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Black Hole as Wormhole? 
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#1
Feb1613, 05:52 PM

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PF Gold
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A recent thread on Hacker News led me to this paper by Poplawski:
http://arxiv.org/abs/0902.1994 The abstract says: "We consider the radial geodesic motion of a massive particle into a black hole in isotropic coordinates, which represents the exterior region of an EinsteinRosen bridge (wormhole). The particle enters the interior region, which is regular and physically equivalent to the asymptotically flat exterior of a white hole, and the particle's proper time extends to infinity. Since the radial motion into a wormhole after passing the event horizon is physically different from the motion into a Schwarzschild black hole, EinsteinRosen and Schwarzschild black holes are different, physical realizations of general relativity. Yet for distant observers, both solutions are indistinguishable. We show that timelike geodesics in the field of a wormhole are complete because the expansion scalar in the Raychaudhuri equation has a discontinuity at the horizon, and because the EinsteinRosen bridge is represented by the Kruskal diagram with Rindler's elliptic identification of the two antipodal future event horizons. These results suggest that observed astrophysical black holes may be EinsteinRosen bridges, each with a new universe inside that formed simultaneously with the black hole. Accordingly, our own Universe may be the interior of a black hole existing inside another universe." Has anyone else come across this paper before? It looks questionable to me because of the known properties of isotropic coordinates, but perhaps I'm missing something. (Note: I see from searching PF that other papers by Poplawski have been commented on, but I haven't seen anything about this one specifically. This one doesn't seem to rely on his views about torsion, which are crucial in his other papers.) 


#2
Feb1713, 07:15 AM

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#3
Feb1713, 10:31 AM

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#4
Feb1713, 11:26 AM

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PF Gold
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Black Hole as Wormhole?



#5
Feb1713, 11:29 AM

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PF Gold
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#6
Feb1713, 11:54 AM

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#7
Feb1713, 12:26 PM

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Naty had a thread in cosmology section with his torsion model. The thread was Can torsion avoid the black hole singularity. Or domething like that lol. I pulled the link to the paper. Its one I've been looking at. I still have to study the OP paper.
http://arxiv.org/abs/1007.0587 


#8
Feb1713, 12:34 PM

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#9
Feb1713, 01:29 PM

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PF Gold
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[tex]ds^2 = \frac{\left( 1  M/2r \right)^2}{\left( 1 + M/2r \right)^2} dt^2  \left( 1 + \frac{M}{2r} \right)^4 \left( dr^2 + r^2 d\Omega^2 \right)[/tex] Substitute [itex]r = M^2 / 4R[/itex]; that means [itex]dr =  (M^2 / 4R^2) dR[/itex], and [itex]M / 2r = 2R / M[/itex]. This gives: [tex]ds^2 = \frac{\left( 1  2R/M \right)^2}{\left(1 + 2R/M \right)^2} dt^2  \left( 1 + \frac{2R}{M}\right)^4 \left( \frac{M^4}{16 R^4} dR^2 + \frac{M^4}{16 R^2} d\Omega^2 \right)[/tex] Refactor the terms: [tex]ds^2 = \frac{\left( M / 2R \right)^2}{\left( M / 2R \right)^2} \frac{\left( 1  2R/M \right)^2}{\left(1 + 2R/M \right)^2} dt^2  \left( 1 + \frac{2R}{M}\right)^4 \frac{M^4}{16 R^4} \left( dR^2 + R^2 d\Omega^2 \right)[/tex] [tex]ds^2 = \frac{\left( M/2R  1 \right)^2}{\left(M/2R + 1 \right)^2} dt^2  \left( 1 + \frac{2R}{M}\right)^4 \left( \frac{M}{2 R} \right)^4 \left( dR^2 + R^2 d\Omega^2 \right)[/tex] [tex]ds^2 = \frac{\left( 1  M/2R \right)^2}{\left(1 + M/2R \right)^2} dt^2  \left( 1 + \frac{M}{2R} \right)^4 \left( dR^2 + R^2 d\Omega^2 \right)[/tex] So he's right that the metric is formally unchanged by the substitution; but he claims that by putting an infinitely dense sheet of lightlike radiation at the horizon, he can construct a solution where the patch 0 < r < M/2 is a *different* region than the patch M/2 < r < infinity, so a timelike geodesic that falls in to r = M/2 can then "fall" back outward from r = M/2 to smaller and smaller values of r, which correspond to larger and larger values of R (the transformed radial coordinate), so it takes an infinite amount of proper time to reach r = 0 (which corresponds to R = infinity). I'm not sure the infinitely dense sheet thing works, though. 


#10
Feb1713, 03:00 PM

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#11
Feb1713, 05:16 PM

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