Measuring refractive index gradient of sugar solution

To measure refractive index at a particular altitude in a solution with vertical refractive index gradient, a transparent wedge-shaped container was constructed altogether with the development of mathematical formula derived from the Snell’s law. The refractive index of the solution can be calculated by measuring the angles of incoming and outgoing laser beams relative to respective normal line. By varying height of the laser beam, the refractive index as a function of height of a sugar solution was obtained. This technique is applied to investigate Fata Morgana which is a kind of superior mirage resulting from bending of light in a medium with density gradient.

The question on the existence of black holes

Simulation shows that general relativity would lead to the existence of black holes if gravitation is always attractive. However, although we observed an invisible and extremely heavy object governs the orbits of stars at the center of our galaxy, we still cannot determine the existence of a black hole. Thus, one may ask whether black holes actually exist. Einstein’s general relativity has been established, because its prediction on the bending of light rays has been confirmed by observation. However, Einstein’s prediction on the increment of weight for a piece of metal as the temperature increases is proven incorrect by experiments, which actually show a reduction of weight. This leads to the necessary existence of repulsive gravitational force, which has been demonstrated by a charged capacitor hovering above the earth. Thus, Einstein, Newton, Galileo, and Maxwell all made the error of overlooking the repulsive gravitational charge-mass interaction. Thus, it is necessary to rejustify the existence of black holes, because gravity is not always attractive. Moreover, repulsive gravitational force makes it necessary to extend general relativity to a five-dimensional theory. Thus, to find out whether black holes exist, it is necessary to investigate the repulsive gravitation and a five-dimensional space.

Geometrization of light bending and its application to SdS w spacetime

The mysterious dark energy remains one of the greatest puzzles of modern science. Current detections for it are mostly indirect. The spacetime effects of dark energy can be locally described by the SdS$_w$ metric. Understanding these local effects exactly is an essential step towards the direct probe of dark energy. From first principles, we prove that dark energy can exert a repulsive dark force on astrophysical scales, different from the Newtonian attraction of both visible and dark matter. One way of measuring local effects of dark energy is through the gravitational deflection of light. We geometrize the bending of light in any curved static spacetime. First of all, we define a generalized deflection angle, referred to as the Gaussian deflection angle, in a mathematically strict and conceptually clean way. Basing on the Gauss-Bonnet theorem, we then prove that the Gaussian deflection angle is equivalent to the surface integral of the Gaussian curvature over a chosen lensing patch. As an application of the geometrization, we study the problem of whether dark energy affects the bending of light and provide a strict solution to this problem in the SdS$_w$ spacetime. According to this solution, we propose a method to overcome the difficulty of measuring local dark energy effects. Exactly speaking, we find the lensing effect of dark energy can be enhanced by 14 orders of magnitude when properly choosing the lensing patch in certain cases. It means that we can probe the existence and nature of dark energy directly in our solar system. This points to an exciting direction to help unraveling the great mystery of dark energy.

Remarks on inverse electrodynamics

We study physical aspects for a new nonlinear electrodynamics (inverse electrodynamics). It is shown that this new electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field, hence we compute the bending of light. Afterwards we compute the lowest-order modification to the interaction energy within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a long-range ($${1 \big / {{r^5}}}$$ 1 / r 5 -type) correction to the Coulomb potential.

Null geodesics in five-dimensional Reissner–Nordström anti-de Sitter black holes

The study of the motion of photons around massive bodies is one of the most useful tools to find the geodesic structure associated with said gravitational source. In the present work, different possible paths projected in an invariant hyperplane are investigated, considering a five-dimensional Reissner–Nordström anti-de Sitter black hole. Also, we study some observational tests, such as the bending of light and the Shapiro time delay effect. Mainly, we found that the motion of photons follows the hippopede of a Proclus geodesic, which is a new type of trajectory of the second kind, the Limaçon of Pascal being their analog geodesic in four-dimensional Reissner–Nordström anti-de Sitter black hole.

On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity

This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.