Redshift of a photon emitted along the black hole horizon

Abstract

In this work we derive some general features of the redshift measured by radially moving observers in the black hole background. Let observer 1 cross the black hole horizon emitting of a photon while observer 2 crossing the same horizon later receives it. We show that if (i) the horizon is the outer one (event horizon) and (ii) it is nonextremal, received frequency is redshifted. This generalizes previous recent results in literature. For the inner horizon (like in the Reissner-Nordström metric) the frequency is blueshifted. If the horizon is extremal, the frequency does not change. We derive explicit formulas describing the frequency shift in generalized Kruskal- and Lemaitre-like coordinates.

arXiv comment17 pages, no figures. Minor corrections, matches published version

References in corpus (5)

• Kerr Black Holes as Particle Accelerators to Arbitrarily High Energy
• Collision of an innermost stable circular orbit particle around a Kerr black hole
• The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes
• Nonthermal nature of incipient extremal black holes
• Acceleration of particles near the inner black hole horizon

Cited by in corpus (6)

• Free-falling test particles in a charged Kalb-Ramond black hole: gravitational Doppler effect and tidal forces
• Kinematic censorship as a constraint on allowed scenarios of high energy particle collisions
• Unified approach to redshift in cosmological /black hole spacetimes and synchronous frame
• Redshift/blueshift inside the Schwarzschild black hole
• On strategies of motion under the black hole horizon
• Dynamics of redshift/blueshift during free fall under the Schwarzschild horizon