Unfortunately, nature is rarely so kind. Still, under suitable conditions, qualitative and even quantitative strong-field tests of GR could be carried out.
One example is the exploration of the spacetime near black holes and neutron stars. Studies of certain kinds of accretion known as advection-dominated accretion flow (ADAF) in low-luminosity binary X-ray sources may yield the signature of the black hole event horizon . The spectrum of frequencies of quasi-periodic oscillations (QPO) from galactic black hole binaries may permit measurement of the spins of the black holes . Aspects of strong-field gravity and frame-dragging may be revealed in spectral shapes of iron fluorescence lines from the inner regions of accretion disks [336, 337]. Using sub-mm VLBI, a collaboration dubbed the Event Horizon Telescope could image our galactic center black hole Sgr A* and the black hole in M87 with horizon-scale angular resolution; observation of accretion phenomena at these angular resolutions could provide tests of the spacetime geometry very close to the black hole . Tracking of hypothetical stars whose orbits are within a fraction of a milliparsec of Sgr A* could test the black hole “ho-hair” theorem, via a direct measurement of both the angular momentum and quadrupole moment of the black hole, and a test of the requirement that . Such tests could also be carried out using pulsars, if any should be found deep in the galactic center .
Because of uncertainties in the detailed models, the results to date of studies like these are suggestive at best, but the combination of future higher-resolution observations and better modelling could lead to striking tests of strong-field predictions of GR.
For a detailed review of strong-field tests of GR using electromagnetic observations, see .
Another example is in cosmology. From a few seconds after the Big Bang until the present, the underlying physics of the universe is well understood, in terms of a standard model of a nearly spatially flat universe, 13.6 Gyr old, dominated by cold dark matter and dark energy (CDM). Some alternative theories of gravity that are qualitatively different from GR fail to produce cosmologies that meet even the minimum requirements of agreeing qualitatively with Big-Bang nucleosynthesis (BBN) or the properties of the cosmic microwave background (TEGP 13.2 ). Others, such as Brans–Dicke theory, are sufficiently close to GR (for large enough ) that they conform to all cosmological observations, given the underlying uncertainties. The generalized scalar–tensor theories and theories, however, could have small effective at early times, while evolving through the attractor mechanism to large today.
One way to test such theories is through Big-Bang nucleosynthesis, since the abundances of the light elements produced when the temperature of the universe was about 1 MeV are sensitive to the rate of expansion at that epoch, which in turn depends on the strength of interaction between geometry and the scalar field. Because the universe is radiation-dominated at that epoch, uncertainties in the amount of cold dark matter or of the cosmological constant are unimportant. The nuclear reaction rates are reasonably well understood from laboratory experiments and theory, and the number of light neutrino families (3) conforms to evidence from particle accelerators. Thus, within modest uncertainties, one can assess the quantitative difference between the BBN predictions of GR and scalar–tensor gravity under strong-field conditions and compare with observations. For recent analyses, see [350, 116, 89, 90].
In addition, many alternative theories, such as theories have been developed in order to provide an alternative to the dark energy of the standard CDM model, in particular by modifying gravity on large, cosmological scales, while preserving the conventional solar and stellar system phenomenology of GR. Since we are now in a period of what may be called “precision cosmology”, one can begin to envision trying to test alternative theories using the accumulation of data on many fronts, including the growth of large scale structure, cosmic background fluctuations, galactic rotation curves, BBN, weak lensing, baryon acoustic oscillations, etc. The “parametrized post-Friedmann” framework is one initial foray into this arena . Other approaches can be found in [15, 121, 135, 134, 454, 189].