Frozen stars

Escape velocity, as we know, is the speed at which an object must travel to be released from another object’s gravitational field. It depends on the mass of the second object and how far apart the two are. We’re familiar with velocities calculated for escaping planets or stars, but in fact they can be calculated for any collection of objects: a solar system, a galaxy, the universe. While we may escape the Earth, or the sun, or the solar system, or even the galaxy, today I listened to Dr. Richard Wolfson posit that the escape velocity of the universe might well exceed the speed of light, rendering us forever trapped within its immense gravity well. (He did not elaborate on what might possibly be “outside” the universe for us to visit.) Even more interesting is that, if the escape velocity does exceed the speed of light, then the universe itself meets the definition of a black hole. We could all be living inside a black hole with such a large diameter that we haven’t (yet) felt any distorting forces (“tides”) that would be created by whatever and wherever its center would be. On the other hand, if the universe has infinite extent then it isn’t even meaningful to talk about “escaping” it. [Image by Don Dixon.]

I was listening to the other lecture on the sampler CD from The Teaching Company, which was lecture 15 from “Einstein’s Relativity and the Quantum Revolution.” This was an interesting contrast to the great books lecture on Gibbon’s Decline and Fall of the Roman Empire. For one thing, I knew more about the basic subject here (general relativity and black holes) than I did with Gibbon. But it was still thoroughly enjoyable and a fun educational experience.

Dr. Wolfson used the word “gravitating” in an unusual (to me) fashion: he employed it as an adjective to describe an object that exerts a gravitational field. I’m more familiar with it used as a verb, as one object may “gravitate” towards another. It seems a little odd to bother with it as an adjective, since isn’t every object in the universe “gravitating”?

He also made a nice point about the common conception that black holes sit around “sucking things up”. As he pointed out, the black hole has no more gravitational force than the object(s) it originally came from–mass is mass. What’s special about black holes is that their mass is compressed into a small enough volume that the escape velocity ramps up past that magical number, c. “Regular” objects avoid this phenomenon by filling more space; gravitational force falls off as distance squared, keeping us all safe from such extremes. But a black hole and a planet with the same total mass exert the same gravitational force at a distance. So long as you’re outside a black hole’s event horizon, you’re just as safe as you would be if it were a whole and healthy planet.

One last interesting tidbit: our term, “black hole”, focuses on the inability of light to escape from the object. But the Russians’ word for it instead captures the notion that (from the outside perspective) time inside the black hole slows down… and stops. They call them “frozen stars.”

1 Comment
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  1. Terran said,

    February 15, 2009 at 1:50 pm

    (Learned something new!)

    Frozen stars… I like that!

    To take some things in reverse order:

    It’s true that a black hole and an equivalent-mass star don’t exert any different absolute gravitational force for a fixed r>d_E (event horizon radius). But that underemphasizes some important differences, I think. The fact that d_E<<radius of the star means that you can get a lot closer to the gravitational center of the frozen star, while still being outside the event horizon. Because of the r^2 falloff, that means that you’re experiencing drastically greater gravitational forces than you would at the star’s surface. Also, tidal forces fall off, IIRC, with r^4, so you experience really frightening tidal forces in that regime. So you can still be outside the event horizon and yet be in far more danger than you would have been at the star’s (or planet’s) surface.

    isn’t every object in the universe “gravitating”? Not massless particles, I assume. Though I’m a little out of my depth on that stuff, so I can’t be completely sure.

    Re: escape velocity of the universe>c. Fascinating! I’d never considered it in those terms. I wonder if that’s the same observation as the cosmological hypothesis that the universe is gravitationally closed and will eventually collapse in the big crunch? (I thought that they had nailed this down in the past 15 years or so and decided that the universe was, in fact, closed, but a casual perusal of wikipedia suggests that there’s still debate, given questions about dark energy.) Did he comment on whether the event horizon for this hypothetical universe-hole would be bigger than the light cone?

    I do wonder how this notion of a big ol’ singularity at the “center” of the universe fits in with the usual description that the universe has no center, but that everything is expanding uniformly in all directions. Wouldn’t such a singularity *define* a center and, therefore, impose a preferred coordinate frame? In principle, you should be able to see evidence of it in tides, at the least. I would guess in Doppler shifts and possibly even temporal effects as well. Given that we can see at least 13 billion light years radius, I would expect that you could find some observational evidence of such a thing at that scale.

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