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The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light,…
A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. An exact time-dependent solution of Einstein's gravitational field equation…
The turbulent jets are usually described by classical velocities. The relativistic case can be treated starting from the conservation of the relativistic momentum. The two key assumptions which allow to obtain a simple expression for the…
Within the weak-field approximation of general relativity, new exact solutions are derived for the gravitational field of a mass moving with arbitrary velocity and acceleration. A mass having a constant velocity greater than 3^-1/2 times…
Achieving relativistic flight to enable extrasolar exploration is one of the dreams of humanity and the long term goal of our NASA Starlight program. We derive a fully relativistic solution for the motion of a spacecraft propelled by…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
By relativity we show that, although the superluminal motion of classical particles is forbidden, the superluminal transportation of quanta of any massive matter field is possible. Exact theoretical derivation and precise numerical…
The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is…
The fundamental equations of relativistic dynamics are derived from a thought experiment and from the transformation of relativistic velocity avoiding collisions and conservation laws of momentum and energy.
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of a slightly inhomogeneous intense laser field are obtained. In weak low-frequency background fields, such a particle on average…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…
One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous…
Gravitational repulsion is an inherent aspect of the Schwarzschild solution of the Einstein-Hilbert field equations of general relativity. We show that this circumstance means that it is possible to gravitationally accelerate particles to…
Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal coordinate system…
Radiatively-driven transfer flow perpendicular to a luminous disk is examined in the relativistic regime of $(v/c)^2$, taking into account the gravity of the central object. The flow is assumed to be vertical, and the gas pressure as well…
A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
We use moment formalism of relativistic radiation hydrodynamics to obtain equations of motion of radial jets and solve them using polytropic equation of state of the relativistic gas. We consider curved space-time around black holes and…