SaToR-G (Satellites Tests of Relativistic Gravity) is a new experiment of gravitation that aims to test the gravitational interaction beyond the predictions of General Relativity (GR) in search for effects foreseen by other alternative theories of gravitation and possibly connected with “new physics”. SaToR-G is financed by the Astroparticle Physics Experiments of the Italian “Istituto Nazionale di Fisica Nucleare” (INFN) and takes advantage of the improved dynamical model of the two LAGEOS laser-ranged satellites and of the LARES one achieved within the previous experiment LARASE (LAser RAnged Satellites Experiment). The improvements mainly concern the modeling of the non-conservative forces (NCF) acting on the surface of the satellites considered and that of the Earth's gravitational field during their precise orbit determination (POD). Regarding the NCF, the main efforts were in the development of a model for the spin of the satellites (LASSOS: LArase Satellites Spin mOdel Solutions) and a model for thermal thrust forces (LATOS: LArase Thermal mOdel Solutions). For the gravitational field, the monthly solutions of the GRACE mission have been implemented in the code used for the POD. After a summary of the main results obtained by LARASE in the field of gravitation the main objectives of SaToR-G and the planned strategy for achieving them will be presented.

Candidate theories of quantum gravity predict the presence of a minimal measurable length at high energies. Such feature is in contrast with the Heisenberg Uncertainty Principle, which does not present any minimal length. Therefore, phenomenological approaches to quantum gravity introduced models spelled as modifications of quantum mechanics including a minimal length. Such models are often described by modifying the commutation relation between position and momentum. The effects of such modification are expected to be relevant at large energies/small lengths. One first consequence is that position eigenstates are not included in such models due to the presence of a minimal uncertainty in position. Furthermore, depending on the particular modification of the position-momentum commutator, when such models are considered from momentum space, the position operator is changed and a measure factor appears to let the position operator be self-adjoint. Although such modifications in momentum space represent small complication, at least formally, the (quasi-)position representation acquires numerous issues, source of misunderstandings. In fact, such representation is formally similar to that in which states are described in terms of Gaussian states in standard quantum mechanics. Consequently, the position operator is no longer a multiplicative operator and the momentum of a free particle does not correspond directly to its wave-number, with a consequent modification of the de Broglie relation.

In this presentation, I will review such issues, clarifying some of the aspects of minimal length models, with particular reference to the representation of the position operator. Furthermore, I will show how such a (quasi-)position description of quantum mechanical models with a minimal length affects results concerning simple systems, resulting in effects not accounted for in the literature.

This paper aims to investigate the existence and properties of
anisotropic quark stars in the context of self-interacting
Brans-Dicke theory. In this theory, the gravitational constant in
general relativity is replaced by a dynamical massive scalar field
accompanied by a potential function. Researchers believe that
strange stars may evolve from neutron stars when neutrons fail to
endure the extreme temperature and pressure in the interior region.
As a consequence they breakdown into their constituent particles
known as quarks. In order to construct a well-behaved quark star
model under the influence of massive scalar field, we formulate the
field equations by employing the MIT bag model. The MIT bag model
(strange quark matter equation of state) is the most suitable choice
for quark stars as it has successfully described the compactness of
certain stellar bodies. Furthermore, the estimates of mass of quark
stars based on the data from the cosmic events GW170817 and GW190425
support the choice of MIT bag model. The model is developed by
considering three types of quark matter: strange, up and down. The
bag constant involved in the model differentiates between false and
true vacuum. We consider a static sphere with anisotropic fluid and
employ the observed masses and radii of the strange star candidates
(RXJ 1856-37 and PSR J1614-2230) in the matching conditions at the
boundary to evaluate the value of bag constant. Further, we evaluate
the impact of the massive scalar field on state parameters and
investigate the viability (via energy conditions) as well as
stability (through the speed of sound constraints) of the
self-gravitating objects. It is found that the obtained values of
the bag constant lie within the accepted range
($58.9MeV/fm^3\leq\mathcal{B}\leq91.5MeV/fm^3$). Moreover, the
anisotropic structure meets the necessary viability and stability
criteria.

Generic theories of quantum gravity often postulate that at some high energy/momentum scale there will be a fixed, minimal length. Such a minimal length can be phenomenologically investigated by modifying the standard Heisenberg Uncertainty relationship. This is generally done in practice by modifying the commutator between position and momentum operators, which in turn means modifying these operators. However, modifications such that the uncertainty relation changes lead to conflicts with observational data (gamma ray bursts). This arises in the form of a predicted minimal length energy scale that is above the Planck energy rather than below it. As a result there seems to be an implication that there is no minimal length scale in these generic theories. Meanwhile, modifying the operators such that the standard uncertainty relation retains the same form, leads to no such conflict with observational data. We show that it is this modification of the position and momentum operators that is the key determining factor in the existence (or not) of a minimal length scale. By focusing primarily on the role of these operators we also show that one can avoid the constraints from the observations of short gamma ray bursts, which in certain cases seem to push the minimal length scale above the Planck scale.

(4+1) and (3+1+1) reductions of the geodetic equations in 5D theory with a scalar field and out of 5D optics lead to the new concept of the Lorentz-type 5D mass of the particle. Due to the imposition of the x⁵-cylindricity condition, one can obtain an integral of the 5D particle’s motion along the x⁵, that gives one an electric charge of it. Thus, one can obtain an exact expression for 5D mass, that depends on the scalar field through an electric charge, so maybe there is no need in a scalar charge in the Nature. One can compactly express 5D mass through the mass angle and additionally to hypothesize about the possible complex structure of it. It leads one to the deeper understanding of the quantum properties of the matter. All of these new conceptions turns one also to the idea, that 5D mass may contribute to the recently discovered in the Universe dark matter and dark energy and also to be one of the possible reasons of the Universe’s expansion. The next suggestive result in 5D theory is connected with the (4+1) reduction of the 5D Ricci identities. It leads one to the certain connections between the 4D physico-geometrical values and permits one to obtain the first pair of the Maxwell equations with the nonzero soliton-type r.h.s. and establishes the connection with the second pair of them. It leads one to the idea about the magnetic monopoles’ existence in the early Universe. It is shown, that this nonzero r.h.s. vanishes together with the imposition of the x⁵-cylindricity condition. This process permits one to hypothesize soundly about the existence of the topological second-order transition of the Universe’s matter, which leads it to the superfluid state and maybe accelerates its expansion.

We investigate the gravitational collapse of a gravitational bounded object constituted of dust cloud and dark energy. We considered the the effects of homogenous and isotropic fluid on newly suggested 4D limit for Einstein-Gauss-Bonnet gravity(EGB) (For detail about EGB gravity, arXiv:1905.03601v3). For this purpose, we consider the gravitational collapse of gravitational object made of dust cloud ρ_DM in the background of dark energy, p = wρ with (w < −1/3). We illustrate that the procedure is qualitatively equivalent to the scenario of theory of Einstein for the collapse of the gravitational object composed of homogeneous dust. Further, we consider the collapse for dark energy by considering the equation of state p = wρ to find that black hole also may form in EGB case, which predict that end state of gravitational collapse in EGB case is consistent with results carried out in pure Einstein’s gravity theory.

We have discussed two separate case, first, gravitational collapse of dust cloud in the context of EGB, in the second case, gravitational collapse of dark energy in EGB background. It is found that, gravitational collapse leads to formation of black hole in both cases. It is also worth mentioning that, end state of gravitational collapse in EGB context is same as in pure Einstein's gravity. Here, in this study dark matter refer to dust cloud, a matter with zero pressure.

Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar $R$ by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical fields such as torsion and non-metricity. The aim of this project is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein-Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). In TEGR a flat spacetime is considered as well as an asymmetric connection metric. In CGR, gravity is constructed in an equally flat tortionless spacetime which is ascribed to non-metricity.
The strength and weakness of each formulation is tested in the framework of a homogeneous and isotropic cosmological background. Mainly, the equivalence between GR and TEGR is examined at the level of equation of motion.
Also, we study the interactions between dark energy, dark matter and radiation and the stability of these models is explored. The implications of the interaction were tested in both early and late epoch of the Universe. It has been found that mostly there is a similarity of description of the evolution of the Universe provided by GR and TEGR while CGR always showed different description.

The need of transforming scientific knowledge to material suitable for teaching school students is a constant challenge for the educational community. Although it has been more than a century since quantum mechanics and the theory of relativity were established, both topics continue to be treated as modern physics, and only recently did they begun to be taught to students of levels prior to higher education. The work at hand is part of a larger effort to introduce the general theory of relativity in schools. To this end, we have devised appropriate experiments and computer simulation software. In particular, we present an educational simulation software that we created for the teaching of the principle of equivalence. The implementation was applied to 120 undergraduate students of the Pedagogical Department of the University of Athens, who do not major in physics but will be expected to teach young students the basic principles of relativity. The simulation software enables the user to measure forces inside a gravitational field and compare them to those exerted on bodies being accelerated. The controls incorporated in the software aim to motivate students to perform a variety of experiments, investigating every possible combination of parameters, in the hope to help them overcome most of the learning difficulties highlighted by previous research. The encouraging results of the research confirm the need to continue filling gaps in the fragmented instruction of physics in schools.

At school and university, gravity is taught essentially in the Newtonian way. Newtonian mechanics originated at a time when there were no fields, when energy did not exist as a physical quantity, and when one still had to be satisfied with the concept of actions at a distance. A theory without such shortcomings, Maxwell’s electromagnetism, came into being about 150 years later. It could have served as a model for a modern theory of gravitation. In fact, such a theory of gravitation, gravitoelectromagnetism, was proposed by Heaviside. However, it did not establish itself, because, firstly, many effects it describes are very, very small, secondly, it makes certain statements that seemed unacceptable to some researchers, and thirdly, shortly thereafter, General Relativity was born, which removed the old deficiencies and seemed to make a classical field theory of gravity superfluous. We argue that the subject of gravitoelectromagnetism has its legitimacy in teaching at school and university even now.

On the one hand, general relativity is impractical for many applications because the mathematical effort is high, and on the other hand, the theory of gravitoelectromagnetism by no means describes only tiny effects. Rather, it solves a problem that is deliberately ignored in the traditional teaching of Newtonian mechanics: To which system do we assign the so-called potential energy? Where is the “potential” energy located? We also encounter some peculiarities of gravitoelectromagnetism, the cause of which is the fact that compressive and tensile stresses within the gravitational field, are swapped against each other in comparison with the electromagnetic field.

At high school as well as undergraduate level, Quantum Mechanics (QM) is usually introduced through an overview of the main experiments and theoretical attempts which took place at the beginning of 20-th century. Even if retracing the historical path which led to the introduction of the new conceptual and mathematical framework has undoubted advantages, there are also significant drawbacks, mainly in contexts, such as a high school, where students' lack of advanced mathematical tools puts severe constraints to the understanding of quantum concepts.

Indeed QM implies major changes in understanding the physical reality. Introducing issues such as probability, uncertainty and entanglement, is a highly non trivial task. Students have to face with a matter, which is in conflict with the usual classical view of the physical world. Furthermore, the introduction of wave functions and Schroedinger equation implies the solution of second order ordinary differential equations, which are usually beyond high school students' knowledge in calculus.

All these considerations led us to think that a better strategy could be to introduce, from the very beginning, a simple 2х2 matrix formulation of QM, where quantum states are identified with 2-vectors belonging to a finite vector space and observables are 2х2 matrices. In this way students have the possibility to become familiar with the unique conceptual issues of QM, such as superposition principle, non locality and entanglement without an advanced mathematical background. That allows them to have also a glimpse to topics such as qubits and quantum computers.

The inspiring source of our proposal is the 1925 seminal paper by Heisenberg (Z. Phys. 33 (1925) 879), which provides a simple calculational method to deal with quantum mechanical states and observables, based on the identification of the physical quantities of interest with transition frequencies and amplitudes. Indeed such frequencies and amplitudes form matrices.