Friday, 11 September 2009

Dark Stars and Hawking Radiation

The fictional spaceship 'Dark Star', from the 1974 movie of the same name, directed by by John CarpenterSome people have trouble getting used to the idea of Hawking radiation outside the context of strict quantum mechanics. For those people, I'd suggest that they consider the mechanics of a crusty old Nineteenth-Century “Dark Star” model.

The Dark Star was the predecessor to the modern black hole, and the basic properties of the object were worked up and published by John Michell back in 1784. Michell worked out many of the “modern” Twentieth-Century black hole properties from Newtonian principles, including the r=2M event horizon radius, gravitational spectral shifts, and a method of calculating the number of these “invisible” gravitationally-cloaked objects by finding the proportion of unseen “companion stars” in binary star systems, and then using statistics to extrapolate that proportion to the larger stellar population.

The main difference between an old “dark star” and John Archibald Wheeler's 1950's-era “black hole” was that dark stars could emit faint traces of indirect radiation. In theory, signals and particles could still migrate upstream out of the dark star's gravitational trap by using local objects as accelerational stepping-stones, whereas under GR1915, this mechanism couldn't exist – objects smaller than their r=2M event horizon radius weren't just incredibly dark, but totally black. Their signals and radiation-pressure signature weren't just absurdly faint, but entirely missing. The thing really was, as Wheeler memorably described it, a truly black "hole" in the surrounding landscape.

From the perspective of the Twenty-First Century, we can describe the difference in another way: dark stars emit classical Hawking radiation and GR1915 black holes don't.
Some people will take issue with that statement. They'll say that a hypothetical dark star's radiation-pattern is about acceleration effects rather than QM, and that Hawking radiation is all about particle-pair-production, a completely different mechanism.

So here's the sanity-check exercise. Suppose that the GR1915 description of horizon behaviour was wrong, and that a more "dark-starry" description was right … but that we still believed in GR1915. More general approaches (like statistical mechanics) would have to insist that the radiation effect was real, even though GR1915 disagreed. So how would we explain the reappearance of our naughty radiation effect?

There are number of stages we'd have to go through:
  1. In a thought-experiment, catch an escaped particle and measure its trajectory.
  2. Extrapolate that trajectory back to the originating body as a smooth ballistic trajectory. In our "dark star" scenario, this extrapolated trajectory is wrong – the particle only escaped by being "bumped" out of the gravitational pit by interactions with other bodies or radiation – but in our GR1915 description there's no self-supporting atmosphere outside the black hole to allow this sort of acceleration mechanism, so we have to (wrongly) assume an unaccelerated path.
  3. Notice that the earliest part of this (fictional!) escape-path is superluminal. In order to escape along a ballistic trajectory, a particle would have to have started out travelling at more than the speed of light (!).
  4. Apply coordinate systems. Using a distant stationary observer's coordinates, we break the fictitious trajectory into two parts, an initial superluminal section, and the later, legal, sub-lightspeed part of the calculated path. The first section appears to be off-limits in our coordinate system, and an orderly transition between the two, as the particle supposedly jumps down through the lightspeed barrier seems impossible, but …
  5. … then we then notice that in a very idealised description of a superluminally-approaching particle, the particle ends up described as time-reversed ("tachyonic" behaviour). If an (over-idealised) particle approaches at more than the speed of its own light (which shouldn't normally happen, but ...), we'd end up describing it as being seen to arrive before it was seen to set out. Our artificial coordinate system approach then describes the particle as being seen to originate at the nearest part of its path, and to be apparently moving away from us at sub-light speeds, as its earlier signals eventually arrive at our location in reverse order.
  6. Time-reversal counts as a reversal of one dimension, which flips a left-handed object into its right-handed twin, and vice versa (chiral reversal). So if our particle was an electron, this artificial approach would describe the earlier part of its supposed path as belonging to a positron, instead.
  7. Our final description would then say that a particle and its antiparticle both appeared to pop into existence together outside the horizon (from nowhere) and moved in opposite directions, with the "matter" particle escaping and being captured by our detector, and its "antimatter" twin moving towards the black hole to be swallowed.
And this is, essentially, the 1970's QM description of Hawking radiation.


Anonymous said...

Your blog entry seems to be confused. It begins by saying you're going to explain how Hawking radiation can be seen from a "dark star" perspective, and your objective is to say that special relativity is not consistent with this phenomenon. But then your "explanation" is completely based on things like "tachyon behavior" and anti-particles, both of which are concepts that originated in special relativity, and both of which make no sense outside the context of (local) special relativity. So your demonstration demonstrates the exact opposite of what you claim. Very strange.

ErkDemon (Eric Baird) said...

Anonymous, why are you even here? :)

You've just complained that antiparticles "make no sense outside the context of (local) SR" ... but actually one of the most productive areas of quantum gravity research for the last 10-15 years has been the subject of acoustic metrics and Hawking radiation in non-SR contexts (arXiv suggests the rate of relevant papers peaking in 2004 with about sixty submissions).
and Hawking radiaiton is still (AFAIK) typically taight and described in terms of particle-pair production.

So not only is your logic bad, your factual accuracy bad and your general knowledge of the subject bad, your criticism would seem to have been conclusively overturned by peer revewed work over ten years ago.

I'm trying to discuss the path to next-generation physics in this blog, and you're still hung up on results that got widely accepted last century.

I think you're fighting a losing battle, here! On the plus side, your total anonymity means that at least people won't tease you about it at work.