Genesis of general relativity — A concise exposition

Abstract

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, Eötvös experiment, Newcomb's improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity: gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in 4-dimantional spacetime and derived the 4-dimensional electromagnetic stress-energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended the Minkowski's method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911-13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a "tensor" theory of gravity (the "Entwurf" theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress-energy tensor (1915); Einstein, based on 1913 Besso-Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stressenergy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of general relativity was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), De Sitter solution (1917), Lense-Thirring effect (1918).

VLBI with SKA: Possible Arrays and Astrometric Science

“…If the Sun acts as a lens, the deflection angle of light 1°away from the Sun (which is favorable for successful observations; see Titov et al 2018) can reach ∼500 mas, and the number of sources within 1°is ∼63. Therefore, the measurement precision of γ with 10 epochs of observations is expected to reach ∼10 −8 , achieving the advanced level in the next few decades (see chapter 8 in Ni 2017). In such a case, using measurements of light deflection caused by the gravitational fields of celestial bodies in the solar system via SKA-VLBI may allow astronomers to test the (noninertial) motion and multipole moment effect of celestial bodies, and test and develop secondorder or higher PPN formalisms and/or different metric theories of gravity (e.g., Damour & Nordtvedt 1993;Kopeikin & Makarov 2007;Fomalont et al 2009;Li et al 2022c).…”

“…where G is the gravitational constant, M e and R e are the solar mass and radius, respectively, a and e are the semimajor axis and the eccentricity of the orbit of Mercury, respectively, c is the speed of light, and J 2 , the solar quadrupole moment, is ∼10 −7 (see chapter 8 in Ni 2017). The second term is smaller than the first term by a factor of ∼6 × 10 −4 , and the precision of J 2 can currently reach ∼10 −2 (e.g., Pitjeva et al 2022).…”

“…As mentioned in Section 3.3.3, SKA-VLBI will likely play an important role in improving the precision of ICRF and planetary ephemerides. In fact, while fitting ephemerides, combined with orbital data of (artificial) satellites, GR can also be tested (such as the PPN parameters γ and β and the solar quadrupole moment, J 2 ); it may even be possible to obtain the time derivative of Newton's gravitational constant (e.g., Anderson et al 2002;Fienga et al 2011;Pitjeva 2013;Verma et al 2014) and whether dark matter is present in the solar system (e.g., ; for more details see the review in chapter 8 in Ni (2017).…”