From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

By bearing the Komar’s definition for the mass, together with the entropic origin of gravity in mind, we find the Einstein field equations in (n + 1)-dimensional spacetime. Then, by reflecting the (4 + 1)-dimensional Einstein equations on the (3 + 1)-hypersurface, we get the Einstein equations onto the 3-brane. The corresponding energy conditions are also addressed. Since the higher dimensional considerations modify the Einstein field equations in the (3 + 1)-dimensions and thus the energy-momentum tensor, we get a relation for the Komar mass on the brane. In addition, the strongness of this relation compared with existing definition for the Komar mass on the brane is addressed.     

Debye Entropic Force and Modified Newtonian Dynamics

Verlinde has suggested that the gravity has an entropic origin, and agravitational 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 while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant a₀ involved in MOND is linear in the Debye frequency ω_D, which can be regarded as the largest frequency of the bits in screen.We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is takento be bound of the Universe. The Debye frequency is linear in the Hubble constant H₀.     

A Note on Friedmann Equation of FRW Universe in DeformedHo\v{r}ava-Lifshitz Gravity from Entropic Force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Ho\v{r}ava-Lifshitz gravity. It is shown that, when the parameter of Ho\v{r}ava-Lifshitz gravityω→∝, 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 Ho\v{r}ava-Lifshitz gravity.     

Dilatonic Entropic Force

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.     

Modified Friedmann equations from Debye entropic gravity

A remarkable new idea on the origin of gravity was recently proposed by Verlinde who claimed that the laws of gravitation are no longer fundamental, but rather emerge naturally as an entropic force. In Verlinde derivation, the equipartition law of energy on the holographic screen plays a crucial role. However, the equipartition law of energy fails at the very low temperature. Therefore, the formalism of the entropic force should be modified while the temperature of the holographic screen is very low. Considering the Debye entropic gravity and following the strategy of Verlinde, we derive the modified Newton’s law of gravitation and the corresponding Friedmann equations which are valid in all range of temperature. In the limit of strong gravitational field, i.e. high temperature compared to Debye temperature, T » T _D , one recovers the standard Newton’s law and Friedmann equations. We also generalize our study to the entropy corrected area law and derive the dynamical cosmological equations for all range of temperature. Some limits of the obtained results are also studied.     

Einstein's Gravitational Equations in the Friedmann Space

This paper proposes the vacuum solution for Einstein's gravitational equations, based on the nonisotropic generalized Friedmann's metric, and considers the equations of motion.     

Black Holes and Photons with Entropic Force

We study the entropic force effects on black holes and photons. It is found that application of an entropic analysis restricts the radial change △R of a black hole of radius RH, due to a test particle of a Schwarzschild radius Rn moving towards the black hole by △x near a black body surface, to be given by a relation RH△R = Rh△x/2, or △ R/λM = △x /2λm. We suggest a new rule regarding entropy changes in different dimensions, △S = 2πkD △l/λ, which unifies Verlinde＇s conjecture and the black hole entropy formula. We also propose the extension of the entropic force idea to massless particles such as photons. It is realized that there is an entropic force on a photon of energy Eγ with F = GM（Eγ/c^2）/R^2, and therefore the photon has an effective gravitational mass mγ= Eγ/c^2.     

Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton’s law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.     

Time Varying Gravitational Constant G via Entropic Force

If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton's second law of mechanics in the Planck's scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependentquantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis (L.N.H.). We propose that the corrected entropic terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.     

Minimal Length, Maximal Momentum and the Entropic Force Law

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.     

Modified Holographic Dark Energy and Phantom Behaviour of Randall-Sundrum Brane

In this work, we discuss the evolution of modified Holographic Dark Energy (HDE) derived from the UV/IR cutoff in the Randall-Sundrum II (RS-II) braneworld scenario. Choosing future event horizon as the IR cutoff, it is seen that the equation of state parameter for the modified HDE can cross the phantom crossing line ω=−1.     

Schwarzschild Solution on the Brane

In this paper it is shown that Schwarzschild solution is possible in brane world for some specific choices of brane matter and the non-local effects from the bulk. A conformally flat bulk space time with fine-tuned vacuum energy (brane tension) shows that Schwarzschild solution may also be the vacuum solution for brane world scenario.     

Negative Energies on the Brane

It has recently been proposed that our universe is a three-brane embedded in a higher dimensional spacetime. Here I show that black holes on the brane, black strings intersecting the brane, and gravitational waves propagating in the bulk induce an effective energy-momentum tensor on the brane that contains negative energy densities.     

General Entropic Approximations for Canonical Systems Described by Kinetic Equations

In this paper we extend the general construction of entropic approximation for kinetic operators modelling canonical systems. More precisely, this paper aims at pursuing to thermalized systems the works of Levermore, Schneider and Junk on moments problems relying on entropy minimization in order to construct BGK approximations and moments based equations.     

Warm Standard Scalar Field Modified Chaplygin Gas Inflation Inspired by Generalized Dissipative Coefficient on the Brane

We discuss the warm inflation in the presence of standard scalar field model and modified Chaplygin gas in brane-world scenario. We consider weak and strong dissipative regimes with generalized dissipative coefficient. We extract various inflationary parameters. For example, we analyze the behavior of different ratios(ratio of dissipative co-efficient and Hubble parameter Γ/3H, ratio of temperature and Hubble parameter T/H, scalar-to-tensor ratio r) with respect to spectral index ns for the weak and strong dissipative regimes through parametric plotting. It is found that T/H and Γ/3H satisfied the required conditions in both dissipative regimes. It is also noted that the spectral index(ns)attain the range n_s = 0.96_(-0.10)~(+0.10). It is remarked here that our results are consistence with observational data WMAP7,WMAP9, and recent Planck data.