GRAVITATIONAL BENDING OF PHOTONS OR GRAVITATION LENSING OF SPACE-TIME

Markos Georgallides — 2026-02-19

One of the most important concept in Geometry is, distance , which is the Quanta in geometry, while in Material-Geometry the composition of Opposite , the Material-Point which is the Quanta in Chemistry and Physics. As in Algebra Zero, 0 , is the Master-key number for all Positive and Negative numbers and this because their sum and multiplication becomes zero, and the same on any coordinate- system where ± axes pass from zero . The Rolling of Positive ⊕, constituent on the Negative ⊖ , constituent , creates the Neutral Material Point which Equilibrium. Angular-Momentum is identical with Spin and consists the First-Discrete-Energy-Monad which occupies, Discrete Value and Direction, in contradiction to the Point which is nothing, Dimensionless and without any Direction. Quaternion [(+) ∪ (-)] ≡ Box Bᵣ which carries the Principal stress σ between A (+), B(-) which σ, as Centripetal-acceleration is the minimum Energy becoming from the in-storage AB acceleration and is equal to the Gravity g . The Geometry-Spaces → Explain the How and the WHY, by filling the Gap with a Double-Ocean of the Pointy-Spinning Material Points, become from the Stationary-Material-Points, either these are the Photons or the Electrons. From the moving-Energy-Storages, as this is Duality Photon with equation → v⃗ [ B⃗₀ + B⃗ₙ ] = | v / π²·r² ₙ | [ B⃗ₙ ] + |c| B⃗ₙ ← When c = 0 , then Photon-motion is | v / π²·r² ₙ | [ B⃗ₙ ] = The Spin with mass. The Photons Electric-field is the motion and Magnetic Field is the reaction to this motion, which is thus the mass of Photons (Newton’s third law Action-Reaction). Because of the Screw-motion of velocityvector on a radius r , allows to apply at a Point C of this circle [C , r] The , (2-Vectors 3-Poles Mechanism), of two Perpendicular CA ⟂ CP and equal vectors for distribution to the two Vectors ⊕ Electric field Vector → F = q · E , and the ⊖ Magnetic field Vector → F⃗ = q · v⃗ × B⃗ . The Two-Perpendicular and equal Vectors , CA , CP , Slide on (O,OA) circle and through the Three Poles , A , C , P , carry the Stress ± σ = w² · B / v , of Square ACPC″ , To the Two Equal and Opposite Squares |COAB|, |COPB’| for Halve Area - Stress-Energy Acceleration of Gravity g ≡ ± σ , is altered Locally by changing the Principal-stress σ with an Local- uniform-Pressure → gₗ ≡ g k = g.[Force/Area] = G , i.e. The minimum Local - Energy acceleration is the known , Universal Gravitational-constant G = g k = kₑ g = kₗ σ , for Macrocosm and Microcosm , It was proved that Constant G , is the mechanism for the First-kick-Start on the Granular-Energy-monad , g , which Acts in the lightest and less-mass Particle and which is Hydrogen . The Electron- Nutation-Energy due to g , effect is the minimum frequency fₙ ≡ fᵣ = 2 , 8398447 · 10¹⁰ s⁻¹ , and which so exists in all Atoms . This Energy in Hydrogen-Cave as E-M , Conductor is the Resonance frequency between all Atoms , and because of Common Hydrogen , Bond to Molecules and all Compounds in this Cosmos . In this E-M , Conductor is stored the Work = The Nutation-Energy produced , and is called , [BH] . These [BH] are the Hands and Brain of Atoms and Compounds . The Gravitational Force F_G between Photon’s velocity vector c⃗ and an Object , is Proportional to their masses m_c and m_o and Inversely Proportional to the square of their distance d_co . This Centripetal Force F_G produces a New velocity vector c⃗₀ which is added to c⃗ vector . Their Resultant velocity vector v⃗_R forms an angle w to the c⃗ velocity vector , which is the Photons’ - Bending.

GPH-International Journal of Mathematics

GRAVITATIONAL BENDING OF PHOTONS OR GRAVITATION LENSING OF SPACE-TIME