mvp@v7fs1.UUCP (Mike Van Pelt) (02/09/89)
In article <8902080259.AA04715@cmr.icst.nbs.gov> roberts@CMR.ICST.NBS.GOV (John Roberts) writes: >My own area of skepticism: I'm not convinced that it's possible for a >black hole to come into existence in a finite period of time, from the >viewpoint of an outside observer. I'm convinced you're right. Since time slows down, asymptotically approaching 'stopped' at the event horizon, the closest there can be is a "black hole in progress". -- Mike Van Pelt Video 7 ...ames!vsi1!v7fs1!mvp "... Local prohibitions cannot block advances in military and commercial technology.... Democratic movements for local restraint can only restrain the world's democracies, not the world as a whole." -- K. Eric Drexler
bbowen@megatest.UUCP (Bruce Bowen) (02/14/89)
In article <210@v7fs1.UUCP> mvp@v7fs1.UUCP (Mike Van Pelt) writes: >In article <8902080259.AA04715@cmr.icst.nbs.gov> roberts@CMR.ICST.NBS.GOV (John Roberts) writes: >>My own area of skepticism: I'm not convinced that it's possible for a >>black hole to come into existence in a finite period of time, from the >>viewpoint of an outside observer. > >I'm convinced you're right. > >Since time slows down, asymptotically approaching 'stopped' at the >event horizon, the closest there can be is a "black hole in progress". >-- This is not true. The total time for a black hole to form for an outside observer is the integral of the ratio of outside time to local time integrated over the local time for the black hole to form. The ratio goes to infinity as the edge gets close to the event horizon so one has an improper integral, but the value of this integral is finite. As an example the integral from 0 to 1 of 1/sqrt(1-x) = 2 even though 1/sqrt(1-x) goes to infinity as x -> 1 Bruce
ihr@wuphys.wustl.edu (Ian H. Redmount) (12/14/90)
In article <1990Dec12.195033.26427@watdragon.waterloo.edu> jdnicoll@watyew.uwaterloo.ca (James Nicoll) writes: > > Shouldn't relativistic effects prevent an outside observer >from seeing the collapsar form? I can see observing a 'really-quite-close- >to-being-a-collapsar object, but do we ever actually 'see' the event >horizon 'form' or does the collapse appear to an outside observer to >take an infinite amount of time? This question has appeared in other forms on the net before. It is discussed quite thoroughly in C. W. Misner, K. S. Thorne, and J. A. Wheeler, ``Gravitation,'' W. H. Freeman and Company (San Francisco), 1973, pp. 846-850 and pp. 872-875. If I may be permitted to paraphrase the Masters Three and Wise (:-)): Although the surface of a collapsing star crosses the event horizon at infinite t, where t is the time coordinate kept by the clocks of distant observers, this is actually an artifact of the coordinate system. The luminosity of the star decreases exponentially with (distant-observer) time in the late stages of the collapse. The e-folding time of this decrease is proportional to the star's mass, and is approximately 25 microseconds per solar mass. The star ``fades to black'' very fast: The luminosity of a four-solar-mass star in collapse drops by more than forty orders of magnitude in a hundredth of a second! Of course, since the atoms of the star emit light discretely, and since those atoms cross the horizon in a finite amount of their own proper time, the star does not fade forever. In short order it is absolutely black.* There is a time, shortly after the start of the collapse, after which no signal or influence from outside can reach the atoms of the star before they cross the event horizon. After that time the pre-collapse object is, for all operational purposes, gone. The ``collapse appear[ing] to an outside observer to take an infinite amount of time'' is thus illusory. One does not ``see the event horizon form'' because there is nothing to see: The event horizon itself is locally indistinguishable from ordinary space. I hope this clarifies the issue a bit. For more (and better-presented) detail, see MTW, loc. cit. Ian H. Redmount *Neglecting Hawking radiation, which is completely negligible for ``collapsars''---black holes---of stellar masses or larger.