Black holes and gravitational waves – Part II

eeA friendly conversation between popular physicist A.Einstein and A.Eddington, astrophysicist. Probably it never involved black holes existence..

In part I we’ve read Laureti’s informal opinion about an article that clearly demonstrates what happens when speculation gets out of hand. In this part we’ll cover an interesting excerpt by professor Angelo Loinger (University of Milan) about black holes.


None, I say none, of the Great Spirits who created and developed the Theory of relativity, Einstein, Weyl, Hilbert, Levi-Civita, Eddington, Pauli, Fock, had never taken into account the idea that famous Schwarzschild’s solution, which provides the Einstein’s field generated by a material point of finite mass, could even contain the possibility of the existence of a black hole.

The attentive reading of the Founding Fathers memories and treatises is in this regard very enlightening. I’ll say more: every time some “nice spirit” advanced the idea of the possible existence of black holes, they clearly rejected it.

This happened, for example, in conversations between Eddington and Chandrasekhar; and with Einstein, who published in 1939 a work in which he demonstrated, with a very reasonable model, that no collapse of any star can lead to the formation of a black hole. Further demonstration has been exposed by me in [1].However, starting from about the sixties an increasingly large group of eager physicists began to publish an endless series of elaborated articles about the amazing properties of the blacks holes.

In all the libraries of academic physics departments is available a more than 1.200 pages jumble that drips with computations and nonsensical blah-blahs (see for example the grotesque scenery 4 at page 823,§31.3), opus magnum of three authors which I’ll indicate only with the initials M-T-W of their surnames. This book has become the Bible for the Prophets of the New Verb . A such brick obviously contains a large bibliography, but it’s not difficult to notice that authors also mention articles they didn’t read!

This is a very common bad habit today: for example, I’m certain that the very large majority of “blackholeists” doesn’t know the two original Swarzschild’s memories from 1916, related respectively to Einstein’s field in a material point [5] and in a fluid sphere [6]. During the centuries of Western Roman Empire decline it was common the saying Graecum est, non legitur (it’s Greek, can’t read, E.N); today something similar happens, with German language in place of Greek. Thus Salvatore Antoci and I decided to publish in Los Alamos Archive an English version of the work [5], see [7]. In said work that Great, prematurely passed away at 43 in 1916 crushed by the vortex of WWI, rigorously solved the problem by using a general coordinates system proposed by Hilbert [8], Droste [9] and Weyl [10], different from the one that today has become normal.

So,in the form of Swarzschild’s solution [5,7] there is only one singularity in the origin, similarly to what occurs in the simple Newtonian solution.

Starting from this original and early Swarzschild’s solution, the invention of the sci-fi concept of black hole would have been, even psychologically, rather difficult. Naturally Hilbert, Droste, Weyl and all Great Heads perfectly knew Swarzschild’s memory but preferred for calculus simplification reasons the solution form that later became standard (and improperly called Swarzschild’s). For the Founding Fathers of Relativity there was, rightly, no physical difference between the two forms of solution. They knew that original Swarzschild’s solution is diffeomorphic to the external part of standard solution, the one relative to radial coordinates values bigger than the so-called critical gravitational radius.

In the last page of Swarzschild’s second fundamental work [6], he gives some indications about the way of executing the passage from the limit of the fluid sphere of finite radius to the material point of finite mass. By following his instructions I’ve executed the simple calculus [see 1bis], effectively locating Work formula [5]; this demonstrates that Swarzschildian singularity is originally a true physical singularity and not a mathematical mishap, unlike many other singularities of General Relativity.

In these last years I personally verified the effectiveness of the popular (Italian, E.N) saying “there is no worst deaf than who doesn’t want to listen”, but I believe in human reason, not however in the more of less pantheistic way of classic German philosophy and Gentilian idealism, but in a way of the earthly whole and naturalistic. Therefore I’m convinced that tide will reverse and we’ll acknowledge that “the king is naked”.


Stay tuned for Part III: gravitational waves and final thoughts.


[1] A. LOINGER,  (30 Oct. 1998).

[1bis] A. LOINGER, (3 Aug. 1999).

[2] A. LOINGER, (8 Oct. 1998).

[2bis] A. LOINGER,

(20 Apr. 1999);

(3 Jun. 1999);

(30 Sept. 1999).

[3] A. EINSTEIN, Ann. Math., 40 (1939) 922.

[4] A clumsy astronaut, who would go beyond the fatal critical surface, would end like his clumsy earthling counterpart who, by slipping face down on a thin layer of soap and water, comically smashes his head into a wall.

[5] K. SCHWARZSCHILD, Berl Ber. (1916) 189.

[6] K. SCHWARZSCHILD, Berl. Ber. (1916) 424.

[7] K. SCHWARZSCHILD, (12 May 1999).

[8] D. HILBERT, Gott. Nachr., zweite Mitteilung, vorgelegt am 23.Dez.1916; ID., Math. Annalen, 92 (1924) 1.

[9] DROSTE J., Ned. Acad. Wet., S.A, 19 (1917) 197.

[10) H. WEYL, Ann. Phys. (Leipzig), 54 (1917) 117.

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