Can you explicitely state what your problem with EF coordinates is?
I also don't follow your video or the naive explanation of why space must go somewhere and what it means to 'add' a lightcone. Afaik EF coordinates are just frames of references that eliminate the trivial singularities of the metric and as a result the lightcone 'tips'
Not a metric singularity, no. but a coordinate singularity, yes. The coordinate being time and the light cone being closed has a non-arbitrary significance. My position is that because proper time is zero it must exclude particles, and as the surface is light-like to fall below it is equivalent to an acceleration above the speed of light thus excluding all particles and rendering the surface inversely curved and negatively energetic.
>>7762208 >Not a metric singularity, no. but a coordinate singularity, yes. But there is no coordinate singularity in EF coordinates, this is simply not true. And what do you mean by 'proper time' being zero?
If there is a coordinate singularity in the unaltered Schwarzschild metric, but there are none in the EF coordinates then can you see that the alterations to light cones and world lines have changed the expected physics and thus violated the law of general covariance?
>>7762316 No. The lightcones look weird because the standard Schwartzschild coordinates aren't well defined in those areas. That doesn't mean the physics is bad, it's just that some choices of coordinate systems are sometimes better than others.
I submit to you that even in the EF coordinates there is still a singularity at the event horizon because changing coordinate systems should have no effect on closing light cones, and the light cones still close at the event horizon. The depiction of light cones remaining open below the event horizon is wrong. Thus even if there were a is a way to rectify the temporal singularity of the event horizon the EF coordinate system is not one of them.
I know the only metric singularity is at R=0. I have no problem with that singularity because it makes geometric sense.
There is also no problem with a coordinate singularity existing in the field. The metric remains regardless of whether or not a coordinate singularity exists in it.
The only issue that I see is how a temporal singularity effects particles. I view the representation of EF light cones as wrong on the basis of equivalence and the law of general covariance. The coordinate system itself is not wrong as a coordinate transformation cannot be wrong. However the depiction of light cones adopting the outer edge of an inertial frame light cone into itself simply because of a coordinate transformation that incorporates those edges isn't logical.
Current black hole theory only stands if light cone edges are changed, physically, by a coordinate transformation and that does not make sense.
The pure Schwarzschild metric gives us light cones which close at the event horizon, just as would be expected from a Rindler horizon in flat space acceleration. Since gravitation is seen as non-arbitrary relative the gravitating body the only reasonable conclusion is that light cone closure in gravitational fields is also non-arbitrary. A light cone depicted closing anywhere but the event horizon is wrong.
Thus the metric is constant up to r=0 but particles are excluded from that metric at and below r=2GM.
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