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Entropic force approach in a noncommutative charged black hole and the equivalence
principle

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2012 EPL 98 10002
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April 2012
EPL, 98 (2012) 10002
doi: 10.1209/0295-5075/98/10002

www.epljournal.org

Entropic force approach in a noncommutative charged black hole
and the equivalence principle
S. Hamid Mehdipour1(a) andArash Keshavarz2(b)
1
2

Islamic Azad University, Lahijan Branch - P.O. Box 1616, Lahijan, Iran
Islamic Azad University, Central Tehran Branch - P.O. Box 13185-768, Tehran, Iran
received 11 December 2011; accepted in final form 1 March 2012
published online 27 March 2012
PACS
PACS
PACS

04.70.Dy – Quantum aspects of black holes, evaporation, thermodynamics
04.50.Kd – Modified theories ofgravity
05.70.-a – Thermodynamics

Abstract – Recently, Verlinde has suggested a novel model of duality between thermodynamics
and gravity which leads to an emergent phenomenon for the origin of gravity and general relativity.
In this paper, we investigate some features of this model in the presence of noncommutative
charged black hole by performing the method of coordinate coherent statesrepresenting smeared
structures. We derive several quantities, e.g., temperature, energy and entropic force. Our approach
clearly exhibits that the entropic force on a smallest fundamental cell of holographic surface with
radius r0 is halted. Accordingly, we can conclude that the black-hole remnants are absolutely inert
without gravitational interactions. So, the equivalence principle ofgeneral relativity is contravened
due to the fact that it is now possible to find a difference between the gravitational and inertial
mass. In other words, the gravitational mass in the remnant size does not emit any gravitational
field, therefore it is experienced to be zero, contrary to the inertial mass. This phenomenon
illustrates a good example for a feasible experimental confirmation to theentropic picture of
Newton’s Second law in very short distances.
Copyright c EPLA, 2012

The thermal emission from black holes has primarily
proved the firm relations between thermodynamics and
the gravitational treatment of black holes [1]. It seems
that one noticeable evidence for the essence of gravity is
perceived from the precise inspection of black-holes thermodynamics because it isfeasible to prepare a physical
similarity between spacetimes comprising horizons and
the concepts of temperature or entropy. Moreover, since
a quantum theory of gravity tells us that the black-hole
entropy could be connected to a number of microscopic
states, the meticulous assessment of black-hole entropy,
due to possessing the significant concepts for a yet to be
formulated theory of quantumgravity, can be important
to construct a full theory of quantum gravity. This is the
principal reason to investigate the origin of the blackhole entropy at a fundamental level. A few years ago,
Jacobson demonstrated that the Einstein equations are
attained from the thermodynamics laws [2]. In 2009,
Padmanabhan performed the debate of equipartition
(a) E-mail:

(b) E-mail:mehdipour@liau.ac.ir
arash batty2004@yahoo.com

energy of horizons to provide a thermodynamic outlook
on gravity [3]. In 2010, Verlinde proposed a new viewpoint of duality between thermodynamics and gravity
which has emerged, as an entropic force, by information
changes linked to the locations of physical objects [4].
This hypothesis indicates that gravitational interaction
emerges from the statistical...