Related papers: Possible connection between the reflection symmetr…
The Kerr spacetime is symmetric with respect to a well-defined equatorial plane. When testing the equatorial reflection symmetry of an isolated black hole, one is at the same time testing the Kerr hypothesis in General Relativity. In this…
The study of off-equatorial orbits in razor-thin disks is still in its beginnings. Contrary to what was presented in the literature in recent publications, the vertical stability criterion for equatorial circular orbits cannot be based on…
Rotating black holes without equatorial reflection symmetry can naturally arise in effective low-energy theories of fundamental quantum gravity, in particular, when parity-violating interactions are introduced. Adopting a theory-agnostic…
General results on equatorial geodesics are exposed in the case of circular spacetimes featuring an equatorial reflection symmetry. The way the geodesic equation equivalently rewrites in terms of an effective potential is explicitly…
We show that under certain conditions an axisymmetric rotating spacetime contains a ring of points in the equatorial plane, where a particle at rest with respect to an asymptotic static observer remains at rest in a static orbit. We…
A general study of the stability of equatorial circular orbits in static axially symmetric gravitating systems is presented. Important circular geodesics as the marginally stable orbit, the marginally bounded orbit and the photon orbit are…
Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin…
We analyze the relativistic dynamical properties of Keplerian and non-Keplerian circular orbits in a general axisymmetric and stationary gravitational field, and discuss the implications for the stability of co- and counter-rotating…
We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all…
Both circular and epicyclic motion of test particles along equatorial circular orbits in the revisited Kerr-de Sitter spacetime is analyzed. We present relations for specific energy, specific angular momentum and Keplerian angular velocity…
Equatorial circular geodesic orbits of neutral test particles in the exterior spacetime of a charged rotating disc of dust are analyzed in dependence of its specific charge and a relativity parameter. The charged rotating disc of dust is an…
We make a revision of the stability criteria for equatorial circular orbits, obtained from the epicyclic approximation, which is widely used in Newtonian models for axisymmetric galaxies. We find that, for the case of thin disk models, the…
Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the…
Stability of circular orbits of the dust particles within a charged rotating disc of dust with respect to perturbations in the equatorial plane is analyzed. Within Einstein-Maxwell theory, the charged rotating disc of dust is an…
A topological approach has been successfully used to study the properties of the light ring and the null circular orbit, in a generic black hole background. However, for the equatorial timelike circular orbit, quite different from the light…
For a stationary, axisymmetric, asymptotically flat, ultra-compact [$i.e.$ containing light-rings (LRs)] object, with a $\mathbb{Z}_2$ north-south symmetry fixing an equatorial plane, we establish that the structure of timelike circular…
Epicyclic frequencies are usually observed in X-ray binaries and constitute a powerful astrophysical mean to probe the strong gravitational field around a compact object. We consider them in the equatorial plane around a general stationary…
Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due…
We demonstrate that generically an accretion disk around a compact object could have a new type of instability in that the accretion flow need not be symmetric with respect to the equatorial plane even when matter is supplied symmetrically…
We investigate the stable circular orbits of the spinning test particles around the accelerating Kerr black hole on the equatorial plane. To this end, we first calculate the equations of motion and analyze the parameter space for the…