scholarly journals Incompleteness of General Relativity Regarding Einstein's Program

2018 ◽  
Vol 10 (5) ◽  
pp. 47
Author(s):  
Claude Elbaz

The detection of gravitational waves substantiates the undeniable achievement of general relativity theory by increasing its theoretical and experimental accuracy. One century after predicting it has set again Einstein's works at the front of research. Absence of quantum particle associated to gravitation emphasizes that general relativity theory remains not included in the standard model of physics. Then Einstein’s disagreement about it incompleteness regarding wave-particle and matter-field becomes actualized. In order to circumvent these difficulties he privileged field, rather than matter for universe description in his program. In consequence a scalar field e(r0,t0) propagating at speed of light c yields matter from standing waves moving at speed strictly inferior to c, and interactions from progressive waves. Electromagnetic interactions derive from local variations of frequencies, and gravitation from local variations of speed of light. A space-like amplitude functions u0(k0r0) supplements fundamental time-like functions of classical and quantum mechanics. It tends toward Dirac’s distribution Delta (r0) in geometrical optics approximation conditions, when frequencies are infinitely high, and then hidden. More generally, it allows theoretical economies by deriving energy-momentum conservation laws, and least action law. Quantum domain corresponds to wave optics approximation conditions. Variations of frequencies give rise to an adiabatic constant, formally identical with Planck's constant, leading to first quantification for electromagnetic interactions and to second quantification for matter.

The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx 0 dx 1 dx 2 dx 3 where ( x 0 , x 1 , x 2 , x 3 ) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials g v q , which specify the metric by means of the equation dx 2 = ∑ p, q g vq dx v dx q . In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the g vq 's and in the electromagnetic potentials, regarded as functions of x 0 , x 1 , x 2 , x 3 .


1996 ◽  
Vol 165 ◽  
pp. 153-183
Author(s):  
Kip S. Thorne

According to general relativity theory, compact concentrations of energy (e.g., neutron stars and black holes) should warp spacetime strongly, and whenever such an energy concentration changes shape, it should create a dynamically changing spacetime warpage that propagates out through the Universe at the speed of light. This propagating warpage is called gravitational radiation — a name that arises from general relativity's description of gravity as a consequence of spacetime warpage.


Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 87
Author(s):  
Júlio C. Fabris ◽  
Marcelo H. Alvarenga ◽  
Mahamadou Hamani Daouda ◽  
Hermano Velten

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.


2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.


In this contribution, my purpose is to study a new mathematical instrument introduced by me in 1958-9: the tensor and spinor propagators. These propagators are extensions of the scalar propagator of Jordan-Pauli which plays an important part in quantum-field theory. It is possible to construct, with these propagators, commutators and anticommutators for the various free fields, in the framework of general relativity theory (see Lichnerowicz 1959 a, b, c , 1960, 1961 a, b, c ; and for an independent introduction of propagators DeWitt & Brehme 1960).


1983 ◽  
Vol 51 (1) ◽  
pp. 92-93 ◽  
Author(s):  
H. A. Buchdahl ◽  
Daniel M. Greenberger

Sign in / Sign up

Export Citation Format

Share Document