Yaakov Friedman

We investigate the polarization structure of gravitational waves in the framework of extended relativity (ER), a Lorentz-covariant theory in which gravitational fields are described by deviations from flat spacetime defined relative to a distant inertial observer. Starting from the ER point-source solution, we derive the gravitational radiation produced by a compact binary system in the wave zone and compute the associated geodesic-deviation field to second order in the orbital velocity parameter. The analysis does not rely on a weak-field perturbation of Einstein’s equations or on imposing a transverse–traceless gauge condition. The physical polarization content is characterized by the tidal matrix E a b = R 0 a 0 b , which determines the relative acceleration of nearby test particles and provides a gauge-invariant description of gravitational-wave polarization. We show that the transverse tensor sector reproduces the standard quadrupolar + and × modes at leading order. However, the spatial trace of the deviation tensor is non-vanishing, leading to additional breathing, vector, and longitudinal tidal components. These contributions are not independent propagating degrees of freedom but are geometrically correlated with the tensor sector through the source configuration. The resulting polarization pattern provides a potential observational test distinguishing ER from general relativity while remaining compatible with current observational bounds. We derive the corresponding detector response and discuss observational signatures for interferometric detectors and pulsar-timing arrays. The resulting polarization pattern provides a potential observational test distinguishing ER from general relativity.

This paper investigates the Newtonian shell theorem within the framework of relativistic gravity using the Extended Relativity (ER) model. We derive the gravitational field metric of a spherically symmetric extended body by superposing the contributions from its mass elements. The resulting gravitational time dilation is identical to that of a point source, consistent with General Relativity. Although the shell theorem does not hold exactly in ER, it remains a good approximation in the far-field region. We also derive an explicit expression for the motion of a test particle in this field. Corrections due to the extended nature of the source are negligible for non-relativistic velocities, but become comparable to relativistic effects in the round-trip light travel time between Earth and the International Space Station.

We continue Riemann’s program of geometrizing physics, extending it to encompass gravitational and electromagnetic fields as well as media, all of which influence the geometry of spacetime. The motion of point-like objects—both massive and massless—follows geodesics in this modified geometry. To describe this geometry, we generalize the notion of a metric to local scaling functions which permit not only quadratic but also linear dependence on temporal and spatial separations. Our local scaling functions are defined on flat spacetime coordinates. We demonstrate how to construct various geometries directly from field sources, using symmetry and superposition, without relying on field equations. For each geometry, two key visualizations elucidate the connection between the geometry and the dynamics as follows: (1) the cross-sections of the ball of admissible velocities, and (2) the cross-sections of the local scaling function.

We present a simple model for relativistic gravity. The model represents a gravitational field by a metric on a Minkowski space background. We introduce a new Lorentz-covariant metric for a single-source gravitation field, which is determined by the retarded position and the velocity of the source. This metric passes the GR tests and properly describes the strong gravitational field. Using this metric, we define the metric of a field generated by several moving sources. The explicit true acceleration of an object moving in this field is derived from the ‘first-order’ (in the masses of the sources) acceleration, which is linear in the sources. The field splits into near and far fields. We compare the far gravitational field of a binary star with electromagnetic quadruple radiation and present an algorithm for computing accelerations in such a field. These results may lead to a new understanding of gravitational waves and the structure and dynamics of galaxies.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

We present a new model of gravitational waves based on a new representation of the gravitational field. The field is described by a Lorentz-invariant action function is defined directly from the sources of the field at the retarded time on a flat spacetime background. The. The field of a moving, spherically symmetric body can be decomposed into near and far components which are defined explicitly. Assuming a superposition principle, we obtain an explicit description of the strain caused by gravitational waves generated by binary stars or black hole mergers, without the need of a linear approximation and gauge choice. Under this assumption, the gravitational waves are longitudinal. We also obtain an explicit formula for ratios of the amplitudes as measured by different detectors. This able us to test if the polarization can be longitudinal. We show that the event GW170814 can be explained in our model