Solar System tests of general relativity

Lecture of the course "General Relativity With Astrophysical Applications", taught by Prof. Rodrigo Nemmen (USP).

• Parametrized-Post-Newtonian metric (PPN)
• Precession of the perihelion of Mercury measurement
• Deflection of light by the Sun
• The 1919 total eclipse expedition and observations

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

https://rodrigonemmen.com/teaching/relatividade-geral-e-aplicacoes-astrofisicas/

Transcript

1. AGA0319 Rodrigo Nemmen Solar System Tests of General Relativity Astrophysical Applications of GR I
2. Comparing GR with other theories of gravity We need a way of testing GR with observations Specifically: quantify possible deviation from GR in data Standard way: parametrized-Post-Newtonian (PPN)
3. Parametrized-Post-Newtonian (PPN) framework Begin with general static, spherically symmetric metric ds2 = − A(r)(cdt)2 + B(r)dr2 + r2(dθ2 + sin2 θdϕ2) A(r) = 1 − 2GM c2r + ⋯ B(r) = 1 + ⋯ Agreement with Newton requires Define γ and β A(r) = 1 − 2GM c2r + 2(β − γ) ( GM c2r ) 2 + ⋯ B(r) = 1 + 2γ ( GM c2r ) + ⋯ If γ=1 and β=1 → recover general relativity PPN metric
4. Parametrized-Post-Newtonian (PPN) framework ds2 = − A(r)(cdt)2 + B(r)dr2 + r2(dθ2 + sin2 θdϕ2) A(r) = 1 − 2GM c2r + 2(β − γ) ( GM c2r ) 2 + ⋯ B(r) = 1 + 2γ ( GM c2r ) + ⋯ If γ=1 and β=1 → GR is correct PPN metric If γ≠1 and β≠1 → Einstein is wrong
5. Relativistic effects in the PPN metric Δϕ def = ( 1 + γ 2 ) ( 4GM c2b ) Deflection angle of light ray passing by mass M Δϕ prec = 1 3 (2 + 2γ − β) 6πGM c2a(1 − ϵ2) Precession of perihelion of planet per orbit
6. Precession of Mercury’s perihelion
7. Precession of Mercury’s perihelion GR prediction Δφprec = 43″ / century Δϕ prec = 6πG c2 M a(1 − ϵ2) 0.8 0.9 1.0 1.1 1.2 38 40 42 44 46 48 γ Δφprec (″/century)
8. Precession of Mercury’s perihelion GR prediction Δφprec = 43″ / century Observed precession = 5599.74″±0.65 / century Δϕ prec = 6πG c2 M a(1 − ϵ2) Effect Δφ (") Precession of equinoxes 5025.64 Perturbation other planets 532 Oblateness of Sun 0.03 Total 5557 Data - effects 43 γ = 1.000 ± 0.002 β = 1.000 ± 0.003 PPN parameters
9. Deflection of light by the Sun GR prediction Δφdef = 1.75″ Δϕ def = 4GM c2b https://grupos.unican.es/glendama/Historical_intro.htm
10. Deflection of light by the Sun GR prediction Δφdef = 1.75″ Δϕ def = 4GM c2b https://grupos.unican.es/glendama/Historical_intro.htm
11. Deflection of light by the Sun Δφ def = 1.75″ https://medium.com/@GatotSoedarto/how-to-show-gravity-affects-light-ee9e8dfd33af
12. Deflection of light by the Sun apparent position of stars in the sky
13. Deflection of light by the Sun apparent position of stars in the sky M
14. Illustrated London News of November 22, 1919
15. Illustrated London News of November 22, 1919
16. New York Times, 10 Nov. 1919
17. LUZES TODAS TORTAS NOS CÉUS Cientistas inquietos pelos resultados das observações do eclipse Estrelas não estão onde deveriam estar, mas ninguém precisa se preocupar TEORIA DE EINSTEIN TRIUNFA UM LIVRO PARA DEZ SÁBIOS Ninguém mais no mundo consegue compreende-lo New York Times, 10 Nov. 1919
18. Deflection of light by the Sun GR prediction Δφdef = 1.75″ γ Δφdef (″) Δϕ def = 4GM c2b 0.8 0.9 1.0 1.1 1.2 1.60 1.65 1.70 1.75 1.80 1.85 1.90 β=1 γ = 1.007 ± 0.009 β = 1.000 ± 0.003 PPN parameters