3 ms·
Isotropic coordinates have a discontinuity at the event horizon. It is therefore invalid to make any assumptions about worldlines inside the event horizon. Howe
by twiceaday 14y ago
Isotropic coordinates have a discontinuity at the event horizon. It is therefore invalid to make any assumptions about worldlines inside the event horizon. However it is possible to use coordinates that do not have discontinuities. If the papers intent was to consider what happens to world lines as they cross the event horizon the paper should not have used isotropic coordinates.
- pdonis 14y agoIsotropic coordinates have a discontinuity at the event horizon. No, they don't; I think you're thinking of Schwarzschild coordinates. Isotropic coordinates are continuous at the horizon, which is at R = M/2 (where R is the isotropic radial coordinate and M is the mass of the hole); but the region R < M/2 corresponds to the exterior of the horizon, not the interior. The standard interpretation of this is that isotropic coordinates double cover the same exterior region (which is labeled region I on a Kruskal diagram like the one in Figure 2 on the ScienceDirect page); in other words, for every value of R < M/2, there is a corresponding value of R > M/2 that labels the same point in the same exterior region. Poplawski's paper appears to claim that there is a valid alternate interpretation in which the region R < M/2 is a second, separate exterior region (labeled region III on a Kruskal diagram). That interpretation appears to me to violate the Einstein Field Equation, but I'm still digesting the paper (see my other posts in this thread).