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Gravity differs from all other known fundamental forces since it is best described as a curvature of spacetime. For that reason it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and…
We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…
A brief review of main features of the new approach named ``quantum geometrodynamics in extended phase space'' is given and its possible prospects are discussed. Gauge degrees of freedom are treated as a subsystem of the Universe which…
We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity models in which the scalar field potential may be negative, and even unbounded from below. We find a set of viable solutions with nonzero…
We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. Such scenarios are supported by the physics of crystalline structures with microscopic defects…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
Gravity gradiometry within the framework of the general theory of relativity involves the measurement of the elements of the relativistic tidal matrix, which is theoretically obtained via the projection of the spacetime curvature tensor…
I consider the possibility that space experiments be used to search for quantum properties of spacetime. On the basis of recent quantum-gravity results, I argue that insight on some quantum properties of spacetime can be obtained with…
Gravitational interferometers and cosmological observations of the cosmic microwave background offer us the prospect to probe the laws of gravity in the primordial universe. To study and interpret these datasets we need to know the possible…
Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we…
The current effort to test General Relativity employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
There is a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach on a 2-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known…
This paper introduces new definitions of common geodetic measures on a planetary surface (namely surface area, path length, and mean value or other statistical parameters of a surface function) that are not based on a datum such as a…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
In developing mobile robots for exploration on the planetary surface, it is crucial to evaluate the robot's performance, demonstrating the harsh environment in which the robot will actually be deployed. Repeatable experiments in a…
Modified gravity theories may provide an alternative to dark energy to explain cosmic acceleration. We argue that the observational program developed to test dark energy needs to be augmented to capture new tests of gravity on astrophysical…
We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the…
Localization in a global map is critical to success in many autonomous robot missions. This is particularly challenging for multi-robot operations in unknown and adverse environments. Here, we are concerned with providing a small unmanned…