1. Entropic Gravity Miao Li 中国科学院理论物理研究所
中国科学院理论物理研究所　
Institute of Theoretical Physics CAS
兩岸粒子物理與宇宙學研討會
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2. Based on work done with Rong-Xin Miao and Wei Gu
And work done with Rong-Xin Miao and Jun Meng
1. A New Entropic Force Scenario and Holographic
Thermodynamics
arXiv:
2. f(R) Gravity and Maxwell Equations from the Holographic Principle
arXiv:
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3. 1. Verlinde’s entropic force scenario Fdx=TdS
Newton’s second law
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4. Newton’s law of gravitation
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5. Verlinde’s derivation of Einstein Equations
Temperature
Holography, namely the bit number
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6. Equipartition
Thus
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7. From the equipartition
And
From Tolman-Komar
mass
From the equipartition
theorem
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8. 2. Our derivation of Einstein Equations
Verlinde uses a closed holographic screen
We use an open screen
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9. Through the screen, there is an energy flow
This is a bulk flow.
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10. According to holography, this flow can be written
using only the physical quantities on the screen
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11. Naturally, we assume the surface stress tensor
be given by local geometry
Using the Gauss-Codazzi equation
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12. Compare to the bulk flow, we find
We have
Compare to the bulk flow, we find
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13. We almost obtain the Einstein equations. Note that
We deduce
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14. 3. Comparison with Verlinde and Jacobson Verlinde Our proposal
Closed holographic screen Open or closed screen
Temperature T Without or with T
Tolman-Komar mass Brown-York Energy
Equipartition Surface stress tensor
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15. The Brown-York semi-local energy has a form
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16. We see that the second term is an extra compared with Verlinde.
The equipartition theorem does not have to be true
since it is very peculiar.
We have extra datum p, which is important in
studying thermodynamics.
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17. Open null screen Open or closed time-like
Jacobson Our proposal
Open null screen Open or closed time-like
T only T, p chemical potential
First law First law
We have more information.
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18. 4. Holographic thermodynamics Consider a screen adiatically moves in
space-time
r r+dr
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19. E and p are defined (to be substracted), we need To know
The first law
E and p are defined (to be substracted), we need
To know
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20. For a static and spherically symmetric metric
we have
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21. and
We deduce
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22. To derive the chemical potential, we notice that
for a black hole (or a region of vacuum) Nh=1 and
dS=0, so
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23. Assume the above formula be generally true for
other N and h, we can compute the holographic
entropy for a gas with weak gravity.
where for example
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24. and for the gas in particular
We find in general
and for the gas in particular
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25. To make the area term absent, x=0 thus
This is the same form of the Bekenstein bound
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26. Indeed we also have a bound, when
S reaches its maximum, and agrees with the
Bekenstein bound if
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27. 5. Derivation of f(R) gravity
I and Pang Yi showed that it is impossible to acco-
modate f(R) gravity in the Verlinde proposal.
We show that it is rather straightforward to include
it in our program.
We need to simply use a different surface stress
tensor.
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28. The new surface stress is postulated to be
The first term is similar to the Einstein gravity,
proportional to the extrinsic curvature. The scond
term is to be determined by consistency.
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29. Thus, the screen energy change is
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30. So q can be determined. To determine F, we use
We deduce
So q can be determined. To determine F, we use
The Bianchi identity and find
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31. Thus, the f(R) gravity equation of motion:
and the surface stress tensor
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32. 6. The Maxwell equations from holography
Charge flow replaces energy flow in this case.
The bulk charge flow:
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33. The charge change on the open screen:
Equating these two we have
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34. We postulate
and
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35. Solving these conditions, we find A be asymmetric and
These are Maxwell equation. To show that A is F
given in terms of the gauge potential, we consider
the magnetic charge flow which is actually zero. So
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36. We make a different proposal from Verlinde
To conclude:
We make a different proposal from Verlinde
Our proposal makes derivation of the Einstein
equations more complete.
3. Our proposal has a reasonable thermodynamics
while Verlinde’s doen’t.
4. We predict a holographic entropy for a gas.
5. More flexible, F(R) and Maxwell theory are derived
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37. Derive a general formula for the chemical potential.
Future work:
Derive a general formula for the chemical
potential.
2. Discuss various situations such as anti-de
Sitter and cosmology (about holographic
entropy).
3. Apply it to study dark energy.
We are already working in these directions.
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38. Thank You !
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