D. K. Sen

A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold

A new scalar‐tensor theory of gravitation is formulated in a modified Riemannian manifold in which both the scalar and tensor fields have intrinsic geometrical significance. This is in contrast to the well‐known Brans‐Dicke theory where the tensor field alone is geometrized and the scalar field is alien to the geometry. The static spherically symmetric solution of the exterior field equations is worked out in detail.

A static cosmological model

A static cosmological model of the universe based onLyras modified Riemannian Geometry is proposed. The red-shift of spectral lines from extra-galactic nebulae is shown to be a consequence of an inherent geometrical property of the model independent of expansion. The model is similar to the staticEinstein model but shows a red-shift and has a finite density even without the introduction of a cosmological constant.

On Weyl and Lyra Manifolds

It is shown that Weyls geometry and an apparently similar geometry suggested by Lyra are special cases of manifolds with more general connections. The difference between the two geometries and their relationship with Riemannian geometry are clarified by giving a global formulation of Lyras geometry. Finally the outline of a field theory based on the latter geometry is given.

A correction to the Sen and Dunn gravitational field equations

It is shown that the gravitational field equations proposed by Sen and Dunn do not follow from their variational principle and that in the vacuum case the correct field equations are related to Einstein’s field equations by a conformal mapping.

Projective manifolds and projective theory of relativity

We present a global formulation of projective theories of relativity in the framework of projective manifolds, that is, manifolds based on the pseudogroup of homogeneous transformations in R5. Apart from formulating every previously considered geometric object and physical relation in an invariant manner, some new results, such as the theorem on the semidirect product structure of the invariance group of Einstein‐Maxwell equations, and theorems on topological restrictions on the underlying five‐dimensional projective manifold, etc. have been obtained. The relationship between space‐time and the auxiliary 5‐manifold is clarified and investigated in detail. A more general geometric definition of the electromagnetic field tensor and a geometric interpretation of the charge/mass ratio is given.

A Simple Derivation of the Geodesic Equations of Motion from the Matter Tensor in General Relativity Using the δ-Function.

A simple derivation of the geodesic equations of motion of a system of particles from the field equations, similar to Jordans except that the equation of continuity is used, is described. (N.W.R.)

A theoretical basis for two neutrinos

SummaryIt is shown how an antisymmetric tensor of rank two can be split up in a covariant manner to give rise to two 2-component Weyl’s equations for a neutrino. The photon may then be regarded as a combination of two such neutrinos.RiassuntoSi mostra come un tensore antisimmetrico di ordine due può essere diviso in modo covariante dando origine per un neutrino a due equazioni di Weyl a due componenti. Il fotone può quindi essere considerato una combinazione di due di questi neutrini.

Left- and right-handed neutrinos and Baryon-Lepton masses

The self-dual and anti-self-dual parts of the electromagnetic field tensor satisfying the vacuum Maxwell equations are shown to be related in a covariant manner to a left-handed and right-handed two-component Weyl neutrino νL and νR, respectively. A simple quantum mechanical analysis of a composite νL−νR system with a certain interaction shows that such a model can exhibit a two-fold branching and defect in the total energy of the system, which could then be interpreted as Baryon and Lepton mass formation.

Lorentz action on the space of relative velocities and relativity on a three‐manifold

The space of relative velocities in special relativity has a three‐dimensional hyperbolic structure. This provides not only a geometric interpretation of the Einstein velocity addition law, but also a purely three‐dimensional reformulation of both special and general relativity on a three‐manifold whose tangent bundle is endowed with a hyperbolic distance function on each fiber. Here the basic concepts are that of local physical observers and local time in terms of nonsingular vector fields and their local flows. The hyperbolic structure on the tangent space enables one to define a relative velocity function between two physical observers, as well as space and time measurements and inertial physical observers. It is possible to rederive Lorentz time dilation and gravitational and cosmological redshifts and reformulate Maxwell (or Yang–Mills) equations in a purely three‐dimensional framework instead of the traditional four‐dimensional space‐time approach.

A class of singular space-times

We present a singularity theorem for a certain class of space-times. The theorem contains an ‘energy’ condition stronger than Hawkings, but does not require any condition about Cauchy surfaces, normals or time orientability.