1. Solutions of black hole interior, information paradox and the shape of singularities
Haolin Lu

2. But first,
Some connections between classical gravity and classical thermodynamics
Black hole has temperature and entropy, given by Bekenstein and Hawking---the black hole emits thermal radiations

3. Holographic gravity action
The gravity action can be separated to be a bulk term and a boundary term. The bulk term can be expressed from the boundary term by Padmanabhan
Source: Stokes theorem in higher dimensions
Can choose any 2 dimensional sphere which enclose the horizon, and give the same spacetime conserved charge, hence another way of seeing the holographic nature of gravity
The surface action is entropy by Padmanabhan
Einstein field equation can be obtained by extremal entropy principle.

4. Complete thermodynamic potentials

5. Gravity-thermodynamics dictionary
The surface term is entropy.
The bulk term is energy
The cosmology constant term is pressure

6. Cosmological constant

7. Euclidean Method
tau=it
X^2+Y^2+Z^2-t^2=X^2+y^2+Z^2+tau^2

8. Gravity-thermodynamics dictionary

9. Gravity and thermodynamics

10. Statistical Quantum Cosmology
After the gravity-thermodynamics dictionary, statistical mechanics method to apply to the particles or quanta of gravity system
The particles or quanta are gravitational waves or gravitons
The variation of action gives gravity field equation
gravity-thermodynamics dictionary gives graviton statistics
The collection of Euclidean gravitons are an ensemble, go back to Lorentzian signature, different particle number and energy states of gravitons gives an excited state of the wave function of the gravity field
Gravity is curved spacetime, the method gives the wave function of the universe

11. Gravity and thermodynamics

12. Quantum Cosmology

13. Elements and principles about spacetime physics
Spacetime solutions from general relativity----dS and AdS spacetime
Null boundary of Penrose diagram, holographic nature of general relativity----AdS/CFT
Vacuum fluctuations, EPR entanglement pairs fibrates spacetime---- String theory and MERA, core entanglement is dense.
Traced out entanglement pairs, Thermodynamics----Hawking radiation

14. MERA and AdS/CFT

15. MERA and AdS/CFT

16. MERA and AdS/CFT

17. Spacetime physics– black holes and AdS spacetime

18. Spacetime physics– black holes and AdS spacetime

19. Spacetime physics– black holes and AdS spacetime
For Real black hole just replace the lower half with half cylinder, which is nothing but Hawking's Euclidean method

20. Spacetime physics–Black hole interior and spacetime analysis

21. Spacetime physics–Black hole interior and spacetime analysis

22. Thermodynamics and information paradox

23. Thermodynamics and information paradox

24. Elements of string theory
11d sugra is the classical theory of M-theory (membrane or matrix)
Dimensional reduction gives various 10d sugra as classical limit of 10d string theory.
P-form field couples to (p-1)-brane
Basic field of 11d sugra are metric, 3-form field and gravinto.
Dimensional reduction of M2 brane or membrane is the perturbative string theory
Electro-magnetic duality relate M2-brane to M5-brane. Magnetic solutions are higher dimensional solitons.
Branes or strings vibrates and produce gravity fields and RR form fields
Excited states of branes are very massive, also very small, can form horizons and black holes, hence natural object to study quantum gravity.

25. Information paradox--solution from string theory, and structure of singularity
Singularity and M branes
Creation of the universe: the seed/black p-brane’s teleportation or projection of non-local tunneling virtual Hawking Pairs followed by gravitational creation of particles as inflation.
Deep down the interior, one observes black p-brane, which is in string limit. Close to the boundary, the bulk is classical AdS spacetime, which is in the classical gravity regime. Black p-brane transition to CFT energy and AdS/CFT holography are governed by Hawking radiations as RG flow since the energy direction is flow.
Energy transition of CFT-AdS-black p-brane system, more generally black brane-cosmology duality as T duality and tunneling, from zero to infinity, n- fold of spacetime
AdS nucleation, dS and wormhole in dS construction using singularities

26. Transitions from singularity to singularity

27. e.g. AdS BH dynamics, AdS/CFT as black hole holography

28. String theory and quantum entanglement-under construction

29. Goal and the third part
This work aims to finish the complete structure of quantum entanglement, black hole and big bang singularity, and the dynamics and structure of spacetime
And begin the theory work on worm hole physics and spacetime teleportation, and time and the quantum history of the universe

30. Quantum cosmology and the history of the universe

31. Quantum cosmology and the history of the universe