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Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
Understanding quantum phenomena which go beyond classical concepts is a focus of modern quantum physics. Here, we show how the theory of nonnegative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data…
A quantum sl(2,R) coalgebra (with deformation parameter z) is shown to underly the construction of superintegrable Kepler potentials on 3D spaces of variable and constant curvature, that include the classical spherical, hyperbolic and…
We formulate in an intuitive manner several conceptual aspects of the field-to-particle transition problem which intends to extract physical properties of elementary particles from specific field configurations. We discuss the possibility…
Cosmic acceleration can be achieved not only with a sufficiently flat scalar field potential but through kinetic terms coupled to gravity. These derivative couplings impose a shift symmetry on the scalar field, aiding naturalness. We write…
During the past few decades, abundant evidence for physics beyond the two standard models of particle physics and cosmology was found. Yet, we are tapping into the dark regarding our understanding of the dark sector. For more than a…
We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…
We describe a new method to parameterise dark energy theories including massive gravity, elastic dark energy and tensor-metric theories. We first examine a framework to describe any second order Lagrangian which depends on the variation of…
I examine how two specific examples of modified gravity explanations of cosmic acceleration help us understand some general problems confronting cosmological tests of gravity: how do we distinguish modified gravity from dark energy if they…
We have developed a method to study the effects of a perturbation to the motion of a test point--like object in a Schwarzschild spacetime. Such a method is the extension of the Lagrangian planetary equations of classical celestial mechanics…
Nonlinear scalar-tensor theories of gravity have been considered as candidates for dark matter and dark energy. Often, they possess screening mechanisms, which allow the fifth force mediated by the additional scalar degree(s) of freedom to…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the…
An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to…
In this paper we show uniqueness of the conductivity for the quasilinear Calder\'on's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions…
Neutral particles can be guided and focussed using electric field gradients that focus in one transverse direction and defocus in the other, alternating between the two directions. Such a guide is suitable for transporting particles that…
I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We discuss the leading term in the semi-classical asymptotics of Newtonian quantum gravity for the Kepler problem. For dark matter, ice or dust particles in the gravitational field of a star or massive planet this explains how rapidly…
Trajectory of a test particle or a photon around a general spherical black hole is studied and bending of light trajectory is investigated. Pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is…