相关论文: Myron Mathisson: what little we know of his life
The motion of spinning test particles in general relativity is described by Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin supplementary condition, the latter being today still an open question. The…
The Mathisson equations under the Frenkel-Mathisson supplementary condition are studied in a Schwarzschild field. The choice of solutions, which describe the motions of the proper center of mass of a spinning test particle, is discussed,…
We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for…
The physical effects following from the Mathisson equations at the highly relativistic motions of a spinning test particle relative to a Schwarzschild mass are discussed. The corresponding numerical estimates are presented.
It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the…
Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the…
We derive the equations of motion of an electrically neutral test particle for modified gravity theories in which the covariant divergence of the ordinary matter energy-momentum tensor dose not vanish (i.e. $\nabla_{\mu}T^{\mu\nu}\neq0$).…
Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both…
We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole" description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the…
The motion equation of standard cosmology, the Friedmann equation, is based on the stein's equations of gravitational fields. However, British physicist E. A. Milne pointed in 1943 that the same equation could be deduced simply based on the…
It is a little known fact that while he was developing his theory of general relativity, Einstein's initial idea was a variable speed of light theory. Indeed space-time curvature can be mimicked by a speed of light $c(r)$ that depends on…
We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form of the Einstein equations of motion in which the lapse function is determined by specified mean curvature and the shift is arbitrary. We also examine a new…
It is well known that a spinning body moving in a fluid suffers a force orthogonal to its velocity and rotation axis --- it is called the Magnus effect. Recent simulations of spinning black holes and (indirect) theoretical predictions,…
The Hamiltonian formulation of Mimetic Gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of energy-momentum tensor. The Poisson…
We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with…
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's classical electron [Acta Physica Polonica 6,…