Espen

I finally feel we're getting somewhere, Zanket. First you're of course right. In that frame any time intervall observed on the falling watch will eventually become infinite, i.e. the falling watch will appear to reach the horizon, but never fall in. So, we agree that frame of reference depends on what you see. Following that I hope we also agree that choise of coordinate system depends on what results you get? Then you're alleged inconsistency is easily explained by GR as a mere bad choice of coordinates. Let me try to illustrate more easily the situation. The best way to illustrate is to imagine lightcones falling towards the center. As you now, massive particles only exists inside the lightcone. Now, if we use the same coordinates used to derive the almost infamous Eq. (17) we get that the infalling lightcones collapse at the Schwarzschild radius, i.e. the coordinate system and any equations resulting from the use of it breaks down at the Schwarzschild radius, including Eq. (17). Your claim is that Eq. (17) holds even here, whereas I've just shown, by means general relativity allows, that it doesn't. What you have to do to avoid lightcones from collapsing, and thus being able to make sense of what happens inside the Schwarzschild radius is to transform to different coordinates. Some famous examples of such coordinates are the ingoing Eddington-Finkelstein coordinates and the Kruskal-Szekeres analytical extension of the Schwarzschild spacetime properly named Kruskal-Szekeres coordinates. It is thus quite clear that, by means general relativity allows, Eq. (17) only applies outside the Schwarzschild radius, and that different coordinates are required to cover more of the Schwarzschild space-time manifold. Your alleged inconsistency is thereby explained and accounted for, by means general relativity allows. Finally I'd like to bring to your attention something I noticed in your article, the following statement: Likewise, Taylor and Wheeler place no limit on the size of an inertial frame. Here you're referring to pages GL-4 and 2-4, sect. 3 (your ref. #6). I then refer you to page 1-14, sect. 8 in that same book. The sections begins with the following sentence: In practice there are limits on the space and time extent of the free-float (inertial) frame. I just thought you should know if there's a typo or something.

Using the coordinate system that gives Eq. (17) it follows that the infalling particle with it's proper time, T, at a distance r from the center will observe a time t on a watch at rest relative to the center given by t = T/sqrt(1-R/r) where R is the Schwarzschild radius. Now, observe what happens when your infalling particle reaches the Schwarzschild radius, you get a division by zero. Now, I'm pretty confident that you've already decided that you've shown an incosistency in GR, regardless of what the facts may be. So, I'm curious as to see how you'll deal with this division-by-zero error I've pointed to (which you yourself claims can be the end of any theory). Will you dismiss it as irrelevant again? Or will you ignore it and refer to your website and say that you've shown an inconsistency? Regardless, I doubt you'll even attempt to solve this inconsistency!

Indeed v of a massive particle always asymptotes c, locally. Now, Eq. (17) was derived using the metric from Schwarzschild's exterior solution, a metric with a special set of coordinates that exhibit a coordinate singularity at the Schwarzschild radius. Furthermore, like I've said, below the Schwarzschild radius the proper time of the falling object will become imaginary, which means that the analysis breaks down, as well as Eq. (17). Trust me, I know this is hard to grasp, but that doesn't make it any less real. Perhaps a new theory under development, but in order to refute a well tested, well scrutinized and well established theory you need more than an incomplete understanding of it. You know, the more I discuss this with you, the more I begin to realize the futility of convincing you. I believe James "The Amazing" Randi said it the best: No amount of contrary evidence will ever un-convince the true believer.

Well, technically Eq. (17) only applies for radii greater than the Schwarzschild radius. The equation was derived using coordinates that are comoving and at rest relative to the object falling. Such frames cannot readily exist within the Schwarzschild radius. For one thing, the proper time (i.e. the watch following the falling object) would show imaginary time! Furthermore, at the Schwarzschild radius the time and space coordinates are interchanged: r becomes a time coordinate, and t becomes a space coordinate. Well, this is just a tidbit of what there is to know about Schwarzschild geometry and black holes. This is a subject with much to learn, and I know I have far more to learn myself. What we've talked about here in general, and Eq. (17) in particular, are just smidgens of the whole story. I'm afraid your paper is far too lacking in extent, depth and understanding of the subject to be taken even remotely serious, I'm sorry to say...

I'm afraid that section 2 of your paper shows no contradiction of GR whatsoever. The reason for that I've already pointed out: you're completely ignoring the photon! In fact, I searched your paper for the word photon, but it doesn't occur even once! So of course it's easy to show an inconsistency in GR when you're only considering part of the theory! I'll repeat my self. You're only talking about massive particles, and then you're right, their velocities will always asymptote c. For a photon, however, it's velocity will always equal exactly c.

Thanks for your reply Zanket, I now think I know where you're misunderstanding. It appears as if you've forgotten or old pal, the photon. You see, Eq. (17) only applies to massive objects, and as we both know, their velocity is always less than c. For massless objects, however, like the good ol' photon, other rules apply, and, again, as we both know, the speed of light is always constant, so a photon moving radially towards a black hole will always travel at the speed of light. So, if, from Eq. (17) we get a finite, nonzero radius when we plug in v = c (for the photon), there will be areas that require a v > c to escape from, i.e. Black Holes.

Thanks, and ditto, btw. Ahh...well, there's more to theoretical physics than umpteen-dimensional theories with strings and branes and whatknots. I personally am not into all that (at least not yet). But, like I said, I just started on my masters, and I don't think it's quite appropriate to start with such highly speculative conjecturing when there's still a lot that needs to be grasped about already established theories, theories with actual experimental support. Theories like relativity and quantum mechanics are deep and subtle theories with somewhat elusive aspects that I think ought to be explored before I even start considering the hypotheses of the many "rogue theorists" (aka string "theorists") and such. I'm not even ready to abandon a strictly 4-dimensional world-view!

Well, I'm a twisted person I prefer to understand reality, regardless of whether or not i can actually "see" it happening.

Hi there. Not much to say about me really. I've just started on my masters degree in theoretical physics, which is really exciting! That's all I can think of for now, just ask if you have any questions.

I have a comment about a statement from your website, but first I'd like to give an equation I will frequently refer to as Eq. (17) (see reference below), for readers without immediate access to the reference: v = (2M/r)^{1/2} (17) So, I have a comment on the following statement from your website: Where (7) refers to the book "Exploring Black Holes", p. 2-22, Eq. (17). I'm looking in the box "Newton Predicts the Horizon of a Black Hole" where Eq. (17) is listed, but I can't seem to find any statements that says that wherever "v is less than c it equals the escape velocity there". Eq. (17) in the book refers to the velocity obtained by a free-falling object starting at a "great distance" from rest. Technically this "great distance" has to be infinity for Eq. (14) to hold (that's where the potential energy as defined in Eq. (13) also is zero). So, while equation (17) refers to the escape velocity of a black hole, an object at an arbitrary radius (at least if it's larger than the Schwarzschild radius) can have either larger or smaller velocity than that given by Eq. (17). Finally, your statement that "the escape velocity is always less than c" litterally contradicts the book you're referring to, which actually says: If you look at Eq. (17) you'll see that for a small enough radius, the velocity will be larger than c, but because the max escape velocity is c, anything inside that radius will not be able to escape.