1 / 74

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:.

fagan
Download Presentation

Dark Matter in Einstein´s Field Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  14. Ifyouwanttoknowmore, readmynewbook Only 38 Euro

  15. Only28 Euro Orreadmyelderbook

  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

  38. Ifyouwanttoknowmore, readmynewestbook Only 25 Euro

More Related