The study of Kerr geodesics has a long history,particularly for those occurring within the equatorial plane,which are generally well-understood.However,when compared with the classification introduced by one of the au...The study of Kerr geodesics has a long history,particularly for those occurring within the equatorial plane,which are generally well-understood.However,when compared with the classification introduced by one of the authors[Phys.Rev.D 105,024075(2022)],it becomes apparent that certain classes of geodesics,such as trapped orbits,still lack analytical solutions.Thus,in this study,we provide explicit analytical solutions for equatorial timelike geodesics in Kerr spacetime,including solutions of trapped orbits,which capture the characteristics of special geodesics,such as the positions and conserved quantities of circular,bound,and deflecting orbits.Specifically,we determine the precise location at which retrograde orbits undergo a transition from counter-rotating to prograde motion due to the strong gravitational effects near a rotating black hole.Interestingly,the trajectory remains prograde for orbits with negative energy despite the negative angular momentum.Furthermore,we investigate the intriguing phenomenon of deflecting orbits exhibiting an increased number of revolutions around the black hole as the turning point approaches the turning point of the trapped orbit.Additionally,we find that only prograde marginal deflecting geodesics are capable of traversing through the ergoregion.In summary,our findings present explicit solutions for equatorial timelike geodesics and offer insights into the dynamics of particle motion in the vicinity of a rotating black hole.展开更多
The process of covariant conserved charge of gravitational theory, which is covariant under general coordinate and local Lorentz transformations, has been applied to many tetrad fields, which reproduce Kerr-Ads spacet...The process of covariant conserved charge of gravitational theory, which is covariant under general coordinate and local Lorentz transformations, has been applied to many tetrad fields, which reproduce Kerr-Ads spacetime, to calculate their conserved charges. It is shown that this process gives an infinite value of the conserved charges for Kerr–Ads spacetime. Therefore, the method of “regularization through relocalization”, i.e., modification of the Lagrangian of the gravitational field through a total derivative, is used. This method gaves a finite and a consistent result of total energy and angular momentum for Kerr–Ads spacetime.展开更多
In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation appro...In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation approximation, we obtain that the torsion axial-vector possesses the dipole-like structure. Furthermore, the effect of massive neutrino spin precession in this field is mentioned.展开更多
基金the Natural Science Foundation of Shandong Province(ZR2023QA133)Yantai University(WL22B218)+1 种基金B.S.is Supported by the National Natural Science Foundation of China(12375046)Beijing University of Agriculture(QJKC-2023032).
文摘The study of Kerr geodesics has a long history,particularly for those occurring within the equatorial plane,which are generally well-understood.However,when compared with the classification introduced by one of the authors[Phys.Rev.D 105,024075(2022)],it becomes apparent that certain classes of geodesics,such as trapped orbits,still lack analytical solutions.Thus,in this study,we provide explicit analytical solutions for equatorial timelike geodesics in Kerr spacetime,including solutions of trapped orbits,which capture the characteristics of special geodesics,such as the positions and conserved quantities of circular,bound,and deflecting orbits.Specifically,we determine the precise location at which retrograde orbits undergo a transition from counter-rotating to prograde motion due to the strong gravitational effects near a rotating black hole.Interestingly,the trajectory remains prograde for orbits with negative energy despite the negative angular momentum.Furthermore,we investigate the intriguing phenomenon of deflecting orbits exhibiting an increased number of revolutions around the black hole as the turning point approaches the turning point of the trapped orbit.Additionally,we find that only prograde marginal deflecting geodesics are capable of traversing through the ergoregion.In summary,our findings present explicit solutions for equatorial timelike geodesics and offer insights into the dynamics of particle motion in the vicinity of a rotating black hole.
基金Project partially supported by the Science Fund from the Egyptian Ministry of Scientific Research(Grant No.24-2-12)
文摘The process of covariant conserved charge of gravitational theory, which is covariant under general coordinate and local Lorentz transformations, has been applied to many tetrad fields, which reproduce Kerr-Ads spacetime, to calculate their conserved charges. It is shown that this process gives an infinite value of the conserved charges for Kerr–Ads spacetime. Therefore, the method of “regularization through relocalization”, i.e., modification of the Lagrangian of the gravitational field through a total derivative, is used. This method gaves a finite and a consistent result of total energy and angular momentum for Kerr–Ads spacetime.
文摘In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation approximation, we obtain that the torsion axial-vector possesses the dipole-like structure. Furthermore, the effect of massive neutrino spin precession in this field is mentioned.
