Wednesday, January 10 2007
When I was in the bathtub this afternoon I was thinking about black holes, those dead collapsed stars from which nothing can escape, not even light. When things fall into black holes they are accelerated to the speed of light at the event horizon, beyond which they vanish forever from the universe. From a falling object's perspective (assuming it can have one), this fall takes place in a short amount of time. But from the perspective of stationary onlookers nothing ever actually crosses the event horizon, since, due to relativistic effects, falling objects appear to slow asymptotically as they approach the event horizon. According to General Relativity, nothing except massless, ageless photons can ever cross an event horizon during the entire life of the universe! So what does this mean, since evidently there are black holes in the universe (for example, the super-massive one at the center of our galaxy)? Might it mean that black holes are empty inside their event horizons, since nothing has or will ever actually fall through it, not even the mass of the original star that collapsed to form it? But if all that mass is outside the event horizon, even the mass that was near the center of the original collapsing star, then the event horizon must be a mathematical point. Perhaps the entire black hole is frozen in time from some gradually-expanding crust all the way down to its center, and no event horizon actually forms at all.
There are several thresholds onto and through which stars can crunch as they collapse to form black holes. Some linger as stable masses at the less-dense earlier thresholds, while other continue down through the last of them. A white dwarf, for example, is a star whose weight is below the Chandrasekhar limit, and its collapse is halted by electron degeneracy pressure, the inability of two electrons to inhabit one quantum state at the same time. But if a larger mass collapses (or weight is added to a white dwarf), electron degeneracy pressure can be overcome, fusing protons and electrons to form neutrons and doing away with electron shells entirely. The result is a neutron star, which is supported by neutron degeneracy, the inability for two neutrons to occupy the same quantum state. A neutron star has an escape velocity of about half the speed of light, so at this point we would be well on our way to becoming a black hole. If the mass of the collapsing star is greater than the Tolman-Oppenheimer-Volkoff limit then possibly it could collapse into a theoretical quark star or just keep on collapsing. In the preceding paragraph, though, I said that it was impossible for any matter to actually cross an event horizon in the life of the universe. So perhaps these relativistic effects create a final degeneracy pressure that keeps matter from collapsing to form an object so dense that it has an escape velocity equal to or greater than the speed of light. Such a pressure would result in a predictable minimum size for super-massive objects (such as the "black hole" at the center of the Milky Way).
A small amount of snow fell last night. It may have only accumulated to a depth of an eighth of an inch, but there was still something magical to watching it fall. Normally at this time of year I'm already sick of snow, which lies in crusty blue-tinged layers on the ground. But this was the first real snowfall I'd seen since leaving for Guatemala back in March.
By this morning the snow was mostly gone, lurking only in shadows or on the distant peaks of the Catskills.
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