Details
| Original language | English |
|---|---|
| Article number | 124019 |
| Journal | Physical Review D |
| Volume | 108 |
| Issue number | 12 |
| Publication status | Published - 7 Dec 2023 |
| Externally published | Yes |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Physical Review D, Vol. 108, No. 12, 124019, 07.12.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Gravitational lensing of massive particles in the charged NUT spacetime
AU - Frost, Torben C.
N1 - Publisher Copyright: © 2023 American Physical Society.
PY - 2023/12/7
Y1 - 2023/12/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85179815885&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.108.124019
DO - 10.1103/PhysRevD.108.124019
M3 - Article
AN - SCOPUS:85179815885
VL - 108
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 12
M1 - 124019
ER -