Penrose Diagram - Black Holes

Black Holes

Penrose diagrams are frequently used to illustrate the space-time environment of black holes. Singularities are denoted by a spacelike boundary, unlike the timelike boundary found on conventional space-time diagrams. This is due to the interchanging of timelike and spacelike coordinates within the horizon of a black hole (since space is uni-directional within the horizon, just as time is uni-directional outside the horizon). The singularity is represented by a spacelike boundary to make it clear that once an object has passed the horizon it will inevitably hit the singularity even if it attempts to take evasive action.

Penrose diagrams are also used to illustrate the space-time environment of a hypothetical wormhole connecting two separate universes, which is an extension of the Schwarzschild solution of black holes. The precursors to the Penrose diagrams were Kruskal-Szekeres diagrams. These introduced the method of aligning the event horizon into past and future horizons oriented at 45° angles (since one would need to travel faster than light to cross from the Schwarzschild radius back into flat spacetime); and splitting the singularity into past and future horizontally-oriented lines (since the singularity "cuts off" all paths into the future once one enters the hole). The result is a hypothetical object called a grey hole, which is basically a white hole that turns into a black hole after briefly opening up into a wormhole connecting the two asymptotically flat space-time regions called "universes". The wormhole closes off (forming "future" singularities) so rapidly that passage between the two universes would require faster-than-light velocity, and is therefore impossible. The Penrose diagram simply added to Kruskal and Szekeres' diagram the conformal crunching of the regions of flat space-time far from the hole.

While the basic space-like passage of a static black hole cannot be traversed, Penrose diagrams for rotating and/or electrically charged black holes reveal "inner event horizons" (lying in the future) and vertically oriented singularities, which open up what is known as a "time-like wormhole" allowing passage into future universes. In the case of the rotating hole, there is also a "negative gravity" universe entered through a ring-shaped singularity (still portrayed as a line in the diagram) that can be passed through if entering the hole close to its axis of rotation.

With all of this hypothesis regarding wormholes, some scientists have pointed out that

1) This does not describe a typical black hole created from the collapse of a star (which cuts off the past-oriented "white hole" geometry and other universe). Such wormholes would only be possible if a "past singularity" (such as a remnant of the original Big Bang singularity that remained compact) continued erupting into the universe as time went on.

2) The radiation of orbiting, highly blue-shifted light rays surrounding a black hole (called a "blue sheet") would make it impossible for anyone to pass through, and in fact might create another kind of singularity outside the hole!