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We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe…
We propose a new interpretation of the equivalence principle underlying Einstein's general relativity: a free-falling frame with gravitational force eliminated locally in a small spacetime region shows the existence of a boundary level,…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…
Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar results. We have shown…
As is well-known, Newton's gravitational theory can be formulated as a four-dimensional space-time theory and follows as singular limit from Einstein's theory, if the velocity of light tends to the infinity. Here 'singular' stands for the…
We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of…
It is first argued that radiation by a uniformly accelerated charge in flat space-time indicates the need for a unified geometric theory of gravity and electromagnetism. Such a theory, based on a metric-affine $U_4$ manifold, is constructed…
The problem of quantum gravity is treated from a radically new viewpoint based on a detailed mathematical analysis of what the constitution of physical space is, which has been carried out by Michel Bounias and the author. The approach…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
In Einstein's general relativity, geometry replaces the concept of force in the description of the gravitation interaction. Such an approach rests on the universality of free-fall--the weak equivalence principle--and would break down…
We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian $L_{Hilbert} = \frac 1{16\pi} \sqrt{|g|} R$ by a generic scalar density $L=L(g_{\mu\nu}, R^\lambda_{\mu\nu\kappa})$ depending upon…
The Einstein-Hilbert action of general theory of relativity (GR) is the integral of the scalar curvature $R$. It is a theory that is drawn from the Equivalence principle, and has predictions that come out as a consequence of the principle,…
Most early twentieth century relativists --- Lorentz, Einstein, Eddington, for examples --- claimed that general relativity was merely a theory of the aether. We shall confirm this claim by deriving the Einstein equations using aether…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
We first review the cosmological constant problem, and then mention a conjecture of Feynman according to which the general relativistic theory of gravity should be reformulated in such a way that energy does not couple to gravity. We point…
Current generalizations of the classical Einstein-Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles are known to reproduce Einstein's gravitational equations, and should therefore be…