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Dark Matter in Einstein´s Field Equations

BERLIN ICRANet Pescara. Hagen Kleinert, FU BERLIN . Dark Matter in Einstein´s Field Equations. BERLIN ICRANet Pescara. Nizza. ICRANet Pescara. Universe. All Charged Particles in. Homogeneous Poisson Equation : . Solutions: . Aha:.

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Dark Matter in Einstein´s Field Equations

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  1. BERLIN ICRANet Pescara Hagen Kleinert, FU BERLIN Dark Matter in Einstein´sField Equations BERLIN ICRANet Pescara Nizza ICRANet Pescara

  2. Universe

  3. All ChargedParticlesin HomogeneousPoissonEquation: Solutions: Aha: Charge:

  4. Radial Version HomogeneousPoissonEquation: Solution: Radial form: Charge:

  5. Gravitational Field

  6. Schwarzschild Kerr or

  7. Schwarzschild Einstein Equation

  8. closedbosonicstring Now: Singular Surfaces

  9. Note: GravitationalSingularitieshave Finite Energies ExplainsDominanceof Dark Matter ElectrostaticSingularitieshave Infinite Energies

  10. Whyold String Theoryfailed: Short Strings are MIT-Bags

  11. QuantisationofRelativisticParticle Replacebyharmonic Action  Klein-Gordon Propagator

  12. Surfaces = Nambu-Goto Action ReplaceNambu-Goto Action byharmonic Polyakov Action

  13. Removes Tachyons PolyakovaddsLiouville Action IN FACT: Anyinteractingfieldtheoryisfree oftachyonsifenergyhasbottom

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  16. Single-Valued Fields Multi-Valued Fields

  17. Example: ComplexScalar Field • set FALSE! Chain Rule: WrongUniversality Class

  18. Jumps! Correct Chain Rule: In 1D, canberemovedbygoingtocoveringgroup U(1) In >1D impossible

  19. Vortex Gauge Field Invariant Field Strength: Axial Gauge

  20. Simplest MULTIVALUED FIELD in 2D Solve:

  21. NOTE: Mother ofTwoImportant Green Functions

  22. NOTE: Mother ofTwoImportant Green Functions

  23. Now : NontrivialGeometry fromNonholonomicCoordinateTransformations TranslationalDefects DISLOCATIONS Burgers vectorb

  24. RotationalDefects (Disclinations)

  25. ANALOG MODEL: InducedGravity in `World Crystal´ Canonical Form MomentumConservation Enforcedas Bianchi Idty: Double Gauge Theory PlasticGauge Tfs:

  26. Newton OK ifwemodifyactionto FLOPPY CRYSTAL. Directionalmemory lost byKosterlitz-Thouless type Fluctuations in D=4: New: 1.) High-curvatureregimemoltenphase? 2.) Are Strings the World LinesofDefects in a Transplanckian World Crystal

  27. BUT NEED

  28. SUMMARY: String Theoryobtainedfrom Einstein Action ofSurfaceSingularites yields Quantum Gravityof Dark Matter

  29. World isCracking Open (as Gell-Mann usedtosay in 1972)

  30. Path Integrals • fix Products ofDistributions

  31. Distribution Distribution

  32. PERTUBATION SERIES:  Multiplication Rules forDistributions

  33. CURIOSITY: InducedGravity in `World Crystal´ Canonical Form MomentumConservation Enforcedas Bianchi Idty: Double Gauge Theory PlasticGauge Tfs:

  34. Dual Representation

  35. BUT NEED

  36. Newton OK ifwemodifyactionto FLOPPY CRYSTAL. Directionalmemory lost byKosterlitz-Thouless type Fluctuations in D=4: New: 1.) High-curvatureregimemoltenphase? 2.) Are Strings the World LinesofDefects in a Transplanckian World Crystal

  37. Interdependence

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