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By Eduard Alexis Larrañaga R.

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15) toma la forma ∂ v n2 = − nσ ∇σ nµ |N = = = = 1 µ 2 ∂ n 2 N 1 nσ ∂σ (ln N ) nµ |N − N nµ 4M 1 nv ∂v (ln N ) − N nµ 4M 1 ∂v (ln N ) − N nµ . 41) es decir que esta elección de la función N corresponde a la elegir un parámetro afín. 1. HIPERSUPERFICIES NULAS 45 n = ev/4M ∂v . 42) Ejemplo. 44) gϕϕ = r sin θ. 45) Consideraremos las hipersuperficies definidas por la función Φ = U . La hipersuperficie nula r = 2M corresponde a Φ = U = 0. El vector normal a estas hipersuperficies esta definido por n = N g U σ ∂U Φ∂σ = N g U V ∂V r = −N er/2M ∂V .

60 CAPÍTULO 3. HIPERSUPERFICIES Capítulo 4 Formulación de Tétradas La forma usual de resolver problemas en la Relatividad General es resolver las ecuaciones de campo en una base coordenada local. Sin embargo, debido a la libertad en la escogencia de la base utilizada para describir la física, es posible escoger un conjunto de cuatro campos vectoriales linealmente independientes llamados tétradas, que simplifiquen las cantidades relevantes para un cierto problema. De esta forma, se proyectan los objetos de interés (vectores, tensores, etc) para realizar los cálculos en la nueva base y luego es posible devolverse a la base coordenada original con una nueva proyección.

Además, ya que esta función multiplica al resto de factores, podemos definir la métrica compactificada mediante d˜ s2 = ω 2 ds2 = −4dV dU + sin2 (V − U ) dΩ2 . 94) De esta forma, el espacio de Minkowski ha quedado inmerso conformemente dentro del espacio-tiempo definido por d˜ s, el cual tiene una frontera definida por ω = 0. Finalmente podemos realizar un último cambio a una coordenada temporal η y una coordenada radial χ definidas por 34 CAPÍTULO 2. 14: Compactificación conforme del espacio-tiempo de Minkowski.

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Agujeros Negros Clásicos by Eduard Alexis Larrañaga R.


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