A BRIEF STUDY OF THERMODYNAMIC QUANTITIES OF BLACK HOLES IN RAINBOW GRAVITY
Sandip Dutta*, Ritwick Banerjee** and Ritabrata Biswas*
* Department of Mathematics
The University of Burdwan, Golapbag Academic Complex, City : Burdwan-713104,
Dist.:Purba Burdwan, State : West Bengal, India
** Department of Mathematics
Indian Institute of Engineering Science and Technology, Shibpur, India
Email:duttasandip.math@gmail.com, ritwick92@gmail.com and
biswas.ritabrata@gmail.com
(Received : June 19, 2019 ; Revised: June 22, 2019)
Abstract
In this paper, we investigate the thermodynamic properties of black holes under the influence of rainbow gravity. In the metric of Schwarzschild, Reissner-Nordstrom
and Reissner-Nordstrom-de Sitter black hole surrounded by quintessence, we consider a rainbow function and derive the existence of remnant and critical masses of a black hole. Using the Hawking temperature relation we derive the heat capacity and the entropy of the rainbow gravity inspired black holes and closely study the relation between entropy and area of the horizon for different values of n of the rainbow function. The entropy relation is expressed in terms of the area of the event horizon of the black hole and from the area-entropy graphs we make several meaningful interpretations and closely analyse the effects of the different values of the rainbow parameters on thermodynamic properties. It is interesting to observe that the introduction of rainbow gravity keeps the overall physical interpretations similar to the Einstein gravity but it gives a quantum correction to the latter at the Planck scale and gives us new and interesting insights into the thermodynamic journey of a BH.
2010 Mathematics Subject Classifications: 83C75, 83D05, 83E99.
Keywords and phrases: Black hole physics, Rainbow gravity, Thermodynamics