Related papers: Non inertial dynamics and holonomy on the ellipsoi…
The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint.…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
The analysis of the dynamics of radial movement in different reference frames used in cosmology is made. Use of different frames leads to the difference in inertial forces resulting in different observable effects. The important effect is…
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
Gravitational analogues of the nonlinear electrodynamics of Born and of Born and Infeld are introduced and applied to the black hole problem. This work is mainly devoted to the 2-dimensional case in which the relevant lagrangians are…
We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald's formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
It is argued that there is a connection between the fundamental forces of electromagnetism and gravitation. This connection occurs because of: 1) the fundamental significance of the finite and invariant velocity of light in inertial…
The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link…
The description of gravitation in the framework of soliton interaction is considered for two nonlinear field models. These models are Born -- Infeld nonlinear electrodynamics and so-called Born -- Infeld type scalar field model. The last…
The classical question whether nonholonomic dynamics is realized as limit of friction forces was first posed by Carath\'eodory. It is known that, indeed, when friction forces are scaled to infinity, then nonholonomic dynamics is obtained as…
Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity,…
We study dynamical friction in the Newtonian regime of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein's theory of gravitation. The nonlocal aspect of NLG simulates dark matter. The attributes of the…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…