muruep00

Thank you for response Markus. Yes, 1916, my bad again... Wouldnt it be better if we use Schwarzschild metric? I mean, we dont know what lies inside black holes. Perhaps there's a singularity solved by quantum gravity, or perhaps its something different... Let me repeat again, the Schwarzschild solution might be valid at the exterior, but in the interior, there could be something different than what you are forcing the Schwarzschild metric to have, that is, a point-like center of mass. What if you dont need quantum gravity to explain the inside of black holes because in reality (independent of what math suggests), something happens at the event horizon and the whole interior solution is different than the Schwarzschild interior solution, not only the singularity. I know about Einstein-Cartan theory, but what Im proposing does not have any issues since the runaway motion paradox is solved and Einsteins equivalence principle holds. Why no body has thought about this idea before? Because you cant be 100% sure that the interior solution only differs from GR to quantum gravity at the singularity, it could be very different entirely! As I said, you are forcing the interior solution to be one way in the math. You can glue the exterior solution to other different interior solution (for instance, an Einstein-Rosen bridge), and now the mathematically speaking, math suggests other different thing (still smooth at the horizon, but the interior is different)... Why not develop a non-singular interior solution and glue it to the exterior solution? The easiest way to do that is by violating energy conditions at all the interior with a perfect fluid of negative energy density, which is my proposal. Having clarified that I know what math suggests (nothing happens at the event horizon, and GR holds until being close the "singularity"), but it can perfectly be other way because it has not been proved by observation, why no body has tried these non-singular interior solutions in a reasonable way (that is, not allowing negative energy densities to exist outside black holes before collapse, which is what most "negative mass black holes" research has been about, check R. Mann)? What if one of these proposals could be verifiable by inconsistent observations such as huge supermassive black holes that no one knows how they formed? What are your thoughts about my proposal?

Hello, Markus, thanks again for your response. Yes, you are right he did not make any coordinate transformations. My bad. The coordinate transformation done in the Schwarzschild metric is to show that the event horizon is a coordinate singularity. But this transformation is always done to the Hilbert's metric, not the one Schwarzschild published (correctly as you said, in 1912). I dont know if the Schwarzschild metric and Hilberts metric are the same (might want to check this: https://www.researchgate.net/publication/331936281_Schwarzschild's_family ), as I have not applied a curvature invariants of the Riemann tensor to the original Schwarzschild metric. Im also very skeptical about the interior solution of Schwarzschild metric, since you are building it starting from the assumption that there is actually a central point-like mass. But what if that singularity does not exist in real black holes? The exterior solution might be correct anyways for black holes, but the interior, including what happens at the event horizon, can be something different. My proposal is very clear: there is a gravitational change happening at the event horizon, which does not violate Einstein's equivalence principle. This is the only way to violate energy conditions only at the interior of black holes ir order to prevent the formation of the central gravitational singularity and at the same time be consistent with observations (since we have never observe macroscopic violation of energy conditions in the spacetime we observe, that is, outside black holes). This can only be justified by a time transformation taking place at the event horizon, but GR (neither does SR) does not allow this by arbitrarely decisions of "time transformations are unphysical", done of course long before black holes were studied. What are you thoughts about this idea? Its the only way I found to 1. Be consistent with observations, 2. Include negative masses but solve the runaway paradox, 3. Solve the gravitational singularity and the crazy interior of Kerr BH (wormholes...etc), withour violating Einstein's equivalence principle, 5. Propose a mechanism of BH growth that may solve SMHB formation

Thank you for your quick answer. This a loong discussion. But first, I was referring to the original Schwarzschild metric, here you have it: http://old.phys.huji.ac.il/~barak_kol/Courses/Black-holes/reading-papers/Schwarzschild.pdf As you see, this is not the metric we use nowadays (we use the Hilberts metric). In the Schwarzschild metric, the interior is not described by the metric, because coordinate r=0 is the event horizon, and there the metric ends in a singularity. As I said, Schwarzschild did this trying to avoid the change of the signature of the metric, which leads to time and space switching roles and so on. So he invented an auxiliary quantity, called R (page 195), which he uses in the metric. He defined the auxiliary quantity R to be the cube root of the r coordinate cubed plus the schwarzschild radius cubed. As you see, this coordinate transformation he did, was not linear. Now, Im not an expert in this, but I've read that a metric and a non-linear coordinate transformation metric are not the same, and have different geodesics. I am not sure if both the original's 1912 Schwarzschild metric and the one we all study which was done by Hilbert are the same. Hilbert's metric can be checked here: https://www.jp-petit.org/Hilbert-1916-de.pdf in equation (45) and to my understanding, he defines time as an imaginary number (page 70), (isnt that a wick rotation?). Schwarzschild treated time as real coordinate, not an imaginary one. But even if Im wrong and you are right, we don´t know whats inside, so you can actually propose than x thing happens at the event horizon and it does no contradict observations. Proposals of "something happens at the event horizon" are usually not considered serious, just because they violate Einsteins equivalence principle. But if the "change" that you consider only implies gravitational effects, the principle holds. Of course, the Schwarzschild spacetime is vacuum, but we are talking about real black holes.

I might go straight to the proposal. Consider that the interior of black holes (BH)s only contain negative energy densities, also known as negative masses. These negative masses have been predicted to be repulsive by other famous physicists such as H. Bondi and W. B. Bonnor, but have not been taken seriously due to a paradox called "runaway motion" which takes place between masses of different signs. These negative masses would be created from infalling particles to the BH by a time transformation taking place at the event horizon, which only switches to antigravitational interactions, without violating Einstein's equivalence principle. The original Schwarzschild solution for 1912 is singular at the event horizon, because Schwarzschild did not want to change the signature of the metric when inside the solution, so he chose a radial variable in his metric which is a non-linear auxiliary quantity dependent of the black hole radius and the radial coordinate. This singularity might just be a time transformation, which is not allowed in relativity since the antichronous transformations are arbitrarely prohibited already in special relativity. This is supported by the time transformation of the Feynman Stueckelberg interpretation in relativistic particle physics, and if considered unitary, it implies negative masses (this has been proved by other researchers). The runaway motion would be solved since no interaction is allowed from inside to outside, and all particles crossing the event horizon would suffer this transformation. This violation of the energy conditions clearly solves the central singularity, since no gravitational singularity can arise only from repulsive matter. This solution not only solves the gravitational singularity, the strange theoretical interior of Kerr BHs and the runaway motion, but also it's trivial that the interior of the negative mass BH undergoes an inflation, which is slowed down by time dilation for external observers. This inflation would be noticed by exterior observers, which would perceive BHs as having a greater apparent mass than estimated due to accretion and merging, being this solution another mechanism of growth to be taken into account in studies of supermassive BH formation, which remain a mystery. I can develop it further, but the basic idea is that. What do you think? This proposal has never been published, only negative mass black holes forming from matter which already violates energy conditions outside the black hole (which contradicts observations).