Gravitational Waves and Black Holes: Beyond the Mirror

J.-F. Pommaret graduated from French”Grandes Ecoles” (Ecole Polytechnique, Ecole Nationale des Ponts et Chauss ́ees) but also from Paris 6 U...

J.-F. Pommaret graduated from French”Grandes Ecoles” (Ecole Polytechnique, Ecole Nationale

des Ponts et Chauss ́ees) 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 equa-

tions 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 me-

chanics, 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.