Modified Entropic Force

I. IntroductionII. Modified Newtonian GravityIII. Modified Friedmann equation IV. Conclusion and discussion

Classical Black Holes,,.

Quantum Black holes,, .

, , , . , , .

1. Using the Causius relation and equiveverlece principle, Jacobson derived the Einstein equations in 1995. 2. Using the equipartition law of energy and a thermodynamic relation, Padmanabhan derived the Newtonian Gravity in 2009. 3. This year, Verlinde proposed an interesting idea that gravity may be not fundamental but can be interpreted as an entropic force. The entropic force is caused by the changes of the information associated with the system. Using the equipartition law of energy and holographic principle, he obtains the Newtonian gravity.

Entropic Force

In their derivations, the equipartition law of energy is important.

Newtonian GravityA. N gUnruh T

Modified Newtonian Gravity

When x approaches infinityGeneral Relativity is the strong field extension of Newtonian gravity.This model is the weak field extension of Newtonian gravity.

Modified Poissons equation

Different from MOND theory

III. Cosmology

Friedmann equationWhen we have the Friedmann equation in GR;

Conclusion and discussion1. Using the Debye model, we find the cosmic acceleration can be interpreted without invoking dark energy.

2. In the Solar system and Galaxy scales, the model can be very well approximated as Newtonian gravity.

3. This Debye model is for three dimensional. How about for one dimensional and two dimensional Debye model? Holographic principle reveals that two dimensional Debye model seems much reasonable.

4. The Poissons equation is derived. The how to derive the corresponding Einstein equations from the variation principle?

5. How to derive this model from the specific microscopic structure of space-time?

Two dimensional Debye model: One dimensional Debye model: n dimensional Debye model: