French version.

Document: Memoir on hup chapter ii 1Memoir on hup chapter ii 1 (289.16 Ko) (also available on vixra.org).

This document discovers an important coincidence between a mathematical and a physical problem.

I remark the existence of circumstances which are compatible with coincidence between

(i) the Bowen solutions for the York Lichnerowicz equations associated with the initial data problem in Einstein’s theory of gravitation


(ii) the decompositions proposed by the TEQ for deformed angular momentum.


Einstein's master work [01-a; see a translation for example in 01-b] is published in 1916. In 1935, Einstein and Rosen propose in [02] a very original concept for the description of particles within a specific context which can be obtained in starting from the prescriptions exposed in [01]. The proposition was presumably supposed to allow a correct understanding of the atomic structures; at least the ones which was known at this time. In 1944, A. Lichnerowicz writes his famous equations [03-a]; see also [04-c; § 8.2.4, pp. 130-131]. They are then reworked by J. York. Approximately thirty years later, Bowen and all. proposes solutions for the York-Lichnerowicz initial data problem (see [04-c; chapter 8; § 8.2.6, pp. 136-139]).

The main results:

The Bowen-York solutions for the initial data problem in general relativity have the generic formalism:

|BYX > ~ [P]. |p >


  1. p is the ADM three-dimensional classical kinetic momentum; 
  2. [P] is the main part of a non-trivial decomposition ([P], z) in M(3, R) x E(3, R) for some angular momentum which has been deformed by a specific family of matrices [A]:

|dx, x][A] > = [P].|x > + |z >

That family generates polynomial of degree at most two (the so-called “initial theorem”) of which the coefficients of degree one must be of the following type:

da(x) = -(G. m/r3). xa + ga(x), a = 1, 2, 3.

With different words : they are a modified expression of the Newtonian gravitational potential.


The demonstration  made in that document suggests that we are living on a surface surrounding a Bowen-York-Lichnerowicz like black hole, alias a void.

The document EAN-9782369231134, v2, 14 March 2020, written in the French language is going a little bit further. A precise formalism for the modification, g, is not really imposed by the TEQ. It may eventually be one of the post-Newtonian propositions. The unique constraint is a strange one concerning the spatial position:

x = rot g(x)


[01] (a) Einstein, A. : Die Grundlage der allgemeinen Relativitaetstheorie; Annalen der Physik, vierte Folge, Band 49, (1916), N 7.

(b) Einstein, A. and Minkowski, H.: The principle of relativity; translated in english by Saha, M.N. and Bose, S.N. published by the university of Calcutta, 1920; available at the Library of the M.I.T.

[02] Einstein A., Rosen, N.: The particle problem in the theory of relativity; pp. 73-77, physical review, vol. 48, July 1, 1935.

[03] Lichnerowicz, A.:

(a) L'intégration des équations de la gravitation relativiste et le problème des n corps, J. Math. Pures Appl. 23, 37 (1944); reprinted in A. Lichnerowicz: Choix d'oeuvres mathématiques, Hermann, Paris (1982), p. 4;

(b) Champs spinoriels et propagateurs en relativit\'{e} g\'{e}n\'{e}rale, Bulletin de la S.M.F., tome 92 (1964), pp. 11-100.


(a) J. M. Bowen, General Relativity and Gravitation 11, 227 (1979);

(b) Gourgoulhon: 3 + 1 formalism and bases of numerical relativity - lecture notes; arXiv: gr-qc/0703035v1, 06 March 2007; (c) Cook, Gregory B. Initial data for numerical relativity. Living Rev. relativity 3 (2000), 5; DOI: 10.12942/lrr-2000-5. [online]; seen on the 11th June 2015.

[05] Bowen York Type Initial Data for Binaries for Neutron Stars; arXiv:1606.03881v1 [gr-qc] 15 June 2016.

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Date de dernière mise à jour : 11/05/2022

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