Nonlocal metric realizations of MOND

A Nonlocal Metric Formulation of MOND

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 c...

Optimal and Hereditarily Optimal Realizations of Metric Spaces

Searching for realizations of finite metric spaces in tight spans

An important problem that commonly arises in areas such as internet trafficflow analysis, phylogenetics and electrical circuit design, is to find a representation of any given metric D on a finite set by an edge-weighted graph, such that the total edge length of the graph is minimum over all such graphs. Such a graph is called an optimal realization and finding such realizations is known to be ...

Mond and Cosmology

I review various ideas on MOND cosmology and structure formation beginning with non-relativistic models in analogy with Newtonian cosmology. I discuss relativistic MOND cosmology in the context of Bekenstein’s theory and propose an alternative biscalar effective theory of MOND in which the acceleration parameter, a0 is identified with the cosmic time derivative of a matter coupling scalar field...

The MOND Fundamental Plane

Modified Newtonian dynamics (MOND) has been shown to be able to fit spiral galaxy rotation curves as well as giving a theoretical foundation for empirically determined scaling relations, such as the Tully-Fisher law, without the need for a dark matter halo. As a complementary analysis, one should investigate whether MOND can also reproduce the dynamics of early-type galaxies (ETGs) without dark...