Nd gravity with n 2 killing vectors tonatiuh matos http www fis cinvestav mx tmatos
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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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Nd gravity with n 2 killing vectors tonatiuh matos http www fis cinvestav mx tmatos

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


The nd einstein equations with n 2 commuting killing vectors

The nD-Einstein equationswith n-2 commuting Killing Vectors


The ricci tensor

The Ricci Tensor

  • i


Ricci tensor in matrix notation

Ricci tensor in matrix notation


In vacuum

In vacuum

  • Implies:


Brane cosmology

Brane Cosmology

  • Inflation


The matter components of the universe

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


The dark energy

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


The dark energy1

The Dark Energy


The dark energy2

The Dark Energy


The dark energy3

The Dark Energy


5d gravity

5D Gravity

  • Potential Space


The corresponding lie algebra

The corresponding Lie Algebra

  • Define:

  • Then:


The metric and the lagrangian

The metric and the Lagrangian

  • The equivalent Lagrangian


The field equations in the potential space

The field equations in the potential space

=0

If we define

implies


The ansatz

The ansatz

A= A(i)

  • And the Killing equation:


Implies

Implies


The main theorem

The main theorem


The harmonic maps

The harmonic maps

  • The monopole:

  • The dipole:


The rotating solutions

The rotating solutions

  • The gravitational potential:

  • The scalar field potential:


Charged solutions

Charged solutions


Rotating wormhole

Rotating Wormhole


Rotating wormhole1

Rotating Wormhole


Rotating wormhole2

Rotating Wormhole


Wormholes

Wormholes

  • Pelicula


Wormholes1

Wormholes


Wormholes2

Wormholes


Wormholes3

Wormholes

  • Pelicula


Wormholes4

Wormholes


Wormholes5

Wormholes


Wormholes6

Wormholes


Rotating wormhole3

Rotating Wormhole

  • Then


Wormhole rotante

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


Across the universe

Across the Universe


Across the universe1

Across the Universe

  • Milenio


Across the universe2

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


Nd gravity with n 2 killing vectors tonatiuh matos http www fis cinvestav mx tmatos

  • and

  • Magnetic monopole

  • ω= sin()


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