Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens

Abstract

The leading-order gravitational time delay of relativistic neutral massive particles (e.g., neutrinos or high-energy cosmic-ray particles) caused by a moving Schwarzschild black hole with a constant radial velocity is investigated for the first time. On the basis of the equations of motion in the spacetime of the moving lens, we achieve a new unified formula for the travel times of relativistic massive and massless particles propagating from the source to the observer within the first post-Minkowskian approximation. The analytical form of the difference between the travel times of a relativistic massive particle and a light signal in this geometry, as well as that of two relativistic massive particles, is thus obtained in the weak-field and slow-motion limit. The influence of the radial lens motion on the leading-order Schwarzschild time delay of relativistic massive particles is then discussed. It is found that in the slow-motion limit, the radial lens motion towards the observer decreases the flight time of an ultrarelativistic massive particle, when compared with the case of no translational motion of the central body. Conversely, if the lens gets away from the detector radially under the same conditions, the propagation process of the particle will slow down and its flight time will thus increase in comparison with the Schwarzschild case. Finally, we analyze the magnitude of the full radial motion effect of the lens and evaluate the possibility of its astronomical detection by modeling three typical black holes as the lens respectively.

arXiv comment10 pages, 1 figure. Accepted for publication in Physical Review D

References in corpus (78)

• The Galaxy in Context: Structural, Kinematic and Integrated Properties
• Multi-messenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A
• GAIA: Composition, Formation and Evolution of the Galaxy
• Massive Black Holes as Population III Remnants
• Intermediate-Mass Black Holes
• Origin and Propagation of Extremely High Energy Cosmic Rays
• Measurement of the neutrino velocity with the OPERA detector in the CNGS beam
• Total recoil: the maximum kick from nonspinning black-hole binary inspiral
• First Year Performance of The IceCube Neutrino Telescope
• The Astrophysics of Ultrahigh Energy Cosmic Rays
• Intermediate-Mass Black Holes
• The Mass of the Black Hole in Cygnus X-1
• Calibration and Characterization of the IceCube Photomultiplier Tube
• The Extreme Spin of the Black Hole in Cygnus X-1
• The First LHAASO Catalog of Gamma-Ray Sources
• Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case
• Investigating stellar-mass black hole kicks
• Mass Measurements of Stellar and Intermediate Mass Black-Holes
• The Trigonometric Parallax of Cygnus X-1
• Lorentz Covariant Theory of Light Propagation in Gravitational Fields of Arbitrary-Moving Bodies
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• IceCube: An Instrument for Neutrino Astronomy
• Getting Its Kicks: A VLBA Parallax for the Hyperfast Pulsar B1508+55
• Micro-Arcsecond Radio Astrometry
• Detection of a particle shower at the Glashow resonance with IceCube
• Gravitomagnetic Effects in the Propagation of Electromagnetic Waves in Variable Gravitational Fields of Arbitrary-Moving and Spinning Bodies
• Multi-Messenger Astrophysics
• Parallaxes for W49N and G048.60+0.02: Distant Star Forming Regions in the Perseus Spiral Arm
• General post-Minkowskian expansion of time transfer functions
• Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center
• Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
• Enabling real-time multi-messenger astrophysics discoveries with deep learning
• Multi-Messenger Time Delays from Lensed Gravitational Waves
• The ANTARES Optical Beacon System
• High Precision Astrometry with MICADO at the European Extremely Large Telescope
• World function and time transfer: general post-Minkowskian expansions
• Precise radio astrometry and new developments for the next generation of instruments
• Resurvey of order and chaos in spinning compact binaries
• Null Geodesics in Perturbed Spacetimes
• Tracking black hole kicks from gravitational wave observations
• A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies
• A Modified Scalar-Tensor-Vector Gravity Theory and the Constraint on its Parameters
• Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments
• Microarcsecond Astrometry: Science Highlights from Gaia
• Deflection of light and particles by moving gravitational lenses
• 2PN Light Propagation in the Scalar-Tensor Theory: an $N$-Point-Masses Case
• Using a multi-messenger and multi-wavelength observational strategy to probe the nature of dark energy through direct measurements of cosmic expansion history
• Gravitational Deflection of Light and Massive Particle by a Moving Kerr-Newman Black Hole
• On the importance of special relativistic effects in modelling ultra-fast outflows
• The Second Post-Newtonian Light Propagation and Its Astrometric Measurement in the Solar System
• Gravitational lensing by spinning and escaping lenses
• Analytical Derivation of Second-Order Deflection in Equatorial Plane of a Radially Moving Kerr-Newman Black Hole
• Numerical Simulations of the Light Propagation in the Gravitational Field of Moving Bodies
• First Very Long Baseline Interferometry Detections at 870μm
• The Hubble Space Telescope Extragalactic Distance Scale Key Project XXIII. The Discovery of Cepheids In NGC 3319
• Light propagation in the field of a moving axisymmetric body: theory and application to JUNO
• Second-order time delay by a radially moving Kerr-Newman black hole
• Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies
• Fermat Potentials for Non-Perturbative Gravitational Lensing
• Second post-Newtonian approximation of Einstein-aether theory
• The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments
• Gravitational lensing of massive particles by a black-bounce-Schwarzschild black hole
• Time delay of timelike particles in gravitational lensing of Schwarzschild spacetime
• The gravitational time delay in the field of a slowly moving body with arbitrary multipoles
• Aberration by gravitational lenses in motion
• On gravitational lensing by deflectors in motion
• Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes
• Effects of Lens Motion and Uneven Magnification on Image Spectra
• Velocity Effects on the Deflection of Light by Gravitational Microlenses
• Second Post-Minkowskian Metric for a Moving Kerr Black Hole
• Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem
• Discovery of An Active Intermediate-Mass Black Hole Candidate in the Barred Bulgeless Galaxy NGC 3319
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem
• Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit
• Refining the mass estimate for the intermediate-mass black hole candidate in NGC 3319
• The Effect of Light Deflection by Solar System Objects on High-Precision SKA Astrometry
• Modulations of Gravitational Waves due to Non-static Gravitational Lenses
• Astronomical relativistic reference systems with multipolar expansion: the global one