Gravitational Lensing of Massive Particles in the Charged NUT Spacetime

Abstract

In astronomy, gravitational lensing of light leads to the formation of multiple images, arcs, Einstein rings, and, most important, the shadow of black holes. Analogously in the vicinity of a massive compact object massive particles, following timelike geodesics, are gravitationally lensed. So far gravitational lensing of massive particles was mainly investigated in the weak and strong field limits. In this paper we will, for the first time, investigate exact gravitational lensing of massive particles using the example of the charged Newman-Unti-Tamburino (NUT) metric (and its special cases) which contains three physical parameters, the mass parameter $m$, the electric charge $e$, and the gravitomagnetic charge $n$. We will first discuss and solve the equations of motion for unbound timelike geodesics using elementary and Jacobi's elliptic functions and Legendre's elliptic integrals. Then we will introduce an orthonormal tetrad to relate the $z$ component of the angular momentum and the Carter constant to the energy $E$ of the particles along the timelike geodesics and latitude-longitude coordinates on the celestial sphere of a stationary observer in the domain of outer communication. We will use these relations to derive the angular radius of the particle shadow of the black hole, to formulate an exact lens equation, and to derive the travel time of the particles in terms of the time coordinate and the proper time. Finally, we will discuss the impact of the physical parameters and the energy of the particles on observable lensing features. We will also comment on how we can use these features alone and in a multimessenger context together with the corresponding features for light rays to determine if an astrophysical black hole can be described by the charged NUT metric or one of its special cases.

arXiv comment55 pages, 16 figures, journal version with three minor typos corrected; extends parts of the work in arXiv:2112.10260 to massive particles

References in corpus (42)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector
• A Measurement of Atmospheric Neutrino Oscillation Parameters by Super-Kamiokande I
• Gravitational lensing in the strong field limit
• The geometry of photon surfaces
• First Year Performance of The IceCube Neutrino Telescope
• Photon Regions and Shadows of Kerr-Newman-NUT Black Holes with a Cosmological Constant
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Neutrino masses and cosmology with Lyman-alpha forest power spectrum
• On the exact gravitational lens equation in spherically symmetric and static spacetimes
• Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra
• Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment
• Light propagation in a plasma on Kerr spacetime: Separation of the Hamilton-Jacobi equation and calculation of the shadow
• Neutrino oscillations in curved spacetime: an heuristic treatment
• Detection of a particle shower at the Glashow resonance with IceCube
• Photon Regions and Shadows of Accelerated Black Holes
• The Null Geodesics of the Kerr Exterior
• Gravitational Effects on the Neutrino Oscillation
• Physics Potentials with the Second Hyper-Kamiokande Detector in Korea
• Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
• What does a binary black hole merger look like?
• Rehabilitating space-times with NUTs
• Gravitational lensing of massive particles in Reissner-Nordström spacetime
• An Exact Universal Gravitational Lensing Equation
• Physical interpretation of NUT solution
• NUT wormholes
• PINGU: A Vision for Neutrino and Particle Physics at the South Pole
• Gravitational lensing of massive particles in Schwarzschild gravity
• YNOGK: A new public code for calculating null geodesics in the Kerr spacetime
• Neutrino Interferometry In Curved Spacetime
• Unbound motion of massive particles in the Schwarzschild metric: Analytical description in case of strong deflection
• Circular motion in NUT space-time
• Signature of neutrino mass hierarchy in gravitational lensing
• Black hole interference patterns in flavour oscillations
• Spin effects in neutrino gravitational scattering
• Application of the Gauss-Bonnet theorem to lensing in the NUT metric
• Time delay of timelike particles in gravitational lensing of Schwarzschild spacetime
• Bose-Einstein Condensates in Charged Black-Hole Spacetimes
• Gravitational Lensing in the Charged NUT-de Sitter Spacetime
• Gravitational lensing in Brill spacetimes

Cited by in corpus (5)

• Gravitational lensing of massive particles by a black-bounce-Schwarzschild black hole
• Strong deflection of massive particles in spherically symmetric spacetimes
• Gravitational Lensing in the Kerr Spacetime: An Analytic Approach for Light and High-Frequency Gravitational Waves
• Strong field gravitational lensing of particles by a black-bounce-Schwarzschild black hole
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime