Tensor–vector–scalar gravity

MOND and requiring consistency between the near horizon geometry of a black hole in TeVeS and that of the Einstein theory, as observed by the Event Horizon Telescope leads to K=-30 + \frac{72 \pi}{k}. So the coupling constants read: :K= 3(\pm\sqrt{29}-5), \qquad k = 6\pi (\pm \sqrt{29}-5) The function F in TeVeS is unspecified. TeVeS also introduces a "physical metric" in the form :{\hat g}^{\mu\nu}=e^{2\phi}g^{\mu\nu}-2u^\alpha u^\beta\sinh(2\phi). The action of ordinary matter is defined using the physical metric: :S_m=\int{\mathcal L} \left ({\hat g}_{\mu\nu},f^\alpha,f^\alpha_{|\mu},\ldots \right)\sqrt{-{\hat g}}d^4x, where covariant derivatives with respect to {\hat g}_{\mu\nu} are denoted by |. TeVeS solves problems associated with earlier attempts to generalize MOND, such as superluminal propagation. In his paper, Bekenstein also investigated the consequences of TeVeS in relation to gravitational lensing and cosmology. == Problems and criticisms ==

In addition to its ability to account for the flat rotation curves of galaxies (which is what MOND was originally designed to address), TeVeS is claimed to be consistent with a range of other phenomena, such as gravitational lensing and cosmological observations. However, Seifert shows that with Bekenstein's proposed parameters, a TeVeS star is highly unstable, on the scale of approximately 106 seconds (two weeks). The ability of the theory to simultaneously account for galactic dynamics and lensing is also challenged. A possible resolution may be in the form of massive (around 2 eV) neutrinos. A quantity E_G probing general relativity (GR) on large scales (a hundred billion times the size of the Solar System) for the first time has been measured with data from the Sloan Digital Sky Survey to be E_G=0.392\pm{0.065} (~16%) consistent with GR, GR plus Lambda CDM and the extended form of GR known as f(R) theory, but ruling out a particular TeVeS model predicting E_G=0.22. This estimate should improve to ~1% with the next generation of sky surveys and may put tighter constraints on the parameter space of all modified gravity theories. TeVeS appears inconsistent with recent measurements made by LIGO of gravitational waves. ==See also==