nD Gravity with n-2 Killing vectors Tonatiuh Matos tmatos
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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
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The nD-Einstein equationswith n-2 commuting
Killing Vectors
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The Ricci Tensor
• i
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Ricci tensor in matrix notation
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In vacuum
• Implies:
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Brane Cosmology
• Inflation
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The matter components of the Universe
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
• Concordance!!.
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The Dark Energy
• p= • =A0+A1a=0+a z/(1+z)
• Constante Cosmológica: 0 = -1, 1 = 0• Quintessence: • Phantom: K=-,,
• Quintom:
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The Dark Energy
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The Dark Energy
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The Dark Energy
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5D Gravity
• Potential Space
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The corresponding Lie Algebra
• Then:
• Define:
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The metric and the Lagrangian
• The equivalent Lagrangian
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The field equations in the potential space
=0
implies
If we define
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The ansatz
A= A( i)
• And the Killing equation:
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Implies
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The main theorem
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The harmonic maps
• The monopole:
• The dipole:
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The rotating solutions
• The gravitational potential:
• The scalar field potential:
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Charged solutions
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Rotating Wormhole
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Rotating Wormhole
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Rotating Wormhole
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Wormholes
• Pelicula
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Wormholes
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Wormholes
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Wormholes
• Pelicula
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Wormholes
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Wormholes
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Wormholes
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Rotating Wormhole
• Then
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Wormhole Rotante•Ejemplo: Ejemplo: J=10J=10-10-10, , •Entonces Entonces 11»» 1.4 1.4££101055 •Para una estrella fantasma (phantom) Para una estrella fantasma (phantom) con la masa de la tierra, la carga escalar con la masa de la tierra, la carga escalar eses q q 0.003 m0.003 mPlankPlank por metro. por metro.
• v- = 15 km/seg• v+ = 7 c
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Across the Universe
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Across the Universe
• Milenio
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Across the UniverseLas 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
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• and
• ω = sin()• Magnetic monopole