Multi-Messenger Astrophysics of a Millisecond Pulsar Orbiting around a Massive Black Hole

Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar are gravitational-wave sources that emit also electromagnetic radiation. The millisecond pulsars in these binaries have complex orbital and spin dynamics, which are observable because of spin–orbit and spin–spin coupling (through spin–curvature interaction). The strengths of the couplings generally depends on the mass ratio between the pulsar and the black hole. The narrow mass range of neutron stars gives an advantage in parameter extraction as it greatly reduces the search space, in particular, in the determination of the black-hole mass, in gravitational wave experiments and radio pulsar timing observations. Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar will help to resolve the astrophysical problems, concerning the applicability of the M-σ relation for galactic spheroids extending to the very low-mass galaxies and whether or not low-mass dwarf galaxies and globular clusters would harbour a nuclear intermediate-mass black hole. The high-precision that can be achieved in gravitational wave experiments and radio pulsar timing observations will provide an opportunity to directly detect gravitational clock effects that are arisen from spin couplings. Radio monitoring of the orbital and spin evolution of the millisecond pulsar in an extreme-mass-ratio binary can be used as a bootstrap method for correcting the drifts in the phases in the gravitational waves from the extreme-mass-ratio and intermediate-mass-ratio binaries caused by self-force.

Theory of Spinors in Curved Space-Time

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To split the spinor connection into the Keller connection Υμ∈Λ1 and the pseudo-vector potential Ωμ∈Λ3 not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton’s second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields; however, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table Sabμν, which plays an important role in the interaction between spinor and gravity. From this paper we find that Clifford algebra has irreplaceable advantages in the study of geometry and physics.

Spinning Test Particle in Four-Dimensional Einstein–Gauss–Bonnet Black Holes

In this paper, we investigate the motion of a classical spinning test particle in a background of a spherically symmetric black hole based on the novel four-dimensional Einstein–Gauss–Bonnet gravity [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)]. We find that the effective potential of a spinning test particle in this background could have two minima when the Gauss–Bonnet coupling parameter α is nearly in a special range −8<α/M2<−2 (M is the mass of the black hole), which means a particle can be in two separate orbits with the same spin-angular momentum and orbital angular momentum, and the accretion disc could have discrete structures. We also investigate the innermost stable circular orbits of the spinning test particle and find that the corresponding radius could be smaller than the cases in general relativity.

Quantum spin dynamics in external classical fields

We study the quantum and classical dynamics of spinning particles in the framework of the general-relativistic covariant Dirac theory. The exact Foldy-Wouthuysen transformation for the most general case of a fermion in arbitrary configurations of the gravitational, inertial and electromagnetic fields is derived. We demonstrate the complete consistency of the quantum and classical dynamics. As physical applications, we discuss prospects of probing spacetime structure and using spin effects for gravitational wave detection.