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

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

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.

Complete thermodynamic potentials

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

Cosmological constant

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

Gravity-thermodynamics dictionary

Gravity and thermodynamics

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

Gravity and thermodynamics

Quantum Cosmology

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

MERA and AdS/CFT

MERA and AdS/CFT

MERA and AdS/CFT

Spacetime physics– black holes and AdS spacetime

Spacetime physics– black holes and AdS spacetime

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

Spacetime physics–Black hole interior and spacetime analysis

Spacetime physics–Black hole interior and spacetime analysis

Thermodynamics and information paradox

Thermodynamics and information paradox

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.

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

Transitions from singularity to singularity

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

String theory and quantum entanglement-under construction

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

Quantum cosmology and the history of the universe

Quantum cosmology and the history of the universe