Traversible Worm Holes and Time Travel

See G.H. George 1990, Journal Royal Astronomical Society of Canada, 84, 28, Inside Black Holes for more detailed remarks on solutions to Einstein's Equations.

Static Black Holes: Schwarzschild Metric

Static Black Holes are spherical in shape. The Event Horizon marks the outer edge of the black hole. The Event Horizon is the radius inside of which the escape speed from the Black Hole is greater than the speed of light c. Once objects cross the Event Horizon, they are cut-off from our Universe and inexorably fall into the center of the Black Hole, the singularity.

Rotating Black Holes: Kerr Metric

A spinning black hole drags spacetime around in its vicinity (Frame Dragging). The outer surface marking the ergosphere, is the static limit as objects cannot be stationary within the ergosphere. Inside the ergosphere sits the Event Horizon. As normal, once objects cross the Event Horizon, they are cut-off from our Universe.

In a static black hole, the Event Horizon has radius,
Rs=2GM/c2 = 3 km (M/Ms),
the Schwarzshild Radius. Once inside the event horizon, one is cut-off from the outside Universe. After crossing the event horizon, space and time change character in the sense that one must flow spatially into the singularity, and one has a limited freedom for movement in time. In a Kerr metric, there are two critical surfaces given by the - and + signs of
R = 0.5 Rs[1-+(1-(lc/GMm)2)1/2].
Here, l is the angular momentum of the black hole. In the literature you see the quantity a defined as
a = (lc/GMm).
The + sign corresponds to the Schwarzschild radius and the - sign is the Cauchy Horizon. In a rotating black hole, a similar thing as occurred in the Schwarzschild black hole occurs as one crosses the Event Horizon. However, for the rotating black hole, the second critical surface, the Cauchy Horizon causes the character of time and space to flip again. For the Kerr metric, the singularity is not a point, it is a ring which has interesting consequences.

Schwarzschild Black Hole

Kerr Solution

Einstein-Rosen Bridge

Black holes distort space-time in a much more extreme manner (note the cusp or point the depression comes to at its bottom). An interesting discovery was made by Einstein-Rosen in the 1930's, they found that the black holes would close down but then actually re-open into another Universe. If one end is a black hole and the other is a white hole, this passage way may be traversible and form an Einstein-Rosen bridge. An alternative interpretation is that the black hole opened up into another part of the space-time of our Universe. Such a passageway (wormhole ) leads to the possibilities of rapid travel through the Universe (or between universes--through hyperspace or Star Trek-like warp-drives) and time travel!!

The wormhole is formed by gluing the ends of a black hole and a time-reversed black hole (a white hole). Such tunnels may connect different points of space-time or, more speculatively, different universes.

Wormholes were shown to be unstable by several workers. In the panel to the left, two white holes connect, become unstable and break apart into two black holes. In the 1980s, Kip Thorne and students demonstrated that an arbitrarily advanced civilization (AAC) make exotic matter which exerts an outward pressure rather than an inward directed gravitational force.