Zoran Narančić

The envelope of projectile trajectories

The paper presents yet another elegant solution to the classical problem of maximizing the range of a projectile fired from above or from below the horizontal target plane. The method makes use of the envelope of the family of the projectile trajectories and it not only solves the original problem, but can be applied to maximize the projectile range on a target surface of arbitrary shape. Three different ways of deriving the equation of the envelope are shown. As an example the range of a projectile is maximized on a parabolic target surface. The envelope can also be used to minimize the kinetic energy of a projectile given the target point.

Formation of photon spheres in boson stars with a nonminimally coupled field

A static, spherically symmetric, asymptotically flat spacetime may allow for circular, closed null-geodesics which are said to belong to a photon sphere. In the context of gravitational lensing in the strong deflection regime, the presence of a photon sphere leads to an unbounded angle of deflection of light (multiple turns) and formation of relativistic images. In this paper, we show that photon spheres may form in some configurations of boson stars constructed with a free massive complex scalar field nonminimally coupled to gravity. Assuming that the boson star is transparent to light, photon spheres would give rise not only to phenomena in the realm of strong gravitational lensing, but also to considerably increased photon flux in the central region of the star, relative to the flux in its surroundings.

Maximizing the range of a projectile

The problem of maximizing the horizontal range of a projectile fired from a height above or a depth below the assumed horizontal target plane has been discussed and solved in several different ways. However, it seems to be a neverending story. This paper offers a remarkably simple solution to the problem that does not require the use of calculus. It is based on the fact that the equation θ = f(R), where θ is the firing angle and R is the range, must have a unique solution for R = Rmax .

Nonminimally coupled scalar field in teleparallel gravity: boson stars

We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the theory in the sense that the resulting equations of motion depend on the choice of a tetrad. For the assumed static spherically symmetric spacetime, we find a tetrad which leads to a self-consistent set of equations, and we construct the self-gravitating configurations of the scalar field—boson stars. The resulting configurations develop anisotropic principal pressures and satisfy the dominant energy condition. An interesting property of the configurations obtained with sufficiently large field-to-torsion coupling constant is the outwardly increasing energy density, followed by an abrupt drop towards the usual asymptotic tail. This feature is not present in the boson stars with the field minimally or nonminimally coupled to the curvature scalar, and therefore appears to be a torsion-only effect.

Regular and quasi black hole solutions for spherically symmetric charged dust distributions in the Einstein–Maxwell theory

Static spherically symmetric distributions of electrically counterpoised dust (ECD) are used to construct solutions to Einstein–Maxwell equations in the Majumdar–Papapetrou formalism. Unexpected bifurcating behaviour of solutions with regard to source strength is found for localized, as well as for the delta-function ECD distributions. Unified treatment of general ECD distributions is accomplished and it is shown that for certain source strengths one class of regular solutions approaches Minkowski spacetime, while the other comes arbitrarily close to black hole solutions.

Note on the charged boson stars with torsion-coupled field

Within the framework of the extended teleparallel gravity, a new class of boson stars has recently been constructed by introducing the nonminimal coupling of the scalar field to the torsion scalar. An interesting feature of these static, spherical, self-gravitating configurations of the massive complex scalar field is their central region with outwardly increasing energy density, surrounded by a thick shell within which the joining with the usual asymptotically Schwarzschild tail takes place. In this work we extend the original model with the U(1) gauge field and we find that the combined effect of the charge and coupling of the field to torsion leads to a significant increase of the maximal mass and the particle number that can be supported against gravity. We also show that some charged configurations preserve the property of having the outwardly increasing energy density over the central region, regardless of the fact that charging the configurations affects the anisotropy of the pressures in the opposite way relative to that of the field-to-torsion coupling terms.

Nonleptonic kaon decays and nonperturbative QCD effects in chiral-bag model

AbstractThe instanton induced-term, proposed by Konishi and Ranfone [1] was introduced in the chiral-bag model based analysis ofK→2π decays. Almost perfect fit of the experimental data was possible with the induced-term coefficient

Weak nucleon-nucleon-kaon vertices and hyperon nonleptonic decays

\tilde C_1 \cong 1,4