Jamil Kooli A better way to think about it is to consider the matter density required to form a black hole. The important point when considering a mass of radius R and calculating the Schwarzschild radius, for an event horizon to form the entire mass must be located within the radius.

So for example you could calculate the Schwarzschild radius for the sun and you would find it to be around 3km. But the radius of the sun is much greater than 3km so no event horizon forms.

If you then consider a neutron star of greater than or equal to 3.4 solar masses then an event horizon will form outside the surface of the star and you have a black hole.

If you then ask if it is possible to form a black hole of less than 3.4 solar masses the answer is no because it would require an object with matter density greater than a neutron star.

So the conclusion which is consistent with astronomy observations is that the smallest possible black hole is 3.4 solar masses.

This rules out the possibility of quantum black holes and no new equations are required.

Richard

I believe the schwarzschild radius equation is like "the boat in a storm", you have to save it to survive. The Scharzschild radius formula is similar to this boat asking for help because on the one hand you have to know the mass to have the value of the radius and on the other hand you don't even know if you have to give the mass of a quantum black hole or the mass of a cosmological black hole and if it turns out that it can be used for both means two definitions of the masses of a quantum black hole and a cosmological black hole and that is where Schwarzschild fails!

“Do you think the Schwarzschild radius equation somehow "failed" because Schwarzschid didn't give the equation for the mass of a black hole?”

- that isn’t so; the black hole mass is completely defined in the Schwarzschild radius equation RS=GM/c2 – any mass M with this radius RS is a black hole.

So, say, that

“…A better way to think about it is to consider the matter density required to form a black hole.…”

- isn’t correct. Since density is ~M/r3, black holes can have arbitrary density, say, Milky Way central SMBH inside its sphere “event horizon” surface that has Schwarzschild radius has average density in 104 times lesser than neutron star density. That is another thing, that the “GR black hole” are rather strange material objects - are fantastic real “holes in the spacetime”, and so in the mainstream it is principally impossible to know – what is under the “event horizon”.

Really any “holes in spacetime” are fundamentally impossible, however, indeed, the “black holes” create so extreme Gravity Force fields, that are extremely exotic [and so the term “black hole” is rather appropriate] – but completely real - material objects about matter state in which mainstream physics knows completely nothing, since the GR is standard theory in this physics;

- while in real physics something is clear yet now, and possible ways how to study these objects can be clarified – see the Shevchenko-Tokarevsky’s initial cosmological model in

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics, section “Cosmology”

- SS posts in https://www.researchgate.net/post/Can_we_think_that_general_relativity_rather_predicted_that_the_universe_is_a_black_hole are relevant in this case as well.

Cheers

Sergey Shevchenko

Thank you very much for the explanation and the documentation. Without an explicit definition of black hole mass by schwarzschild, the constant ratio between rs and ms does not contradict the possibility of tiny black holes, I can say that this ratio is "blind" on the subject. For me the equation of the radius of Schwrzschild must be supplemented by two new definitions one for the mass of a cosmological black hole and the other for the mass of a quantum black hole. And there must be a linking equation between the mass of a quantum black hole and the mass of a cosmological black hole, which in this case relates the infinitely small to the infinitely large. After Planck's wall, any particle with mass is a black hole obeying the Schwarzschild radius, that's what I think. I had no problem working with this, and makes things much easier for me.

Dear Jamil Kooli,

“…Without an explicit definition of black hole mass by schwarzschild, the constant ratio between rs and ms does not contradict the possibility of tiny black holes, I can say that this ratio is "blind" on the subject…”

- again, the unique – and so explicit – definition of black hole exists – see the SS post above, while corresponding definitions of masses concrete BH are corresponding concrete tasks in concrete cases. Including the existent BHs in observed Matter differ in mass on many orders by magnitude [in at least in hundreds of millions times], and so matter’s density, and so matter’s states in the compact objects in BHs can be even principally different; more see again the section “Cosmology” in the link in SS posts above.

Including so that

“… For me the equation of the radius of Schwrzschild must be supplemented by two new definitions one for the mass of a cosmological black hole and the other for the mass of a quantum black hole. And there must be a linking equation between the mass of a quantum black hole and the mass of a cosmological black hole, which in this case relates the infinitely small to the infinitely large….”

- is incorrect, there is no physical relations between “quantum” and “macro” BHs; besides, though, that there can exist, and with a well non-zero probability, exist the unique “quantum BH” - the Planck mass particles [which were the primary particles that were created at Matter’s Beginning, again see the link above],

- and so, say, the matter’s states of small, i.e. star mass scale, BHs, in principle can be something like exotic, but “ordinary” matter state; say, as a next state after neutron star as some “quark BHs” [again see the link], while the central objects in SMBH can have some quantum states compositions of the Planck mass particles.

As well as that

“… After Planck's wall, any particle with mass is a black hole obeying the Schwarzschild radius, that's what I think..…”

- is incorrect. Matter fundamentally doesn’t contain particles with mass is a black hole, beside the above one. There can be, in principle some compositions of Planck mass particles as some “micro BHs”, however that looks as practically impossible, since the probability of creation of a such composition is tooo near zero, because of that Gravity Force is tooo weak Force.

Cheers

Sergey Shevchenko

Many thanks for you ample explications. But i really don't understand why people refute the idea of ​​quantum gravity? I think it's really absurd to worry about the possibility of imagining a large gravitational force in a sphere of the radius of a proton or a neutron when the mechanism of mass formation of protons and neutrons is 100% misunderstood. ? This is what is very disturbing in current physics. Kind regards.

Jamil Kooli,

“…But i really don't understand why people refute the idea of ​​quantum gravity?...”

- that most of mainstream physical people refute the idea of quantum gravity isn’t really correct, even in the mainstream physics for many people it is clear, that some “quantum gravity” must exist.

However, since in the mainstream the general relativity is standard theory, and so in the mainstream even there is no fundamental Nature force “Gravity”,

- while, at that, since the GR is fundamentally based on fundamentally wrong postulate that the gravitational objects/events/interactions are based on interactions in systems “mass-spacetime-mass”, what is fundamentally impossible – the Matter’s spacetime fundamentally is nothing else than some fundamentally infinite “empty container”, where Matter is placed, and emptiness by no means impact on something in Matter, and anything in Matter fundamentally cannot impact on space/time/spacetime,

- and so QM, which is based on rather rational scientifically postulates, is fundamentally incompatible with the GR. So, again, really rather numerous attempts to “quantize the GR” in the mainstream physics really exist, and quite logically inevitably resulted – and rather vividly result till now – only in some fantastic theories of “loop quantum gravities”, “strings”, “brans”, etc., “theories”. Really Gravity fundamentally is, of course, nothing else that some fundamental Nature force

, which in a number of traits is similar to the fundamental Nature Electric force, and really – as that happened with Electric force – there is no any principal problem in development of QM Gravity.

However Gravity Force fundamentally differs from Electric Force in that Gravity is extremely weaker than Electric force, and so electric charges of particles compose QM systems, say, atoms, on rather large distances between the particles, which [particles] have also rather large “sizes” –their Compton lengths,

- while on these distances Gravity impact practically exactly is zero, so really practically everything in Matter is composed by Electric and Strong Forces, and in Matter some “quantum gravity” systems practically don’t exist.

More see the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

However here is a couple of important points else:

- first of all the quantum nature of Gravity can be, nonetheless, experimentally observed at experiments with particles that have very small masses, and are well observable, in this case with photons, the corresponding experiment was offered yet in 2007, see - http s://www.researchgate.net/publication/215526868_The_informational_model_-_possible_tests ; http://arxiv.org/abs/0706.3979 section 2.1.2. “Monochromatic photon beam distortion”; and

- the extremely compact, and large, masses “black holes” with a large probability are really essentially quantum objects, because of in BHs Gravity is so extremely strong, that “destroys” by some, though unknown now, but really acting, ways, action of Electric Force impacts, and in SMBH – impacts of Strong Force also;

- as, say, the white dwarf [where Electric Force dominates], and neutron [where Electric Force practically doesn’t act], stars are really quantum objects, where, say, the purely QM Pauli principle acts, making these stars be stable.

Cheers

Sergey Shevchenko

Thanks again for the documentation and explanations. Best regards.