TeVeS/MOND is in harmony with gravitational redshifts in galaxy clusters

Wojtak, Hansen & Hjorth have recently claimed to confirm general relativity (GR) and to rule out the tensor-vector-scalar (TeVeS) gravitational theory based on an analysis of the gravitational redshifts of galaxies in 7800 clusters. However, their ubiquitous modelling of the sources of cluster gravitational fields with Navarro-Frenk-White mass profiles is neither empirically justified out to the necessary radii in clusters, nor germane in the case of TeVeS. Using MONDian (where MOND stands for MOdified Newtonian Dynamics) isothermal sphere models consistently constructed within MOND (equivalent to TeVeS models), we can fit the determined redshifts no worse than does GR with dark haloes. Moreover, Wojtak, Hansen & Hjorth have inappropriately used the simple MOND interpolating function for the mu function of the scalar field of TeVeS; the consequent MOND effective interpolating function turns out to enhance the gravitational potential, and so contributes to the discrepancy which forms the basis of their claims.