Related papers: The Roche problem: some analytics
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
Recently developed simple approach for the exact/approximate solution of Schrodinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
Using a general solution-generating technique for electrically charged relativistic stars with spherical symmetry, we derive a new bound on the mass-radius ratio. This compactness bound is based on the already established bounds for…
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…
We study the dynamics in the neighborhood of the collinear Lagrangian points in the spatial, circular, restricted three--body problem. We consider the case in which one of the primaries is a radiating body and the other is oblate (although…
Exploiting the explicit mass formulae for logarithmic potential model of Quigg and Rosner it is shown that at least on the level of mass-relations this model reproduces the naive quark model relations and generalizes the last one in case of…
This review explores the physical mechanisms driving the evolution of low- and intermediate-mass binary star systems, with particular emphasis on emerging mechanisms that challenge classical paradigms. We begin by describing the principal…
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the…
The Roche lobe formalism describes mass transfer from one star to another. We develop an extension to hierarchical triples, considering the case in which a star donates mass to a companion which is itself a binary. The L1 point moves as the…
By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing…
We perform a detailed physical analysis for a class of exact solutions for the Einstein-Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact…
In this note, we use Rouch\'e's theorem and the pleasant properties of the arithmetic of the logarithmic derivative to establish several new results regarding the geometry of the zeros, poles, and critical points of a rational function.…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for…
I review the main options one has of introducing mass to neutrinos, including broken R-parity models, as well as the constraints on neutrino properties that follow from astrophysics, cosmology as well as laboratory observations.