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Dark Matter in Einstein´s Field Equations

Dive into the complexities of dark matter and gravitational singularities through groundbreaking insights in string theory and Einstein's field equations. This work discusses charged particles in homogeneous Poisson equations, solutions to radial forms, and the significance of finite energy singularities. Discover how recent developments redefine our understanding of the universe, tackle the challenges of tachyons, and introduce advanced concepts such as induced gravity in a world crystal. For further exploration, check out my latest book, available at a special price.

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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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