Agujeros Negros Clásicos by Eduard Alexis Larrañaga R.

By Eduard Alexis Larrañaga R.

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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 . 16M 3 En este caso, al evaluar el vector normal en la hipersuperficie nula r = 2M se tiene n = −N e ∂V . 50) y ya que es idénticamente igual a cero, entonces ∂ µ n2 = 0. 51) nσ ∇σ nµ |N = 0. 53) ∂ . 54) N =− y con ello el vector normal será simplemente n= 46 CAPÍTULO 3.

Definimos además J (U ) y J (U ) como la clausura topológica del pasado causal y el futuro causal de U respectivamente. 8. − + (U ) − J − (U ) (U ) − J + (U ) . 114) Horizonte de Eventos Futuro El horizonte de eventos futuro H+ se define como la frontera de la clausura del pasado causal del infinito futuro nulo I + , es decir H+ = j − I + . 9. 115) Horizonte de Eventos Pasado De manera similar, se define el horizonte de eventos pasado H− como la frontera de la clausura del futuro causal del infinito pasado nulo I − , es decir H− = j + I − .

Es decir que este espacio es asintóticamente simple. Sin embargo, la variedad de Minkowski además es un débil asintóticamente simple, vacia y asintóticamente plana. ˜ su compactificación conforme, se puede Si se toma M como la variedad de Kruskal y M comprobar que no se satisface la condición 3. ya que existen geodésicas nulas que terminan ˜ Por esta razón, Kruskal no es un espacio asintóticamente en la singularidad y no en ∂ M. simple. Sin embargo, esta variedad si es débil asintóticamente simple, y además es vacia.

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