that, due to finite size effects, the frequency of the radiation made of trapped gravitons can be modified in such a way that a linear equation-of-state PV = gamma U for the pressure P and the internal energy U arises. Firstly, we study the case with U similar to R, where only fluids with gamma -1/3 are possible. If corrections similar to 1/R are added to U, for gamma is an element of[0, 1/3], we found no limitation on the allowed value for the areal radius of the trapped sphere R. Moreover, for gamma 1/3, we have a minimum allowed value for R of the order of the Planck length LP. Conversely, a fluid with P 0 can be obtained but with a maximum allowed value for R. With the added term looking like similar to 1/R to the BH internal energy U, the well-known logarithmic corrections to the BH entropy naturally emerge for any linear equation-of-state. The results of this paper suggest that finite size effects could modify the structure of graviton's radiation inside, showing a possible mechanism to transform radiation into dark energy.