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By Eduard Alexis Larrañaga R.

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32), la coordenada de Regge-Wheeler satisface 1 sin (V − U ) (v − u) = , 2 2 cos V cos U con lo que la métrica se puede escribir como r∗ = ds2 = 1 2M 2 −4 1 − r (2 cos V cos U ) dV dU + r r∗ 2 sin2 (V − U ) dΩ2 . 121) donde ω = 2 cos V cos U. 122) Para dibujar el diagrama de Penrose correspondiente es útil notar que esta métrica es asintóticamente plana, es decir que en el infinito se convierte en el espacio de Minkowski. e. io y I± , son iguales a las del diagrama minkowskiano. 6. 17: Diagrama de Carter Penrose para el espacio-tiempo de Kruskal.

69) se tiene V U = −x2 . 109) x es decir que para partículas en orbitas del vector de Killing ξ, (x = constante), a es constante. Es importante notar que la aceleración propia crece sin límite cuando x −→ 0. Por esta razón a la superficie x = 0 se le denomina un Horizonte de Aceleración. 4. Horizontes de Aceleración y Gravedad Superficial Ahora bien, aún cuando la aceleración propia diverge al acercarse al horizonte x = 0, la aceleración medida por otro observador permanece finita. 110) 1 para trayectorias con x = constante, y donde κ = 4M .

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 − .

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