Related papers: Geometry and Motion in General Relativity
Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying…
The classical uncertainty principle inequalities were imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle was reformulated in terms of proper space-time length element,…
It is shown, that a free motion of microparticles (elementary particles) in the gravitational field is multivariant (stochastic). This multivariance is conditioned by multivariant physical space-time geometry. The physical geometry is…
There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…
We propose an action for a free particle in Horava-Lifshitz gravity based on Foliation Preserving Diffeomorphisms. The action reduces to the usual relativistic action in the low energy limit and allows for subluminal and superluminal…
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…
This paper concerns relational first principles from which the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories. This was accompanied by a number of…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
Standard treatments of general relativity accept the gravitational slowing of clocks as a primary phenomenon, requiring no further analysis as to cause. Rejecting this attitude, I argue that one or more of the fundamental "constants"…
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.
I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
A hypothesis proposed in the paper (Entropy 2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of…