The topic of gravitational lensing in the Mannheim–Kazanas solution of Weyl conformal gravity and the Schwarzschild–de Sitter solution in general relativity has featured in numerous publications. These two solutions represent a spherical massive object (lens) embedded in a cosmological background. In both cases, the interest lies in the possible effect of the background non-asymptotically flat spacetime on the geometry of the local light curves, particularly the observed deflection angle of light near the massive object. The main discussion involves possible contributions to the bending angle formula from the cosmological constant Λ in the Schwarzschild–de Sitter solution and the linear term γr in the Mannheim–Kazanas metric. These effects from the background geometry, and whether they are significant enough to be important for gravitational lensing, seem to depend on the methodology used to calculate the bending angle. In this paper, we review these techniques and comment on some of the obtained results, particularly those cases that contain unphysical terms in the bending angle formula.

General relativity (GR) is an important theory that requires very stringent tests. So far, its supporting evidence comes mainly from measurements of photon gravitational effects, including light bending near the Sun, gravitational lensing in some galaxies and gravitational redshift of light. These previous experiments were designed based on a hidden assumption, namely, the gravitational mass of a photon is zero; thus, light should not be bent in a gravitational field if there is no space-time curving. In this work, we showed that the gravitational mass of a photon is not zero. Instead, it is equal to its quantum mass, which can be determined from its momentum using the de Broglie relation. Based on this understanding, the gravitational effects of light can be explained more simply using quantum physics. Our findings suggest that, in order to fully evaluate the theory of GR, more stringent experimental tests are required. Some examples of future experiments for testing the principle of equivalence are proposed here.

mass, the post-Newtonian expansion), several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in May 1916 and is the accepted description of the gravitation of macroscopic objects in modern physics. General relativity generalizes special relativity and refines Isaac Newton's law of universal gravitation, providing a uni G… General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a massive object. This effect was initially confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun. This and related predictions follow from the fact that light follows what is called a light-like or null geodesic—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity. As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion), several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity. Closely related to light deflection is the Shapiro time delay, the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction. In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.

In 1919, Eddington and Dyson led two famous expeditions to measure the bending of light during a total solar eclipse. The results of this effort led to the first experimental confirmation of Einstein's General Relativity and contributed to create its unique and enduring fame. Since then, similar experiments have been carried out all around the world, confirming the predictions of the General Relativity. Later, developments in radio interferometry provided a more accurate way to measure the gravitation deflection. We believe that--after more than a century--starlight deflection caused by the Su

In 2014, NASA measured with high precision that the universal space has an Euclidean shape. This result is a challenge for new models of gravity and bending of light that challenge General Relativity. We developed a mathematical model where we extend the mass-energy equivalence principle to universal space. We gave universal space the physical property of the variable energy density. Our model elegantly describes gravity as the pushing force of space and the bending of light as a result of the changed refractive index due to the changed variable energy density of space when light moves closer or away from the stellar object.

by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun. Solutions are also used to describe the motion of binary sta The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun. Solutions are also used to describe the motion of binary stars around each other, and estimate their gradual loss of energy through gravitational radiation. General relativity describes the gravitational field by curved space-time; the field equations governing this curvature are nonlinear and therefore difficult to solve in a closed form. No exact solutions of the Kepler problem have been found, but an… Around…

A newly proposed gravity theory suggests that, in addition to mass, electromagnetic (EM) waves—or photons—can generate gravitational forces. The theory introduces two governing equations: one describing gravity between photons, and another describing gravity between a photon and a massive object, with force proportional to photon frequency. This frequency dependence implies that light should bend differently depending on its wavelength when passing near a massive body, potentially producing a dispersion in strong gravitational lensing. In contrast, Einstein's general relativity predicts freque