Equatorial circular motion in Kerr spacetime

Abstract

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 the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles.In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circular orbits. It is shown that the geometric structure of the stability zones of black holes is completely different from that of naked singularities.

Geometrical aspects of Venus transit

“…In general, relativistic frameworks have been used [11,12]. Here we intend to show that it is possible in a very simple case to calculate some astronomical observables with a simple geometrical method and elementary algebra, by solely considering the photos of Venus transit.…”

“…In the literature, investigations concerning to calculations of orbits and astronomical observables associated to them have been considered in many contexts with very sophisticated theoretical frameworks [9][10][11][12], including aspects like either the sensibility to disturbances in the orbit of satellites [9] or the study of equatorial circular orbits in static axially symmetric gravitating systems [10] and the calculation of radius of the orbits as well. In general, relativistic frameworks have been used [11,12].…”

Motion of charged particle in Reissner–Nordström spacetime: a Jacobi-metric approach

“…A major area of interest, especially in recent times, is the motion of particles in the presence of black holes and naked singularities. The exhaustive topical work by Pugliese et al [1,2] (as well as their series of earlier papers [3][4][5][6]) have revealed clearly the possibility of distinguishing between black holes and naked singularities in the case of charged particle dynamics in Reissner-Nordström background. The systematic analysis is based on the nature of particle motion for different charge to mass ratio in the Reissner-Nordström metric, (which is expected), but the non-trivial effect of the charge to mass ratio of the probe particle is indeed a surprising element.…”

“…On the one hand, Pugliese et al [1][2][3] rely on the covariant framework where geodesic motion takes place in the ReissnerNordström spacetime. The Lagrangian equation of motion is derived from the unrestricted variational principle with the charge and mass parameters of the source and probe dictating the particle motion for arbitrary particle energy, which is a derived quantity.…”

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

“…Theoretical models to describe the orbital evolution of the secondary object in various situations have been derived and presented in the literature: circular orbits in the equatorial plane of the primary object [1][2][3][4][5][6], elliptical orbits in the equatorial plane [7][8][9][10][11][12][13], and an extensive body of research on circular or elliptical orbits inclined with respect to the equatorial plane [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Such models are used to generate hypothetical gravitational waveforms (GW), which provide templates for use in the detection of gravitation wave signals by pattern recognition (Punturo et al [32]).…”