(Classical) Tests of General Relativity

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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

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)

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)

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)

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)

Eddington observed the change in position of stars near the Sun during the total solar eclipse (May 29, 1919).

4GM αˆ = (4) b

(ˆαsun = 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)

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)

Light from background is bent because of gravitational lensing phenomenon, and then it is captured in photon sphere.

Critical impact parameter √ 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)

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)

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/