Is Spacetime Non-metric?

Abstract

If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.

Six Decades of Spiral Density Wave Theory

“…From the optical study of the kinematics of stars in the solar neighborhood, Bertil Lindblad (1927) and Jan Oort (1927) deduced that the flattening of the galactic disk is due to rotation, and that this rotation occurred differentially, with the stars near the galactic center taking less time to go once around the center than the material farther out. It was natural to ask whether the same held true for external disk galaxies, and in the late 1950s to early 1970s, optical and radio astronomers discovered that, instead of being in a state of uniform rotation, ( ) = constant, the outer rotation curves of normal and barred spiral galaxies were roughly flat; that is, ( ) = constant, where is the radial distance from the rotation axis in the plane of the disk and ( ) is the angular speed of rotation (Van de Hulst et al 1957, Rubin et al 1964, H öglund & Roberts 1965, Rubin & Ford 1970, Roberts & Rots 1973.…”

Dark matter effects explanation with the torsion in the Minkowski space

“…It should be noted that axial symmetry is not impossible but implies additional restrictions on the mass distribution. Because of the importance of axial symmetry in our Universe, particularly for galaxies, we perform a more detailed investigation in the next section [26].…”

“…To preserve the consistency of the theory, we can add only point mass M b at r = 0 (dashed line in figure 1(c)). The experimental data were obtained from [26,27]. The dash-dotted lines correspond to the classical Newtonian potential.…”

String Theory Explanation of Galactic Rotation Found Using the Geodesic Constraint

“…P : because the scalar-tensor theory involves Palatini variations the underlying geometry is no longer Riemannian but rather Weyl with object of nonmetricity related to the primary dilation function A, see [4].…”

“…From a Newtonian perspective the gravitational modification which works is the replacement of the Newtonian reciprocal gravitational potential by a logarithmic potential; the spherically symmetric relativistic generalization of this [3] has one free function which in the present work is fixed by requiring that the Weyl tensor vanishes. This leaves the problem of finding which field equations the Einstein tensor obeys and both Palatini varied scalar-tensor theory [4] and the low energy limit of string theory with added potential are found to work. The usual method of approaching problems is by starting with a Lagrangian, then deriving field equations, finding solutions, and finally comparing with observations; here this is reversed: in the present case it is observation, then metric, then field equations, and finally Lagrangian.…”