Gravitational Waves and Black Holes: Beyond the Mirror

Author:   J.-F. Pommaret J.-F. Pommaret graduated from French  “ Grandes Ecoles” (Ecole Polytechnique, Ecole Nationale  des Ponts et  Chauss...

Author: J.-F. Pommaret

J.-F. Pommaret graduated from French “Grandes Ecoles” (Ecole Polytechnique, Ecole Nationale des Ponts et Chaussées) but also from Paris 6 University. He retired in 2006 from ENPC as an Emeritus Researcher. He started to study the formal theory of systems of partial differential equations and Lie pseudogroups in 1970 with Prof. D. C. Spencer at Princeton University. He then applied differential homological algebra to study the mathematical foundations of continuum mechanics, electromagnetism and their couplings, control theory (CT), general relativity (GR) and gauge theory (GT). His main results on the possibility or impossibility to parametrize the space of solutions of certain linear partial differential operators have been spread with success through Europe during two series of annual one week solo intensive European courses (1990-1995: ERCIM with INRIA, 1997-2004: CTS with SUPELEC, AACA 2009 in Linz, Austria). He is the author of more than 200 publications, 7 books published by international editors (the first one of them translated by MIR, Moscow, in 1983), 3 book chapters with many thousands of views. 

With more details, in 1995, he solved negatively for the first time a 1970 challenge of J. Wheeler by proving that Einstein equations in vacuum cannot admit a potential parametrization like the Maxwell equations, showing in particular that the Einstein operator is self-adjoint. The crucial point has been to notice that the Airy parametrization of the Cauchy operator, adjoint of the Killing operator was only the adjoint of the Riemann operator in plane elasticity. In 2001, studying the Lanczos problems, he discovered that the Beltrami = ad(Riemann) operator can be parametrized by the Lanczos = ad(Bianchi) operator in the adjoint sequence along the exact dual differential sequences of operators acting on tensors, giving order of operators and number of components:

In 2017, he proved that the operator used to define the gravitational waves (GW) in any textbook was nothing else than the adjoint of the Ricci operator, a result proving that Einstein GR is based on a confusion between the Cauchy operator (left) and the div operator induced from the Bianchi operator (right). Such a result is deeply questioning the foundations of both GR, GT and CT, showing in particular that the Einstein operator, already used by Beltrami in 1892, is useless. In 2025, using the conformal group of space-time like H. Weyl in 1918, he has been able to unify electromagnetism and gravitation in a way contradicting both classical GR and GT.