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nD Gravity with n-2 Killing vectors Tonatiuh Matos http://www.fis.cinvestav.mx/~tmatos/

nD Gravity with n-2 Killing vectors Tonatiuh Matos http://www.fis.cinvestav.mx/~tmatos/. nD-Einstein equations with n-2 commuting Killing vectors Chiral fields The invariance group of chiral fields. Methods of solutions. The nD-Einstein equations with n-2 commuting Killing Vectors.

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nD Gravity with n-2 Killing vectors Tonatiuh Matos http://www.fis.cinvestav.mx/~tmatos/

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  1. nD Gravity with n-2 Killing vectors Tonatiuh Matoshttp://www.fis.cinvestav.mx/~tmatos/ • nD-Einstein equations with n-2 commuting Killing vectors • Chiral fields • The invariance group of chiral fields. • Methods of solutions

  2. The nD-Einstein equationswith n-2 commuting Killing Vectors

  3. The Ricci Tensor • i

  4. Ricci tensor in matrix notation

  5. In vacuum • Implies:

  6. Brane Cosmology • Inflation

  7. The matter components of the Universe • Concordance!!. • M ~ 0.27  0.1, •  ~ 0.73  0.1 • 0 ~ 1. • The matter component • M = b +  +  ~ • 0.04 + DM, • where DM ~ 0.23. • but • DM ni  ??. DM + ~ 0.96

  8. The Dark Energy • p= r • =A0+A1a=0+a z/(1+z) • Constante Cosmológica: 0 = -1, 1 = 0 • Quintessence: f • Phantom: K=-,, • Quintom: f1 + f2

  9. The Dark Energy

  10. The Dark Energy

  11. The Dark Energy

  12. 5D Gravity • Potential Space

  13. The corresponding Lie Algebra • Define: • Then:

  14. The metric and the Lagrangian • The equivalent Lagrangian

  15. The field equations in the potential space =0 If we define implies

  16. The ansatz A= A(i) • And the Killing equation:

  17. Implies

  18. The main theorem

  19. The harmonic maps • The monopole: • The dipole:

  20. The rotating solutions • The gravitational potential: • The scalar field potential:

  21. Charged solutions

  22. Rotating Wormhole

  23. Rotating Wormhole

  24. Rotating Wormhole

  25. Wormholes • Pelicula

  26. Wormholes

  27. Wormholes

  28. Wormholes • Pelicula

  29. Wormholes

  30. Wormholes

  31. Wormholes

  32. Rotating Wormhole • Then

  33. Wormhole Rotante • Ejemplo: J=10-10, • Entonces 1» 1.4£105 • Para una estrella fantasma (phantom) con la masa de la tierra, la carga escalar es q0.003 mPlank por metro. • v- = 15 km/seg • v+ = 7 c

  34. Across the Universe

  35. Across the Universe • Milenio

  36. Across the Universe Las palabras surgen a raudales como una lluvia infinita en un vaso de papel Se deslizan al pasar Desaparecen a través del universo Charcos de tristeza, olas de alegría flotan en mi mente abierta Poseyéndome y acariciándome Jai Guru De Va Om Nada cambiará mi mundo Nada cambiará mi mundo Imágenes de luz que bailan ante mí como un millón de ojos Que me llaman y me llaman a través del universo Pensamientos serpenteando como un viento inquieto en un buzón Tambaleándose ciegamente mientras hacen su camino a través del universo Jai Guru De Va Om Nada cambiará mi mundo Nada cambiará mi mundo Sonidos de risas y sombras de tierra suenan a través de mi vista abierta Incitándome e invitándome Un amor eterno y sin límites brilla a mí alrededor como un millón de soles Llamándome y llamándome a través del universo Jai Guru De Va Om Nada cambiará mi mundo Nada cambiará mi mundo

  37. and • Magnetic monopole • ω= sin()

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