q-deformed Einstein equations from entropic force

Abstract

In this study, we investigate the influences of fermionic q-deformation on the Einstein equations by taking into account of Verlinde's entropic gravity approach and Strominger's proposal on quantum black holes. According to Verlinde's proposal, gravity is interpreted as an entropic force. Moreover, Strominger's suggetion claims that extremal black holes obey deformed statistics instead of the standard Bose or Fermi statistics. Inspired by Verlinde's and Strominger's suggestions, we represent some thermostatistical functions of VPJC-type q-deformed fermion gas model for the high-temperature limit. Applying the Verlinde's entropic gravity approach to the q-deformed entropy function, q-deformed Einstein equations with the effective cosmological constant are derived. The results obtained in this work are compared with the related works in the literature.

Friedmann equations for deformed entropic gravity

“…For this purpose, we considered three different deformed gas models in the high-temperature limits. First two models [25,26] are related one parameter q-deformed fermion and fermion-boson gas system, respectively, and the third one [24] corresponds to two-parameters (q, p)-deformed of fermion gas system. We wrote the temperature function in a compact form depending on these models in Eq.…”

“…In recent years, the study [23] showed us that the deformed Einstein equation can be derived by using deformed statistics rather than standard one to describe gravitational behaviors of the quantum black holes in the framework of the entropic gravity suggestion. From this motivation, the different deformation of Einstein's field equations have been obtained by considering the extremal quantum black holes as q-deformed fermions [25], q-deformed bosons and fermions [26], and (q, p)-deformed fermions [24] for the high-temperature limits. In this section, we briefly review the useful results of these three models.…”

“…On the other hand, the studies [23][24][25][26] show that the deformed Einstein field equations can be derived as follows by using Verlinde's entropic gravity proposal [9],…”

“…In addition to this, one can introduce the effective cosmological constant to the Einstein field equations by changing the active gravitational mass (for more detail see [25]),…”

“…For instance, in the Ref. [23][24][25][26], one and two-parameters deformed Einstein equations were obtained by considering the quantum black holes as deformed bosons or fermions.…”