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Register a new userClassification of radial Kerr geodesic motion
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We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing the constraints from polar, time and azimuthal motion. Four generic root structures with only simple roots give rise to eight non-generic root structures when either one root becomes coincident with the horizon, one root vanishes or two roots becomes coincident. We derive the explicit phase space of all such root systems in the basis of energy, angular momentum and Carters constant and classify whether each corresponding radial geodesic motion is allowed or disallowed from existence of polar, time and azimuthal motion. The classification of radial motion within the ergoregion for both positive and negative energies leads to 6 distinguished values of the Kerr angular momentum. The classification of null radial motion and near-horizon extremal Kerr radial motion are obtained as limiting cases and compared with the literature. We explicitly parametrize the separatrix describing root systems with double roots as the union of the following three regions that are described by the same quartic respectively obtained when (1) the pericenter of bound motion becomes a double root; (2) the eccentricity of bound motion becomes zero; (3) the turning point of unbound motion becomes a double root.
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Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain synchronized in phase.
We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einsteins General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashows Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model.
In a recent paper (Phys. Dark Univ. {bf 31}, 100744 (2021)) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time--like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
In this paper we study geodesic motion around a distorted Schwarzschild black hole. We consider both timelike and null geodesics which are confined to the black holes equatorial plane. Such geodesics generically exist if the distortion field has only even interior multipole moments and so the field is symmetric with respect to the equatorial plane. We specialize to the case of distortions defined by a quadrupole Weyl moment. An analysis of the effective potential for equatorial timelike geodesics shows that finite stable orbits outside the black hole are possible only for $qin(q_{text{min}}, q_{text{max}}]$, where $q_{text{min}}approx-0.0210$ and $q_{text{max}}approx2.7086times10^{-4}$, while for null equatorial geodesics a finite stable orbit outside the black hole is possible only for $qin[q_{text{min}},0)$. Moreover, the innermost stable circular orbits (ISCOs) are closer to the distorted black hole horizon than those of an undistorted Schwarzschild black hole for $qin(q_{text{min}},0)$ and a null ISCO exists for $q=q_{text{min}}$. These results shows that an external distortion of a negative and sufficiently small quadrupole moment tends to stabilize motion of massive particles and light.
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