arXiv subjects

Shlomo Barak

Publications and source records attributed to Shlomo Barak.

5 recordsLinked to original sources

arXiv2025

Geometry of Deformed Cellular Spaces

We present an adaptive geometry in which the yardstick co-deforms with space itself, formulated on cellular spaces where length is a count: distances are shortest cell-crossing counts. No cell shape, angles, or embedding are assumed; the framework is deliberately micro-agnostic. Curvature and deformation are inferred operationally by comparing a measured radius to a radius reconstructed from boundary/area/volume counts; the linear dimension of a cell serves as the single universal unit of length, yielding unified small-ball/small-sphere estimators in 2D/3D/4D. We prove that the count metric on locally finite complexes is geodesic, show flatness on uniform lattices, and establish stability of distances and curvature estimators under small local perturbations. As a bridge to the smooth setting, a line-density field induces a conformal metric $g = e^{2u} g_0$ that reproduces the same operational quantities. We outline a Ricci-like construction from directional slices and give a spherically symmetric illustrative example consistent with Schwarzschild-type spatial behavior. Overall, the model provides an intrinsic, micro-agnostic calculus linking discrete measurements to continuum notions with guarantees, including Gromov--Hausdorff control under mild regularity assumptions.

math.GM↗

arXiv2010

A Universe without Dark Energy and Dark Matter

The universe has evolved to be a filamentary web of galaxies and large inter-galactic zones of space without matter. The Euclidian nature of the universe indicates that it is not a 3D manifold within space with an extra spatial dimension. This justifies our assumption that the FRW space-time evolves in the inter-galactic zones like separate FRW universes. Thus we do not necessarily have to consider the entirety of the universe. Our assumption enables us to prove that: -In the current epoch, space in the intergalactic zones expands at a constant rate. -In and around galaxies, space expansion is inhibited. With these results, and an extended Gauss Theorem for a deformed space, we show that there is no need for the hypothetical Dark Energy (DE) and Dark Matter (DM) to explain phenomena attributed to them.

astro-ph.CO↗

arXiv2009

Cosmology and Astrophysics without Dark Energy and Dark Matter

We show that there is no need for the hypothetical Dark Energy (DE) and Dark Matter (DM) to explain phenomena attributed to them. In contrast to the consensus of the last decade, we show that the time derivative of the cosmological scale factor, is a constant. We derive H(z), the Hubble parameter, as a function of the redshift, z. Based on H(z), we derive a curve of the Distance Modulus versus log(z). This curve fits data from supernovae observations, without any free parameters. This fit is as good as that obtained by current cosmology, which needs the free parameters Omega_M and Omega_Lambda. We obtain these results by using the hitherto un-noticed fact that the global gravitational energy density in our Hubble Sphere (HS) is equal to the Cosmological Microwave Background (CMB) energy density. We derive the dynamic and kinematic relations that govern the motions of celestial bodies in and around galaxies. This derivation does not require any gravitating matter beyond the observed baryonic matter. The theoretical Rotation Curves (RC), resulting from these relations, fit observed RCs. We obtain these results by examining the interplay between the local gravitational energy density, around a galaxy, and the CMB energy density. This interplay causes the inhomogeneous and anisotropic space expansion around a galaxy.

astro-ph.CO↗

arXiv2008

On Dark Energy and Dark Matter (Part I)

Phenomena currently attributed to Dark Energy (DE) and Dark Matter (DM) are merely a result of the interplay between gravitational energy density, generated by the contraction of space by matter, and the energy density of the Cosmological Microwave Background (CMB), which causes space dilation. In the universe, globally, the gravitational energy density equals the CMB energy density. This leads to the derivation of the Hubble parameter, H, as a function of the scale factor, a, the time, t, the redshift, z, and to the calculation of its present value. It also leads to a new understanding of the cosmological redshift and the Euclidian nature of the universe. From H(t) we conclude that the time derivative of a is constant. This is in contrast to the consensus of the last decade. This result is supported by the fit of our theoretically derived flux from supernovae (SN) as a function of z, with observation. This flux is derived based on our H(z) that determines DL, the Luminosity Distance. We obtain this fit without any free parameters, whereas in current cosmology this fit is obtained by using the dependent free parameters Omega_M and Omega_Lambda.

astro-ph↗

arXiv2008

On Dark Energy and Dark Matter (Part II)

Phenomena currently attributed to Dark Matter (DM) and Dark Energy (DE) are merely a result of the interplay between gravitational energy density, caused by the contraction of space by matter, and space dilation, caused by the energy density of the Cosmological Microwave Background (CMB). This interplay causes inhomogeneous and anisotropic expansion, in and around galaxies, where as the expansion of the universe, when viewed globally, is homogeneous and isotropic. These contentions lead to a theoretical derivation of the gravitational central acceleration in and around galaxies, and the determination of g0, the central acceleration where falttening of Rotation Curves (RC) replaces Keplerian behavior. Our results, which fit the observed flattening of RCs, resemble the phenomenological Tully-Fisher and Millgrom MOND relations. However, our central acceleration, g0, depends on the CMB energy density at the time of formation of a galaxy and, as opposed to MOND, is not a universal constant.

astro-ph↗