Effects of gravitational lensing on neutrino oscillation in $$ \gamma $$-spacetime

We study the effects of gravitational lensing on neutrino oscillations in the $$\gamma $$ γ -spacetime which describes a static, axially-symmetric and asymptotically flat solution of the Einstein’s field equations in vacuum. Using the quantum-mechanical treatment for relativistic neutrinos, we calculate the phase of neutrino oscillations in this spacetime by considering both radial and non-radial propagation. We show the dependence of the oscillation probability on the absolute neutrino masses, which in the two-flavour case also depends upon the sign of mass squared difference, in sharp contrast with the well-known results of vacuum oscillation in flat spacetime. We also show the effects of the deformation parameter $$\gamma $$ γ on neutrino oscillations and reproduce previously known results for the Schwarzschild metric. We then extend these to a more realistic three flavours neutrino scenario and study the effects of the parameter $$\gamma $$ γ and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.

Axially symmetric Petrov type II general space–time and closed timelike curves

We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

Nucleation and Structural Identification in Gold Particles of High Aspect Ratios Developed through Mechanistic Approach

<p>A structural identification in different geometrical shapes of gold particles is presented here. Nucleation mechanisms of particles having geometrical shapes are discussed here, which have never been reported before. Dimensional regularity of particles in geometrical shapes incites a new insight. At electronically flat solution surface, different zones have been found dealing with the developing tiny-shaped particles in less elongation of atoms and more elongation of atoms. Tiny-shaped particles in less elongation of atoms nucleate particles of one-dimensional (1D) shapes due to developing in a zone consisting of regions rearward to north-pole at solution surface. Tiny-shaped particles in more elongation of atoms nucleate multi-dimensional (MD) shapes due to developing in a zone consisting of east-west regions at solution surface. To assemble at a common point forming at the centre of concave meniscus, structures of smooth elements at electronically decreasing level solution surface experience force in immersing format. A force exerting in the immersing format is related to the simultaneous actions of four forces to a structure of smooth element coming to assemble. In addition to the acquired orientation of an electron and the position of its atom at solution surface, a manner of energy knot clamping to electron in an atom also varies exertion of force for it. Particles of geometrical shapes show different structures in 1D and MD shapes. On identifying structure, a mechanism of photon reversion is disclosed. In the selected area patterns of particles, printing spots of reverted force in photons reflected from the laterally orientated electrons of less and more elongated atoms validates that photons are not carried by the electrons, so it is a photon reflection instead of an electron diffraction.<br></p>

Nucleation and Structural Identification in Gold Particles of High Aspect Ratios Developed through Mechanistic Approach

<p>A structural identification in different geometrical shapes of gold particles is presented here. Nucleation mechanisms of particles having geometrical shapes are discussed here, which have never been reported before. Dimensional regularity of particles in geometrical shapes incites a new insight. At electronically flat solution surface, different zones have been found dealing with the developing tiny-shaped particles in less elongation of atoms and more elongation of atoms. Tiny-shaped particles in less elongation of atoms nucleate particles of one-dimensional (1D) shapes due to developing in a zone consisting of regions rearward to north-pole at solution surface. Tiny-shaped particles in more elongation of atoms nucleate multi-dimensional (MD) shapes due to developing in a zone consisting of east-west regions at solution surface. To assemble at a common point forming at the centre of concave meniscus, structures of smooth elements at electronically decreasing level solution surface experience force in immersing format. A force exerting in the immersing format is related to the simultaneous actions of four forces to a structure of smooth element coming to assemble. In addition to the acquired orientation of an electron and the position of its atom at solution surface, a manner of energy knot clamping to electron in an atom also varies exertion of force for it. Particles of geometrical shapes show different structures in 1D and MD shapes. On identifying structure, a mechanism of photon reversion is disclosed. In the selected area patterns of particles, printing spots of reverted force in photons reflected from the laterally orientated electrons of less and more elongated atoms validates that photons are not carried by the electrons, so it is a photon reflection instead of an electron diffraction.<br></p>

Surveying and High-Resolution Topography of the Ochtiná Aragonite Cave Based on TLS and Digital Photogrammetry

The Ochtiná Aragonite Cave (Slovakia, Central Europe) is a world-famous karst phenomenon of significant geological, geomorphological, and mineralogical values. Its specific origin is determined by particular lithological and hydrogeological conditions of the Ochtiná karst formed in lenses of Paleozoic crystalline limestones, partly metasomatically altered to ankerite and siderite. Although the cave is only 300 m long, it represents a combined labyrinth consisting in parallel tectonically controlled halls and passages, that are largely interconnected through transverse conduits of phreatic and epiphreatic morphology with many medium- and small-scale forms originated in slowly moving or standing water (flat solution ceilings, wall inward-inclined facets, water table notches, convectional cupolas, and spongework-like hollows). The highly dissected and irregular morphologies of the cave were surveyed with terrestrial laser scanning and digital photogrammetry. Both used surveying technologies proved to be suitable for quick and accurate mapping of the complicated cave pattern. While terrestrial laser scanning can provide a rapid survey of larger and more complex areas with results delivered directly in the field, digital photogrammetry is able to generate very high-resolution models with quality photo-texture for mapping of small-scale morphologies. Several data on cave morphometry were generated from terrestrial laser scanning (e.g., the area of cave ground plan, the peripheral surface of underground spaces, and their volume). The new detailed map, sections, and 3D model create an innovation platform for a more detailed study on the morphology and genesis of this unusual cave also for its environmental protection and use in tourism.

Nucleation and Structural Identification in Gold Particles of High Aspect Ratios Developed through Mechanistic Approach

<p><a>A structural identification in different geometrical shapes of gold particles is being discussed here. Nucleation mechanisms of different particles having geometrical shapes are presented here, which have never been reported before. Dimensional regularity in developed particles gives a new insight.</a> At electronically flat solution surface, two different zones have been found developing tiny-shaped particles in less elongation of atoms and more elongation of atoms. Tiny-shaped particles in less elongation of atoms nucleate particles of one-dimensional (1D) shapes as they developed in the regions covering mainly zone of solution surface belonging to rearward side of north-pole. Tiny-shaped particles in more elongation of atoms nucleate multi-dimensional (MD) shapes as they developed in the regions covering mainly zone of solution surface belonging to east-west poles. To assemble at a common point forming at the centre of concave meniscus, structures of smooth elements deal with exertion of force in immersing <a></a><a>manner at electronically decreasing level solution surface. A force exerting in immersing manner is related to the simultaneous action of four forces to a structure of smooth element coming to assemble. In addition to the orientation of an electron and the position of the atom on solution surface, manner </a>of energy knot clamping electron in an atom also varies exertion of force for it. Particles of geometrical shapes show different structures in their 1D and MD shapes. By identification of a structure, a mechanism of photon reversion is disclosed. In the selected area patterns of particles, experimental proof of printing spots of reverted force in photons reflected from different electronic structures of elongated atoms validates that photons are not necessarily carried by the electrons.</p>

Nucleation and Structural Identification in Gold Particles of High Aspect Ratios Developed through Mechanistic Approach

<a>A precise structure of colloidal particles is being discussed here. Formation mechanism of nanoparticles and particles having geometrical shapes is discussed in a<b> </b>different way. Dimensional regularity of such nanoparticles and particles gives new insight.</a> At electronically flat solution surface, two different zones have been found developing tiny-shaped particles in less elongation of atoms as well as more elongation of atoms. Tiny-shaped particles in less elongation of atoms nucleate particles of one-dimensional (1D) shapes and those in more elongation of atoms nucleate multi-dimensional (MD) shapes. To assemble at a common point forming at the centre of concave meniscus on solution surface, structures of smooth elements at electronically decreasing level solution surface deal with exertion of force in immersing <a></a><a>manner. In addition to the orientation of an electron and the position of its atom, s</a>tyle of energy knot clamping electron also varies exertion of force on it. Particles of geometrical shapes show different structures in their 1D and MD shapes. By identification of a structure, a mechanism of photon reversion is disclosed. In the selected area patterns of particles, experimental proof of printing spots of reverted force of photons reflected from different electronic structures of elongated atoms validates that photons are not necessarily carried by the electrons.

Nucleation and Structural Identification in Gold Particles of High Aspect Ratios Developed through Mechanistic Approach

<p><a>A precise structure of colloidal particles is discussed here. Formation mechanism of nanoparticles and particles having geometrical shapes is discussed in a<b> </b>different way. Dimensional regularity of such nanoparticles and particles gives new insight.</a> At electronically flat solution surface, two different zones found developing tiny-shaped particles in less and more elongation of atoms. Tiny-shaped particles in less elongation of atoms nucleate particles of one-dimensional (1D) shapes and those in more elongation of atoms nucleate multi-dimensional (MD) shapes. To assemble at a common point forming at centre of concave meniscus on solution surface, structures of smooth elements at electronically decreasing level solution surface deal with exertion of force in immersing <a></a><a>manner. In addition to orientation of an electron and the position of its atom, s</a>tyle of energy knot clamping electron also varies exertion of force on it. Particles of geometrical shapes show different structures in their 1D and MD shapes. By identification of structure, a mechanism of photon reversion is disclosed. In selected area patterns of particles, experimental proof of printing spots of reverted force of photons reflected from different electronic structures of elongated atoms validates that photons are not necessarily carried by the electrons.</p>

Gauge approach to the symmetric teleparallel gravity

We discuss a gauge invariant gravity model in a non-Riemannian geometry in which the curvature and the torsion both are zero, the nonmetricity is nonzero. We also argue that only a metric ansatz is enough to start finding solutions to the field equations. As an application, we obtain explicitly a conformally flat solution.

STATIC CYLINDRICAL SYMMETRY AND CONFORMAL FLATNESS

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2, the spacetime has plane symmetry.