Dissipation of Modified Entropic Gravitational Energy Through Gravitational Waves

Abstract

The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde's entropic approach to gravitation in combination with Sorkin's definition of Universe's quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature $\tau=15/16 \frac{\Lambda^{1/2}\hbar G}{c^4}\sim9.27\times10^{-105}$ seconds, which is much smaller than the Planck time $t_{P}=(\hbar G/c^5)^{1/2}\sim 5.38\times10^{-44}$ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter $F_g=32/30\frac{c^7}{\Lambda \hbar G^2}\sim 3.84\times 10^{165}$ Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length $F_{gP}=c^4/G\sim1.21\times10^{44}$ Newtons.