Related papers: The Bakry-\'Emery Ricci tensor: Application to mas…
We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system. We find that the tensor naturally contains essential information of the energy-momentum…
For Riemannian manifolds with a measure $(M,g, e^{-f} dvol_g)$ we prove mean curvature and volume comparison results when the $\infty$-Bakry-Emery Ricci tensor is bounded from below and $f$ is bounded or $\partial_r f$ is bounded from…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
We call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the…
For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on…
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…
We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, $\gamma_{ij} = e^{\epsilon_{ikm}\theta_m} e^{\phi_k} e^{-\epsilon_{jkn}\theta_n}$, where…
We consider the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides an alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations,…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This generalization also follows by restricting variations of the…
The Bakry-Emery Ricci tensor of a metric-measure space (M,g,e^{-f}dv_{g}) plays an important role in both geometric measure theory and the study of Hamilton's Ricci flow. Under a uniform positivity condition on this tensor and with bounded…
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor…
Since the early days of the theory of electromagnetism and of gravity the idea of space, then space-time, as a sort of physical continuum hovered the scientific community. Actually general relativity shows the strong similarity that exists…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…
The 1+3 covariant equations, embedded in an extended tetrad formalism and describing a space-time with an arbitrary energy-momentum distribution, are reconsidered. It is shown that, provided the 1+3 splitting is performed with respect to a…
The classical theory of strain in material continua is reviewed and generalized to space-time. Strain is attributed to "external" (matter/energy fields) and intrinsic sources fixing the global symmetry of the universe (defects in the…
In this contribution I intend to give a summary of the new relevant results obtained by using the general superenergy tensors. After a quick review of the definition and properties of these tensors, several of their mathematical and…
Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian)…
Charge, like mass in Newtonian mechanics, is an irreducible element of electromagnetic theory that must be introduced ab initio. Its origin is not properly a part of the theory. Fields are then defined in terms of forces on either…