Spinning test particles in the γ spacetime

Abstract

We consider the motion of spinning particles in the field of a well known vacuum static axially-symmetric space-time, known as γ-metric, that can be interpreted as a generalization of the Schwarzschild manifold to include prolate or oblate deformations. We derive the equations of motion for spinning test particles by using the Mathisson-Papapetrou-Dixon equations together with the Tulczyjew spin-supplementary condition, and restricting the motion to the equatorial plane. We determine the limit imposed by super-luminal velocity for the spin of the particle located at the innermost stable circular orbits (ISCO). We show that the particles on ISCO of the prolate γ space-time are allowed to have higher spin than the corresponding ones in the the oblate case. We determine the value of the ISCO radius depending on the signature of the spin-angular momentum, s − L relation, and show that the value of the ISCO with respect to the non spinning case is bigger for sL < 0 and smaller for sL > 0. The results may be relevant for determining the properties of accretion disks and constraining the allowed values of quadrupole moments of astrophysical black hole candidates.

On the properties of a deformed extension of the NUT space-time

“…The total gravitational mass of the source is M = mγ and from the computation of the quadrupole moment Q = γ m 3 (1 − γ 2 )/3 one can see that values of γ < 1 (γ > 1) correspond to prolate (oblate) deformations. The properties of the ZV space-time were studied in [12][13][14][15][16][17][18][19][20], while interior solutions for the ZV metric were obtained in [42,43]. A stationary generalization of the ZV metric was obtained by Halilsoy in [37].…”

“…For example in recent times some attention has been given to the Zipoy-Voorhees (ZV) metric which is a static generalization of the Schwarzschild solution to include higher multipole moments and describes the field outside prolate or oblate spheroids [10,11]. The properties of the motion of test particles in the ZV space-time and the possibility of testing the geometry from astrophysical observations has been discussed in several articles [12][13][14][15][16][17][18][19][20]. However, astrophysical compact objects typically rotate and therefore it would be more interesting to study the properties of stationary solutions.…”

Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime

“…These observations opened a qualitatively new stage to reveal black hole's unknown properties and test remarkable nature of the background geometry around black hole's horizon irrespective of the fact that there are still fundamental problems that general relativity faces, i.e., the occurrence of singularity, spacetime quantization, etc. In this framework, the motion of test particles in the strong gravitational field regime has been a productive field of study for several years [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. On the other hand, there is an extensive body of work devoted to understand the nature of radiative inspirals around black holes as a source of gravitational waves and binary systems [20][21][22][23][24][25][26][27][28].…”

Zipoy-Voorhees Gravitational Object as a Source of High-Energy Relativistic Particles

“…Note that these spacetime metrics belong to Weyl's class of solutions [19][20][21]. Several studies in the γ-metric can be found in the recent literature: optical appearance [22], the accretion process [10,23], shadows [24,25], geodesics motion [26], spinning particle motion [27] and charged particles dynamics [28,29].…”