Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests (Classical) Tests of General Relativity Sirachak Panpanich June 20, 2018 Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Gravitational redshift of light Detected in 1960 by Pound and Rebka, ∆λ agz = 2 (1) λ0 c Using gamma rays traveling upward a distance of 72 feet (the height of the physics building at Harvard). f GM GM 2 = 1 + − (2) f1 r2 r1 https://physics.stackexchange.com https://en.wikipedia.org/ Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Perihelion precession of Mercury There is discrepancy between observations and predictions. The problem was known before Einstein invented GR. 3 ∆φ = 2π + (2GM)(2π)(u + u ) (3) 4 a p Observation: 5601 arcsecs/100years Precession of equinox: 5025" + Perturbations of other planets: 532"+ https://en.wikipedia.org/ GR effect: 43" Einstein included this calculation regarding Mercury in his 1915 paper on general relativity. Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Deflection of light by the Sun Eddington observed the change in position of stars near the Sun during the total solar eclipse (May 29, 1919). 4GM α^ = (4) b (^αsun = 1:75 arcsecs) https://www.quora.com/ Newtonian gravity predicts only half of the correct value. Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Photon sphere An area or region of space where gravity is so strong that photons are forced to travel in orbits. Photon sphere (radius) rps = 3GM (5) = 1:5rs Schwarzschild radius rs = 2GM https://www.quora.com/ Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Effective potential Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Black hole shadow Light from background is bent because of gravitational lensing phenomenon, and then it is captured in photon sphere. Critical impact parameter p bcr = 3 3GM = 2:6rs (6) https://www.youtube.com/watch?v=zUyH3XhpLTo Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Shapiro time delay (radar echoes) In 1964 Irwin Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury and measure the round-trip travel time. Maximum excess time General Relativity (Hobson and Efstathiou) ∆τ ∼ 220 µs (7) Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Outline 1 Gravitational redshift of light 2 Perihelion precession of Mercury 3 Deflection of light by the Sun 4 Photon sphere 5 Effective potential 6 Black hole shadow 7 Shapiro time delay (radar echoes) 8 Modern tests Gravitational redshift of light Perihelion precession of Mercury Deflection of light by the Sun Photon sphere Effective potential Black hole shadow Shapiro time delay (radar echoes) Modern tests Modern tests Gravitational lensing by galaxies or clusters (1979) Gravitational Waves (Feb 11, 2016) Direct observation of a black hole (April 10, 2019) more... https://www.cfa.harvard.edu/castles/ https://www.ligo.caltech.edu/images https://eventhorizontelescope.org/.