This was an important early test of general relativity: the amount of light bending predicted by general relativity was confirmed by measuring the positions of stars near the Sun during a solar eclips...This was an important early test of general relativity: the amount of light bending predicted by general relativity was confirmed by measuring the positions of stars near the Sun during a solar eclipse in 1919. This effect has been observed recently by the Hubble Space Telescope in the form of gravitational lensing: the gravity of a relatively nearby galaxy will bend the light from more distant objects, producing multiple images of the distant object.
The Schrödinger equation and Maxwell’s equations treat spacetime as a stage on which particles and fields act out their roles. General relativity, however, is essentially a theory of spacetime itself....The Schrödinger equation and Maxwell’s equations treat spacetime as a stage on which particles and fields act out their roles. General relativity, however, is essentially a theory of spacetime itself. The role played by atoms or rays of light is so peripheral that by the time Einstein had derived an approximate version of the Schwarzschild metric, and used it to find the precession of Mercury’s perihelion, he still had only vague ideas of how light and matter would fit into the picture.
The covariant derivative is the derivative that under a general coordinate transformation transforms covariantly, that is, linearly via the Jacobian matrix of the coordinate transformation.
