Lightlike Geodesics and Gravitational Lensing in the Spacetime of an Accelerating Black Hole

Abstract

The C-metric is a solution to Einstein's vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and the resulting lensing features in this metric. We first solve the lightlike geodesic equation using elliptic integrals and Jacobi elliptic functions. Then we fix a static observer in the region of outer communication of the C-metric and introduce an orthonormal tetrad to parameterise the directions of the light rays ending at the position of the observer using latitude-longitude coordinates on the observer's celestial sphere. In this parameterisation we rederive the angular radius of the shadow, we formulate a lens equation, and we derive the redshift and the travel time of light rays. We discuss the relevance of our theoretical results for detecting accelerating black holes described by the C-metric and for distinguishing them from non-accelerating black holes.

37 pages, 13 figures; updated and added new references, corrected typos, minor changes and additions in the text, (e.g., black holes in uniform motion, brief discussion of accelerating black holes with NUT charge, extended discussion of the shadow), modified figure fonts

References in corpus (13)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• RadioAstron -- a Telescope with a Size of 300 000 km: Main Parameters and First Observational Results
• Lensing by Kerr Black Holes
• Interpreting the C-metric
• What does a binary black hole merger look like?
• Radiation from accelerated black holes in an anti-de Sitter universe
• Aspherical Photon and Anti-Photon Surfaces
• A Two-Year Time Delay for the Lensed Quasar SDSS J1029+2623
• Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions
• Accelerating NUT black holes
• Geodesic motion in the vacuum C-metric
• Null geodesics in the C-metric with cosmological constant
• On the nature of cosmic strings in black hole spacetimes

Cited by in corpus (20)

• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Charged Accelerating BTZ black holes
• Accelerating AdS black holes in gravity's rainbow
• Quasinormal modes and stability of boosted Reissner-Nordström AdS black holes
• Gravitational lensing of massive particles by a black-bounce-Schwarzschild black hole
• Distinguishing a Slowly Accelerating Black Hole by Differential Time Delays of Images
• Null geodesics in the C-metric with cosmological constant
• Lensing Signatures of a Slowly-Accelerated Black Hole
• Exact wave-optical imaging of a Kerr-de Sitter black hole using Heun's equation
• Gravitational Lensing in the Charged NUT-de Sitter Spacetime
• Three-dimensional accelerating AdS black holes in $F(R)$ gravity
• Relevant scales for the $C$-metric with positive cosmological constant
• Timelike orbits around accelerating black holes
• Magnetised relativistic accretion disc around a spinning, electrically charged, accelerating black hole: case of C-metric
• Observational appearance of Kaluza-Klein black holes
• On the Black Hole Acceleration in the C-metric Space-time
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity
• Null integrability and photon phenomenology in the accelerated Schwarzschild black hole
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime
• Gravitational Lensing by Charged Accelerating Black Holes