Bolton et al. (2007) have derived a mass-based fundamental plane using photometric and spectroscopic observations of 36 strong gravitational lenses. The lensing allows a direct determination of the mass-surface density and so avoids the usual dependence on mass-to-light ratio. We consider this same sample in the context of modified Newtonian dynamics (MOND) and demonstrate that the observed mass-based fundamental plane coincides with the MOND fundamental plane determined previously for a set of high-order polytropic spheres chosen to match the observed range of effective radii and velocity dispersions in elliptical galaxies. Moreover, the observed projected mass within one-half an effective radius is consistent with the mass in visible stars plus a small additional component of ``phantom dark matter'' resulting from the MOND contribution to photon deflection.
Clusters of galaxies offer a robust test bed for probing the nature of dark matter that is insensitive to the assumption of the gravity theories. Both Modified Newtonian Dynamics (MOND) and General Relativity (GR) would require similar amounts of non-baryonic matter in clusters as MOND boosts the gravity only mildly on cluster scales. Gravitational lensing allows us to estimate the enclosed mass in clusters on small (20 - 50 kpc) and large (several 100 kpc) scales independent of the assumptions of equilibrium. Here we show for the first time that a combination of strong and weak gravitational …
Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of…
We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specificly TeVeS (Bekenstein 2004), a theory which is consistent with fundamental relativistic principles and the phenomenology of MOdified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we derive analytically the deflection angle for the point lens and the Hernquist galaxy profile, and fit galaxy-quasar lenses in the CASTLES sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios…
We study the amplitude of the weak gravitational lensing signal as a function of stellar mass around a sample of relatively isolated galaxies. This selection of lenses simplifies the interpretation of the observations, which consist of data from the Red- sequence Cluster Survey and the Sloan Digital Sky Survey. We find that the amplitude of the lensing signal as a function of stellar mass is well described by a power law with a best fit slope α= 0.74 \pm 0.08. This result is inconsistent with Modified Newtonian Dynamics, which predicts α= 0.5 (we find α> 0.5 with 99.7% confidence). As a relate…
A proper test of Modified Newtonian Dynamics (MOND) in systems of non-trivial geometries depends on modelling subtle differences in several versions of its postulated theories. This is especially important for lensing and dynamics of barely virialised galaxy clusters with typical gravity of scale $\sim a_0 \sim 1Å{\rm s}^{-2}$. The original MOND formula, the classical single field modification of the Poisson equation, and the multi-field general relativistic theory of Bekenstein (TeVeS) all lead to different predictions as we stray from spherical symmetry. In this paper, we study a class of an…
Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes no definite predictions about gravitational lensing. The most obvious form that MONDian lensing might take is that photons experience twice the deflection of massive particles moving at the speed of light, as in general relativity (GR). In such a theory there is no general thin-lens approximation (although one can be made for spherically-symmetric deflector…
Since Bekenstein's (2004) creation of his Tensor-Vector-Scalar theory (TeVeS), the Modified Newtonian dynamics (MOND) paradigm has been redeemed from the embarrassment of lacking a relativistic version. One primary success of TeVeS is that it provides an enhancement of gravitational lensing, which could not be achieved by other MONDian theories. Following Bekenstein's work, we investigate the phenomena of gravitational lensing including deflection angles, lens equations and time delay. We find that the deflection angle would maintain its value while the distance of closest approach vary in the…
Modified Newtonian Dynamics (MOND) and its relativistic version - TeVeS offer us an alternative perspective to understand the universe without the demand of the elusive cold dark matter. This MONDian paradigm is not only competitive with the conventional CDM in a large range of scales, but also even more successful in the galactic scale. Recently, by studying 6 lensing systems, Ferreras et al. (2008) claimed that MOND still needs dark matter even in galactic scales. When we study the same systems, however, we yield an opposite conclusion. In this contribution, we report our result and conclude…
We present the results of N-body simulations of dissipationless galaxy merging in Modified Newtonian Dynamics (MOND). For comparison, we also studied Newtonian merging between galaxies embedded in dark matter halos, with internal dynamics equivalent to the MOND systems. We found that the merging timescales are significantly longer in MOND than in Newtonian gravity with dark matter, suggesting that observational evidence of rapid merging could be difficult to explain in MOND. However, when two galaxies eventually merge, the MOND merging end-product is hardly distinguishable from the final stell…
I estimate MOND M/L values for nine galaxy groups that were recently studied by Tully et al.. Instead of the large M/L values that they find with Newtonian dynamics (up to 1200 solar units) the MOND estimates cluster around 1 solar unit. Tully et al. find a systematic and significant difference between the M/L values of groups that do not contain luminous galaxies and those that do: Dwarfs-only groups have larger M/L values (by a factor of about 5). The MOND M/L values do not show this trend; the Newtonian disparity is traced back to the dwarfs-only groups having systematically smaller intrins…
To further test MOdified Newtonian Dynamics (MOND) on galactic scales -- originally proposed to explain the rotation curves of disk galaxies without dark matter -- we study a sample of six strong gravitational lensing early-type galaxies from the CASTLES database. To determine whether dark matter is present in these galaxies, we compare the total mass (from lensing) with the stellar mass content (from a comparison of photometry and stellar population synthesis). We find that strong gravitational lensing on galactic scales requires a significant amount of dark matter, even within MOND. On such …
We study weak gravitational lensing of galaxy clusters in terms of the MOND (MOdified Newtonian Dynamics) theory. We calculate shears and convergences of background galaxies for three clusters (A1689, CL0024+1654, CL1358+6245) and the mean profile of 42 SDSS (Sloan Digital Sky Survey) clusters and compare them with observational data. The mass profile is modeled as a sum of X-ray gas, galaxies and dark halo. For the shear as a function of the angular radius, MOND predicts a shallower slope than the data irrespective of the critical acceleration parameter $g_0$. The dark halo is necessary to ex…
We propose a technique to test the idea that non-standard dynamics, rather than dark matter halos, might be responsible for the observed rotation curves of spiral galaxies. In the absence of non-luminous matter, a galactic disk's rotational velocity and its vertical velocity dispersion can be used jointly to test the self-consistency of the galaxy's dynamics. A specific illustrative example, using recent measurements of the disk kinematics of M33, shows this to be a promising approach to assess the viability of Modified Newtonian Dynamics (MOND).
Intercluster filaments negligibly contribute to the weak lensing signal in general relativity (GR), $γ_{N}\sim 10^{-4}-10^{-3}$. In the context of relativistic modified Newtonian dynamics (MOND) introduced by Bekenstein, however, a single filament inclined by $\approx 45^\circ$ from the line of sight can cause substantial distortion of background sources pointing towards the filament's axis ($κ=γ=(1-A^{-1})/2\sim 0.01$); this is rigorous for infinitely long uniform filaments, but also qualitatively true for short filaments ($\sim 30$Mpc), and even in regions where the projected matter density …
We study the orbits in the MOND theory within a dwarf galaxy of mass Md at a distance of ~100kpc from a neighboring galaxy of mass Mg, such as ours. It is assumed that a second mass m<<Md is gravitationally bound to Md by a previously calculated potential for the MOND theory. This potential is obtained for a free falling mass Md in a constant external gravitational acceleration field. The numerical technique of surfaces of section is used to study the stability of the phase-space orbits in the dwarf galaxy. Equatorial orbits with sufficiently small eccentricities e<0.65 are found to be stable …
The outskirts of galaxies are a very good laboratory for testing the nature of the gravitational field at low accelerations. By assuming that the neutral hydrogen gas is in hydrostatic equilibrium in the gravitational potential of the host galaxy, the observed flaring of the gas layer can be used to test modified gravities. For the first time we construct a simple framework to derive the scaleheight of the neutral hydrogen gas disc in the MOND scenario and apply this to the Milky Way. It is shown that using a constant gas velocity dispersion of ~9 km/s, MOND is able to give a very good fit to …
The tight correlation between galaxy bulges and their central black hole masses likely emerges in a phase of rapid collapse and starburst at high redshift, due to the balance of gravity on gas with the feedback force from starbursts and the wind from the black hole; the average gravity on per unit mass of gas is ~ 2 x 10^-10 m/sec^2 during the star burst phase. This level of gravity could come from the real r^{-1} cusps of Cold Dark Matter (CDM) halos, but the predicted gravity would have a large scatter due to dependence on cosmological parameters and formation histories. Better agreement is …
We revisit the application of Modified Newtonian Dynamics (MOND) to galaxy clusters. We confront the high quality X-ray data for eight clusters of galaxies observed by the \xmm satellite with the predictions of MOND. We obtain a ratio of the MOND dynamical mass to the baryonic mass of $M_m/M_b=4.94\pm 0.50$ in the outer parts (i.e $r\sim 0.5$ ~ R$_{vir}$), in the concordance cosmological model where the predicted asymptotic ratio, if any baryons are present, is $7.7^{+1.4}_{-1.1}$ (at $r\geq 0.3$ ~ R$_{vir}$). We confirm that the MOND paradigm lowers the discrepancy between the binding mass an…
Central galaxies in galaxy clusters may be key discriminants in the competition between the cold dark matter (CDM) paradigm and modified Newtonian dynamics (MOND). We investigate the dark halo of NGC 1399, the central galaxy of the Fornax cluster, out to a galactocentric distance of 80 kpc. The data base consists of 656 radial velocities of globular clusters obtained with MXU/VLT and GMOS/Gemini, which is the largest sample so far for any galaxy. We performed a Jeans analysis for a non-rotating isotropic model. An NFW halo with the parameters r_s = 50 kpc and rho_s = 0.0065 M_sun/pc^3 provides…
We compare orbits in a thin axisymmetric disc potential in MOND to those in a thin disc plus near-spherical dark matter halo predicted by a $Λ$CDM cosmology. Remarkably, the amount of orbital precession in MOND is nearly identical to that which occurs in a mildly oblate CDM Galactic halo (potential flattening q=0.9), consistent with recent constraints from the Sagittarius stream. Since very flattened mass distributions in MOND produce rounder potentials than in standard Newtonian mechanics, we show that it will be very difficult to use the tidal debris from streams to distinguish between a MON…
MOdified Newtonian Dynamics (MOND) is evolving from an empirical to a decent theory respecting fundamental physics after Bekenstein (2004) showed that lensing and Hubble expansion can be modeled rigourously in a Modified Relativity. The degeneracy of MOND with Dark Matter can be broken if we examine the non-linear MONDian Poisson's equation in detail. Here we study the effect of tides for a binary stellar system or a baryonic satellite-host galaxy system. We show that the Roche lobe is more squashed than the Newtonian case due to the anisotropic dilation effect in deep-MOND. We prove analytica…
The phenomena customly called Dark Matter or Modified Newtonian Dynamics (MOND) have been argued by Bekenstein (2004) to be the consequences of a covariant scalar field, controlled by a free function (related to the MOND interpolating function) in its Lagrangian density. In the context of this relativistic MOND theory (TeVeS), we examine critically the interpolating function in the transition zone between weak and strong gravity. Bekenstein's toy model produces too gradually varying functions and fits rotation curves less well than the standard MOND interpolating function. However, the latter …
I estimate Modified-Dynamics (MOND), median M/L values for recently published catalogues of galaxy groups. While the median, Newtonian M/L values quoted for these catalogues are 110-200 solar units, the corresponding values for MOND are less than 10 solar units.
I start with a brief introduction to MOND phenomenology and its possible roots in cosmology--a notion that may turn out to be the most far reaching aspect of MOND. Next I discuss the implications of MOND for the dark matter (DM) doctrine: MOND's successes imply that baryons determine everything. For DM this would mean that the puny tail of leftover baryons in galaxies wags the hefty DM dog. This has to occur in many intricate ways, and despite the haphazard construction history of galaxies--a very tall order. I then concentrate on galaxy clusters in light of MOND, which still requires some yet…
The LCDM model is the most commonly admitted to describe our Universe. In spite of a great success with regard to the large scale structure formation, some problems are still unresolved at galactic scales. Alternative scenarios have to be explored such as modified gravity. We have developed an N-body code able to solve in a self consistent way the galactic dynamics in MOND. The first version of the code consists in solving the modified Poisson equation on a uniform Cartesian grid to derive the gravitational force on each particle. With it, we study the evolution of isolated galaxies, like the …
We have recently discovered that the modified dynamics (MOND) implies some universal upper bound on the acceleration that can be contributed by a `dark halo'--assumed in a Newtonian analysis to account for the effects of MOND. Not surprisingly, the limit is of the order of the acceleration constant of the theory. This can be contrasted directly with the results of structure-formation simulations. The new limit is substantial and different from earlier MOND acceleration limits (discussed in connection with the MOND explanation of the Freeman law for galaxy disks, and the Fish law for elliptical…
In previous work (astro-ph/0306228) we have established that a particular quasi-classical theoretical viewpoint about the nature of gravitation in galaxy discs provides extremely high concordance (comparable with MOND) with the observed dynamics in optical discs. In this paper, we consider the possibility that the optical disc and the flat radio disc represent distinct dynamical regions which are inherently described by distinct phases of the same over-arching theory of which the quasi-classical theory is but one phase. This is a defining moment for the theory under discussion since the only n…
It is shown that the MOdified Newtonian Dynamics (MOND) explains the tilt of the fundamental plane of elliptical galaxies without the need of non-baryonic dark matter. Results found for elliptical galaxies extends to globular clusters and galaxy clusters, showing that MOND agrees with observations over 7 order of magnitude in acceleration.
We summarize the status of Modified Newtonian Dynamics (MOND) in galaxy clusters. The observed acceleration is typically larger than the acceleration threshold of MOND in the central regions, implying that some dark matter is necessary to explain the mass discrepancy there. A plausible resolution of this issue is that the unseen mass in MOND is in the form of ordinary neutrinos with masses just below the experimentally detectable limit. In particular, we show that the lensing mass reconstructions of the clusters 1E0657-56 (the bullet cluster) and Cl0024+17 (the ring) do not pose a new challeng…
No more salient issue exists in contemporary astrophysics and cosmology than that of the elusive "dark matter". For many years already Milgrom's paradigm of modified Newtonian dynamics (MOND) has provided an alternative way to interpret observations without appeal to invisible dark matter. MOND had been successful in elucidating economically the dynamics of disk galaxies of all scales, while doing less well for clusters of galaxies; in its original form it could not address gravitational lensing or cosmology. After reviewing some of the evidence in favor of MOND, I recollect the development of…
Using the Tuorla-Heidelberg model for the mass distribution of the Milky Way, I determine the rotation curve predicted by MOND. The result is in good agreement with the observed terminal velocities interior to the solar radius and with estimates of the Galaxy's rotation curve exterior thereto. There are no fit parameters: given the mass distribution, MOND provides a good match to the rotation curve. The Tuorla-Heidelberg model does allow for a variety of exponential scale lengths; MOND prefers short scale lengths in the range 2.0 to 2.5 kpc. The favored value of scale length depends somewhat o…
We use a one dimensional hydrodynamical code to study the evolution of spherically symmetric perturbations in the framework of Modified Newtonian Dynamics (MOND). The code evolves spherical gaseous shells in an expanding Universe by employing a MOND-type relationship between the fluctuations in the density field and the gravitational force, $g$. We focus on the evolution of initial density perturbations of the form $δ_{i}\sim r_{i}^{-s}$ for $0<s<3$. A shell is initially cold and remains so until it encounters the shock formed by the earlier collapse of shells nearer to the centre. During the …
We develop a new method to predict the density associated with weak lensing maps of (un)relaxed clusters in a range of theories interpolating between GR and MOND (General Relativity and Modified Newtonian Dynamics). We apply it to fit the lensing map of the bullet merging cluster 1E0657-56, in order to constrain more robustly the nature and amount of collisionless matter in clusters {\it beyond} the usual assumption of spherical equilibrium (Pointecouteau & Silk 2005) and the validity of GR on cluster scales (Clowe et al. 2006). Strengthening the proposal of previous authors we show that the b…
Dark Matter (DM) theories and mass-tracing-light theories like MOND are by construction nearly degenerate on galactic scales, but not when it comes to the predicted shapes of Roche Lobes of a two-body system (e.g., a globular cluster orbiting a host galaxy). We show that the flattening of the Roche lobe is sensitive to the function mu(g) in modification of the law of gravity. We generalise the analytical results obtained in the deep-MOND limit by Zhao (2005, astro-ph/0511713 and astro-ph/0512425), and consider a binary in the framework of a MOND-like gravity modification function mu(g) or a ge…
The 'dark galaxy' VIRGOHI21 seems to be composed of an unusually high proportion of darkmatter and is situated in a strong external gravitational field. As such it offers a rare test for theories of modified dynamics. If the system is bound then its dynamics are inconsistent with those predicted by theMOND theory.
We compute the Milky Way potential in different cold dark matter (CDM) based models, and compare these with the modified Newtonian dynamics (MOND) framework. We calculate the axis ratio of the potential in various models, and find that isopotentials are less spherical in MOND than in CDM potentials. As an application of these models, we predict the escape velocity as a function of the position in the Galaxy. This could be useful in comparing with future data from planned or already-underway kinematic surveys (RAVE, SDSS, SEGUE, SIM, GAIA or the hypervelocity stars survey). In addition, the pre…
MOND-- modified Newtonian dynamics-- may be viewed as an algorithm for calculating the distribution of force in an astronomical object from the observed distribution of baryonic matter. The fact that it works for galaxies is quite problematic for Cold Dark Matter. Moreover, MOND explains or subsumes systematic aspects of galaxy photometry and kinematics-- aspects that CDM does not address or gets wrong. I will present evidence here in support of these assertions and claim that this is effectively a falsification of dark matter that is dynamically important on the scale of galaxies.
We present interpretations of the line-of-sight velocity distribution of stars in the Draco dwarf spheroidal galaxy in terms of CDM and MOND assuming constant mass-to-light ratio and anisotropy. We estimate the two parameters by fitting the line-of-sight velocity dispersion and kurtosis profiles for stellar samples differing by a number of stars rejected as interlopers. The results of the fitting procedure for CDM, high mass-to-light ratio (131-141 solar units in V-band) and weakly tangential orbits, are similar for different samples, but the quality of the fit is much worse when fewer interlo…
Context: Regarding the significant interest in both dark matter and the application of MOND to early-type galaxies, we investigate the MOND theory by comparing its predictions, for models of constant mass-to-light ratio, with observational data of the early-type galaxy NGC 4649. Aims: We study whether measurements for NGC 3379 and NGC 1399 are typical of early-type systems and we test the assumption of a Newtonian constant M/L ratio underlying most of the published models. Methods: We employ the globular clusters of NGC 4649 as a mass tracer. The Jeans equation is calculated for both MOND and …
We present MOND (Modified Newtonian Dynamics) fits to 15 rotation curves of LSB galaxies. Good fits are readily found, although for a few galaxies minor adjustments to the inclination are needed. Reasonable values for the stellar mass-to-light ratios are found, as well as an approximately constant value for the total (gas and stars) mass-to-light ratio. We show that the LSB galaxies investigated here lie on the one, unique Tully-Fisher relation, as predicted by MOND. The scatter on the Tully-Fisher relation can be completely explained by the observed scatter in the total mass-to-light ratio. W…
A sample of 197 X-ray emitting clusters of galaxies is considered in the context of Milgrom's modified Newtonian dynamics (MOND). It is shown that the gas mass, extrapolated via an assumed $β$ model to a fixed radius of 3 Mpc, is correlated with the gas temperature as predicted by MOND ($M_g \propto T^2$). The observed temperatures are generally consistent with the inferred mass of hot gas; no substantial quantity of additional unseen matter is required in the context of MOND. However, modified dynamics cannot resolve the strong lensing discrepancy in those clusters where this phenomenon occur…
We present a weak lensing mass reconstruction of the interacting cluster 1E0657-558 in which we detect both the main cluster and a sub-cluster. The sub-cluster is identified as a smaller cluster which has just undergone initial in-fall and pass-through of the primary cluster, and has been previously identified in both optical surveys and X-ray studies. The X-ray gas has been separated from the galaxies by ram-pressure stripping during the pass-through. The detected mass peak is located between the X-ray peak and galaxy concentration, although the position is consistent with the galaxy centroid…
The competition between CDM and MOND to account for the `missing mass' phenomena is asymmetric. MOND has clearly demonstrated that a characteristic acceleration $a_0$ underlies the data and understanding what gives rise to $a_0$ is an important task. The reason for MOND's success may lie in either the details of galaxy formation, or an advance in fundamental physics that reduces to MOND in a suitable limit. CDM has enjoyed great success on large scales. The theory cannot be definitively tested on small scales until galaxy formation has been understood because baryons either are, or possibly ha…
We describe some results obtained with N-MODY, a code for N-body simulations of collisionless stellar systems in modified Newtonian dynamics (MOND). We found that a few fundamental dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter. In particular, violent relaxation, phase mixing and galaxy merging take significantly longer in MOND than in Newtonian gravity, while dynamical friction is more effective in a MOND system than in an equivalent Newtonian system with dark matter.
Here we present results from a maximum likelihood analysis of galaxy-galaxy weak lensing effects as measured in a 12.5' x 12.5' field obtained at the Nordic Optical Telescope, on La Palma, Spain. The analysis incorporates photometric redshifts and gives circular velocities consistent with previous weak lensing work.
If a single sterile neutrino exists such that $m_{ν_s}\sim11eV$, it can serendipitously solve all outstanding issues of the Modified Newtonian Dynamics. With it one can explain the dark matter of galaxy clusters without influencing individual galaxies, match the angular power spectrum of the cosmic microwave background and potentially fit the matter power spectrum. This model is flat with $Ω_{ν_s}\sim0.23$ and the usual baryonic and dark energy components, thus the Universe has the same expansion history as the $\lcdm$ model and only differs at the galactic scale where the Modified Dynamics ou…
I consider in light of MOND the three debris galaxies discussed recently by Bournaud et al.. These exhibit mass discrepancies of a factor of a few within several scale lengths of the visible galaxy, which, arguably, flies in the face of the cold dark matter paradigm. I show here that the rotational velocities predicted by MOND agree well with the observed velocities for each of the three galaxies, with only the observed baryonic matter as the source of gravity. There is thus no need to invoke a new form of baryonic, yet-undetected matter that dominates the disc of spiral galaxies, as advocated…
I present an overview of strong and weak gravitational lensing by galaxy clusters. After briefly introducing the principles of gravitational lensing, I discuss the main lessons learned from lensing on the mass distribution in clusters and their relation to cosmology.
The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic. More precisely, I will focus on : (i) galaxy scale substructures, using weak galaxy-galaxy lensing in order to study how does the environment shape their properties; (ii) the mass profile of Abell~1689 as probed combining strong and weak lensing; (iii) the slope of the inner dark matter distribution in Abell~1703 as measured by strong lensing. The lensing resul…
We study a class of nonlocal, but causal, covariant and conserved field equations for the metric. Although nonlocal, these equations do not seem to possess extra graviton solutions in weak field perturbation theory. Indeed, the equations reduce to those of general relativity when the Ricci scalar vanishes throughout spacetime. When a static matter source is present we show how these equations can be adjusted to reproduce Milgrom's Modified Newtonian Dynamics in the weak field regime, while reducing to general relativity for strong fields. We compute the angular deflection of light in the weak …
The Modified dynamics (MOND) has been propounded as an alternative to Dark matter. It imputes the mass discrepancy in galaxy systems to failure of standard dynamics in the limit of small accelerations. After a brief description of the MOND tenets, I discuss how its predictions now compare with the data. I put special emphasis on rotation-curve analysis--whence comes the most clear-cut support for MOND, and on the cores of rich x-ray clusters, where MOND does not yet explain away the mass discrepancy. I then outline the MOND program, especially work still left to do. This is followed by general…
MOND, invented by Milgrom, is a phenomenological scheme whose basic premise is that the visible matter distribution in a galaxy or cluster of galaxies alone determines its dynamics. MOND fits many observations surprisingly well. Could it be that there is no dark matter in these systems and we witness rather a violation of Newton's universal gravity law ? If so, Einstein's general relativity would also be violated. For long conceptual problems have prevented construction of a consistent relativistic substitute which does not obviously run afoul of the facts. Here I sketch TeVeS, a tensor-vector…
