We introduce the isothermal cavity, static holographic screen, and accelerating surface as holographic screen to study the entropic force in the presence of the Schwarzschild black hole. These may merge to provide a consistent holographic screen to define the entropic force on the stretched horizon near the event horizon. Considering the similarity between the stretched horizon of black hole and the entanglement system, we may define the entropic force in the entanglement system without referring the source mass.
We study the entropic force by introducing a bound $S \le A^{3/4}$ between entropy and area which was derived by imposing the non-gravitational collapse condition. In this case, applying a modified entropic force to this system does not lead to the Newtonian force law.
We consider a freely falling holographic screen for the Schwarzschild and Reissner-Nordström black holes and evaluate the entropic force à la Verlinde. When the screen crosses the event horizon, the temperature of the screen agrees to the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.
We show in detail that the entropic force of the static spherically symmetric spacetimes with unusual asymptotics can be calculated through the Verlinde's arguments. We introduce three different holographic screen candidates, which are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)] for Schwarzschild black hole solutions, in order to identify the entropic force arising between a charged dilaton black hole and a test particle. The significance of the dilaton parameter on the entropic force is highlighted, and shown graphically.
We investigate a possibility of realizing the entropic force into the cosmology. A main issue is how the holographic screen is implemented in the Newtonian cosmology. Contrary to the relativistic realization of Friedmann equations, we do not clarify the connection between Newtonian cosmology and entropic force because there is no way of implementing the holographic screen in the Newtonian cosmology.
It has been suggested that the Newtonian gravitational force may emerge as an entropic force from a holographic microscopic theory. In this framework, the possibility is reconsidered that Newton's gravitational coupling constant G can be derived from the fundamental constants of the underlying microscopic theory.
Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation whi…
If we assume that the source of thermodynamic system, $ρ$ and $p$, are also the source of gravity, thermal quantities, such as entropy, temperature, and chemical potential, can induce effects of gravity, or gravity can induce thermal effects. We find only for systems with constant temperature and zero chemical potential, gravity can be seen as an entropic force. The case for Newtonian approximation is discussed.
We introduce the cavity enclosing a source mass $M$ to define the temperature force. Starting with the Tolman temperature in the stationary spacetime, we find a non-relativistic temperature $T_{non}= T_\infty(1-Φ/c^2)$ with the Newtonian potential $Φ$. This temperature could be also derived from the Tolman-Ehrenfest effect, satisfying a relation of $T=T_{\infty}e^{-Φ/c^2}$ with the local temperature $T$. Finally, we derive the temperature force $\vec{F}_{tem}=mc^2(\vec{\nabla} \ln T )$ which leads to the Newtonian force law without introducing the holographic screen defined by holographic prin…
Entropic forces have recently attracted considerable attention as ways to reformulate, retrodict, and perhaps even "explain'" classical Newtonian gravity from a rather specific thermodynamic perspective. In this article I point out that if one wishes to reformulate classical Newtonian gravity in terms of an entropic force, then the fact that Newtonian gravity is described by a conservative force places significant constraints on the form of the entropy and temperature functions. (These constraints also apply to entropic reinterpretations of electromagnetism, and indeed to any conservative forc…
In this paper, we propose a model in which an additional pressure due to the effects of the entropic force is added to the ideal fluid. Furthermore, we obtain the dynamic equation in the FRW universe which contains the quantum gravitational effects based on the description of entropic force and emergence of space. Our model can well explain the age of the universe and the effect of the current accelerating expansion. We give the relation between the luminosity distance and the redshift factor, and compare this relation with that of lambda cold dark matter model($ΛCDM$ model).
Different candidates of quantum gravity proposal such as string theory, noncommutative geometry, loop quantum gravity and doubly special relativity, all predict the existence of a minimum observable length and/or a maximal momentum which modify the standard Heisenberg uncertainty principle. In this paper, we study the effects of minimal length and maximal momentum on the entropic force law formulated recently by E. Verlinde.
In this note by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
In this paper, we study the idea about gravity as entropic force proposed by Verlinde. By applying the identification between partition functions of gravity theory and the dual field theory, we find the gravitational force can be calculated from the changing of entropy induced from its dual field theory side. Unlike Verlinde's calculation, our method does not depend on other assumptions such as equipartition of energy, so it is a safe check on the entropic force idea. Also we show how entropic force can be derived by similar method from gravity side along, which will provide a clue to a better…
By following the spirit of Verlinde's entropic force proposal arXiv:1001.0785, we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is consistent with equipartition principle and the form of Komar mass. The entropy of the holographic screen determines its area, i. e. $S=\frac{A}{4}$. And then we express the metric by thermodynamic variables, to give an illustration of how the space is foliated by the thermodynamical potentials.
We argue that neutron interference experiments and experiments on gravitational bound states of neutron unambiguously disprove entropic origin of gravitation. The criticism expressed in a recent paper [arXiv:1104.4650] concerning our arguments against entropic gravity is shown to be invalid.
We argue certain nonviolent local quantum field theory (LQFT) modification considered at the global horizon ($r=2M$) of a static spherically-symmetric black hole can lead to adiabatic leakage of quantum information in the form of Hawking particles. The source of the modification is (i) smooth at $r=2M$ and (ii) rapidly vanishing at $r\gg2M$. Furthermore, we restore the unitary evolution by introducing extra quanta which departs slightly from the generic Hawking emission without changing the experience of an infalling observer (no drama). Also, we suggest that a possible interpretation of the B…
We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be writte…
We argue that experiments with ultra-cold neutrons in the gravitational field of Earth disprove recent speculations on the entropic origin of gravitation.
Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the en…
In this note we generalize the quantum uncertainty relation proposed by Vancea and Santos [7] in the entropic force law, by introducing Planck scale modifications. The latter is induced by the Generalized Uncertainty Principle. We show that the proposed uncertainty relation of [7], involving the entropic force and the square of particle position, gets modified from the consideration of a minimum measurable length, (which can be the Planck length).
The entropic force has been recently argued to be responsible for dissociation of heavy quarkonia. In this paper, we analyze $R^2$ corrections and $R^4$ corrections to the entropic force, respectively. It is shown that for $R^2$ corrections, increasing $λ_{GB}$ (Gauss-Bonnet factor) leads to increasing the entropic force. While for $R^4$ corrections, increasing $λ$ ('t Hooft coupling) leads to decreasing the entropic force. Also, we discuss how the entropic force changes with the shear viscosity to entropy density ratio, $η/s$, at strong coupling.
We investigate the implications of the entropic force formalism proposed by Verlinde. We show that an UV/IR relation proposed by Cohen et al, as well as an uncertainty principle proposed by Hogan can be derived from the entropic force formalism. We show that applying the entropic force formalism to cosmology, there is an additional term in the Friedmann equation, which can be identified as holographic dark energy. We also propose an intuitive picture of holographic screen, which can be thought of as an improvement of Susskind's holographic screen.
We derive the entropic force in the presence of the Schwarzschild black hole by using the local equipartition rule and holographic principle. On the other hand, when using the Tolman temperature, one does not arrive at the Newtonian force law.
We study the dynamics of the geometric entanglement entropy of a 2D CFT in the presence of a boundary. We show that this dynamics is governed by local equations of motion, that take the same form as 2D Jackiw-Teitelboim gravity coupled to the CFT. If we assume that the boundary has a small thickness $ε$ and constant boundary entropy, we derive that its location satisfies the equations of motion of Schwarzian quantum mechanics with coupling constant $C = {c ε}/{12π}$. We rederive this result via energy-momentum conservation.
After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynami…
The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein's field equation, Newton's law of gravitation and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde's theory, the quantum corrections to the entropic force are obtained. The result shows that…
Motivated by Verlinde's theory of entropic gravity, we give a tentative explanation to Coulomb's law with an entropic force. When trying to do this, we find the equipartition rule should be extended to charges and the concept of temperature should be reinterpreted. If one accepts the holographic principle as well as our generalizations and reinterpretations, then Coulomb's law, the Poisson equation and the Maxwell equations can be derived smoothly. Our attempt can be regarded as a new way to unify the electromagnetic force with gravity, from the entropic origin. Possibly some of our postulates…
We consider E. Verlinde's proposal that gravity is an entropic force -- we shall call this theory entropic gravity (EG) -- and reanalyze a recent claim that this theory is in contradiction with the observation of the gravitationally-bound ground state of neutrons in the GRANIT experiment. We find that EG does not necessarily contradict the existence of gravitationally-bound quantum states of neutrons in the Earth's gravitational field, since EG is equivalent to Newtonian gravity in this case. However, certain transitions between the gravitationally-bound quantum states of neutrons, in particul…
Recently, a new perspective of gravitational-thermodynamic duality as an entropic force arising from alterations in the information connected to the positions of material bodies is found. In this paper, we generalize some aspects of this model in the presence of noncommutative Schwarzschild black hole by applying the method of coordinate coherent states describing smeared structures. We implement two different distributions: (a) Gaussian and (b) Lorentzian. Both mass distributions prepare the similar quantitative aspects for the entropic force. Our study shows, the entropic force on the smalle…
We show that to accommodate inflation in the entropic force scenario of Verlinde, it is necessary to introduce a negative temperature on a holographic screen, this will introduce several puzzles such as energy non-conservation. If one tries to modify the derivation of the Einstein equations to avoid a negative temperature, we prove that it is impossible to find a proper new definition of temperature to derive the Einstein equations.
Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh-Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable…
Very recently, Verlinde considered a theory in which space is emergent through a holographic scenario, and proposed that gravity can be explained as an entropic force caused by changes in the information associated with the positions of material bodies. Then, motivated by the Debye model in thermodynamics which is very successful in very low temperatures, Gao modified the entropic force scenario. The modified entropic force (MEF) model is in fact a modified gravity model, and the universe can be accelerated without dark energy. In the present work, we consider the cosmological constraints on t…
Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can be derived from this holographic scenario.
Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics. This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy. In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state. Specifically, we consider linear fluctuations about BTZ blac…
In this paper, the modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole is investigated. Then, according to Verlinde's theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes, but also to the Planck length and the dimensionless constants $α_{\rm{0}}$ and $β_{\rm{0…
The entropic force and the imaginary part of potential experienced by a moving quarkonia in a plasma, are computed in a charged deformed AdS background by holography approaches. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We show that the charge in deformed AdS background deeply effect on the increasing entropic force and decreasing thermal width. So, the dissociation length of the meson becomes short when charge is increasing. In addition, the entropic force and thermal width are increased by the deformation of the space. Therefore the deformation paramete…
Imaginary potential and entropic force represent different mechanisms for melting the heavy quarkonium. In this paper, we study the chemical potential effect on these two quantities with respect to a moving quarkonium from the AdS/CTF duality. We observe that for both mechanisms the chemical potential has the same effect: the presence of the chemical potential tends to decrease the dissociation length.
We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, an…
We generalize the study of entropic force to a general static spherical spacetime and examine the acceleration, temperature, equation of gravity and the energy associated with the holographic screen in this general background. We show that the virtual degree of freedom on the holographic screen plays a crucial role in interpreting field equations of gravity based on thermodynamical perspective.
In this paper, we consider $(n+1)$-dimensional topological dilaton de Sitter black holes with power-Maxwell field as thermodynamic systems. The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon respectively are interrelated. So the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a corrected term which is produced by the association of the two horizons. We analyze the entropic force produced by the corrected term at given temperatures, which is affected by parameters and di…
We study entropic force effects on black holes and photons. We find that application of an entropic analysis restricts the radial change $ΔR$ of a black hole of radius $R_{\mathrm{H}}$, due to a test particle of a Schwartzchild radius $R_{h}$ moving towards the black hole by $Δx$ near black body surface, to be given by a relation $R_{\mathrm{H}} ΔR= R_h Δx/2$, or ${ΔR}/{\lambdabar_M} = {Δx}/{2 \lambdabar_m}$. We suggest a new rule regarding entropy changes in different dimensions, $ΔS= 2πk D Δl /\lambdabar,$ which unifies Verlinde's conjecture and the black hole entropy formula. We also propos…
We study the entanglement entropy, $S_C$, of a massless free scalar field on the outside region $C$ of two black holes $A$ and $B$ whose radii are $R_1$ and $R_2$ and how it depends on the distance, $r(\gg R_1,R_2)$, between two black holes. If we can consider the entanglement entropy as thermodynamic entropy, we can see the entropic force acting on the two black holes from the $r$ dependence of $S_C$. We develop the computational method based on that of Bombelli et al to obtain the $r$ dependence of $S_C$ of scalar fields whose Lagrangian is quadratic with respect to the scalar fields. First …
We reconsider the entropic-force model in which both kind of Hubble terms ${\dot H}$ and $H^{2}$ appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions, namely the scale factor, deceleration parameter, matter density and growth of linear matter perturbations. However, we find that the entropic-force model is not viable at the background and perturbation levels due to the fact that the entropic formulation does not add a constant term in the Friedmann equations. On the other hand, if on mere phenomenological grounds we replace the ${\dot H}$ …
With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Hořava-Lifshitz gravity. It is shown that, when the parameter of Hořava-Lifshitz gravity $ω\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hořava-Lifshitz gravity.
The theory of statistical thermodynamics tells us the equipartition law of energy does not hold in the limit of very low temperatures. It is found the Debye model is very successful in explaining the experimental results for most of the solid objects. Motivated by this fact, we modify the entropic force formula which is proposed very recently. Since the Unruh temperature is proportional to the strength of gravitational field, so the modified entropic force formula is an extension of the Newtonian gravity to weak field. On the contrary, General Relativity extends Newtonian gravity to strong fie…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entaglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals,…
The entropic force experienced by a moving quarkonia in a plasma, is computed in a hyperscaling violation background by holography approach. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We use the results for HSV parameters which obtained in our paper [1] as appropriate values satisfying condition $ImV_{Q\bar{Q}}< 0$. We will show that, in this background the entropic force of the meson shows a decreasing behaviour corresponds to increasing dissociation length. Results of this paper are in agreement with our mentioned work. In addition we will find diffusion…
Verlinde's ideas considered gravity as an emergent force originated from entropic concepts. This hypothesis generated a huge number of papers through the last recent years concerning classical and quantum approaches about the issue. In a recent paper Kobakhidze, using ultra-cold neutrons experiment, claimed that Verlinde's entropic gravity is not correct. In this letter, by considering the nonadditivity property of the holographic screen, where we assumed that the bits are entangled states, we showed that it is possible to confirm Verlinde's formalism.
An entropic-force scenario, i.e., entropic cosmology, assumes that the horizon of the universe has an entropy and a temperature. In the present study, in order to examine entropic cosmology, we derive entropic-force terms not only from the Bekenstein entropy but also from a generalized black-hole entropy proposed by C. Tsallis and L.J.L. Cirto [Eur. Phys. J. C \textbf{73}, 2487 (2013)]. Unlike the Bekenstein entropy, which is proportional to area, the generalized entropy is proportional to volume because of appropriate nonadditive generalizations. The entropic-force term derived from the gener…
We study the holographic entanglement entropy of an interval in a quantum field theory obtained by deforming a holographic two-dimensional conformal field theory via a general linear combination of irrelevant operators that are closely related to, but nonetheless distinct from, $T{\bar T}, \ J{\bar T}$ and $T{\bar J}$, and compute the Casin-Huerta entropic $c$-function. We find that the entropic $c$-function is ultraviolet regulator independent, and along the renormalization group upflow towards the ultraviolet, it is non-decreasing. We show that the entropic $c$-function exhibits a power law …
With Verlinde's recent proposal which says that gravity can be identified with an entropic force and considering the effects of generalized uncertainty principle in the black hole entropy-area relation we derive the modified equations for Newton's law of gravitation, modified Newtonian dynamics and Einstein's general relativity. The corrections to the Newtonian potential is compared with the corrections that come from Randall-Sundrum II model and an effective field theoretical model of quantum general relativity. The effect of the generalized uncertainty principle introduces a $\sqrt{\text{Are…
The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter θ and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same …
We derive the MOND cosmology which is uniquely corresponding to the original MOND at galaxy scales via entropic gravity method. It inherits the key merit of MOND, that is, it reduces the baryonic matter and non-baryonic dark matter into baryonic matter only. For the first time we obtain the critical parameter in MOND, i.e., the transition acceleration $a_c$ at cosmological scale. We thus solve the long-standing coincidence problem $a_c\sim cH_{0}$. More interestingly, a term like age-graphic dark energy emerges naturally. In the frame of this MOND cosmology, we only need baryonic matter to des…
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…
We propose a new holographic program of gravity in which we introduce a surface stress tensor. Our proposal differs from Verlinde's in several aspects. First, we use an open or a closed screen, a temperature is not necessary but a surface energy density and pressure are introduced. The surface stress tensor is proportional to the extrinsic curvature. The energy we use is Brown-York energy and the equipartiton theorem is violated by a non-vanishing surface pressure. We discuss holographic thermodynamics of a gas of weak gravity and find a chemical potential, and show that Verlinde's program doe…
