Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits

The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for $r=1.5 r_g(1+\delta)$, $0<\delta \ll 1$, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region significantly depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of non-circular highly relativistic orbits of a spinning particle starting from $r>1.5 r_g$ are presented.Comment: 10 pages, 11 figure

Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds

A new representation, which does not contain the third-order derivatives of the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing the motion of a spinning test particle, is obtained under the assumption of the Mathisson-Pirani condition in a Kerr background. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim to investigate the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation. Some numerical examples for a Schwarzschild background are presented.Comment: 21 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1105.240

HIGHLY RELATIVISTIC CIRCULAR ORBITS OF SPINNING PARTICLE IN THE SCHWARZSCHILD AND KERR FIELDS

The solutions of the Mathisson- Papapetrou equations which describe highly relativistic circular orbits of a spinning particle in Schwarzschild's and Kerr's fields are considered. The domain of existence of those orbits and the necessary values of the particle's velocity for their realization are studied. These results can be applied while analyzing the synchrotron radiation in some astrophysical processes

A role for NANOG in G1 to S transition in human embryonic stem cells through direct binding of CDK6 and CDC25A

In this study, we show that NANOG, a master transcription factor, regulates S-phase entry in human embryonic stem cells (hESCs) via transcriptional regulation of cell cycle regulatory components. Chromatin immuno-precipitation combined with reporter-based transfection assays show that the C-terminal region of NANOG binds to the regulatory regions of CDK6 and CDC25A genes under normal physiological conditions. Decreased CDK6 and CDC25A expression in hESCs suggest that both CDK6 and CDC25A are involved in S-phase regulation. The effects of NANOG overexpression on S-phase regulation are mitigated by the down-regulation of CDK6 or CDC25A alone. Overexpression of CDK6 or CDC25A alone can rescue the impact of NANOG down-regulation on S-phase entry, suggesting that CDK6 and CDC25A are downstream cell cycle effectors of NANOG during the G1 to S transition

A role for NANOG in G1 to S transition in human embryonic stem cells through direct binding of CDK6 and CDC25A

In this study, we show that NANOG, a master transcription factor, regulates S-phase entry in human embryonic stem cells (hESCs) via transcriptional regulation of cell cycle regulatory components. Chromatin immuno-precipitation combined with reporter-based transfection assays show that the C-terminal region of NANOG binds to the regulatory regions of CDK6 and CDC25A genes under normal physiological conditions. Decreased CDK6 and CDC25A expression in hESCs suggest that both CDK6 and CDC25A are involved in S-phase regulation. The effects of NANOG overexpression on S-phase regulation are mitigated by the down-regulation of CDK6 or CDC25A alone. Overexpression of CDK6 or CDC25A alone can rescue the impact of NANOG down-regulation on S-phase entry, suggesting that CDK6 and CDC25A are downstream cell cycle effectors of NANOG during the G1 to S transition