Electromagnetic radiation from circular orbits in Schwarzschild--de Sitter spacetime

TL;DR

This work analyzes electromagnetic radiation from a charged particle on circular orbits around Schwarzschild--de Sitter black holes within a semiclassical quantum-field-theory framework. By quantizing the electromagnetic field in the static SdS region in a modified Feynman gauge and computing the one-photon emission amplitude, the authors derive discrete emission frequencies $\\omega_m= m\\Omega$ and separate power contributions for the two photon polarizations. They compare the total and spectral power to scalar-field results for minimal and conformal couplings, finding that at low $\\Omega$ the EM power is about twice the conformal-scalar power but can be surpassed by minimally coupled scalar radiation; near the photon sphere the EM power dominates and spectra are broader with significant low-multipole contributions. The results illuminate how the cosmological constant and coupling choices shape radiative signatures, offering insights for extreme mass-ratio inspirals in de Sitter-like spacetimes and motivating future extensions to massive fields.

Abstract

We investigate the electromagnetic radiation emitted by a charged particle orbiting a four-dimensional Schwarzschild--de Sitter black hole using a semiclassical approach. We calculate the probability amplitude for the charged particle to emit a photon, from which we derive the emitted power and spectral distributions. The results are compared with those obtained for scalar fields, considering both minimal and nonminimal coupling, as well as the corresponding electromagnetic case in the Schwarzschild spacetime. It is found that the total electromagnetic power is approximately twice that of the scalar field with conformal coupling for orbits with low angular velocity, similar to the Schwarzschild case, whereas for minimal coupling, the scalar power can even exceed the electromagnetic power. We also investigate the spectral distributions and possible synchrotron emission by orbits near the photon sphere. The electromagnetic case has a much broader frequency spectrum, with a non-negligible lower multipole contribution.

Figures (10)

• Figure 1: Total emitted power, given by Eq. \ref{['tot_power']}, for electromagnetic (red), minimally coupled scalar (purple), and conformally coupled scalar (blue) fields as a function of $M\Omega$, for $M^2 \Lambda = 0$ (left) and $M^2 \Lambda = 15^{-1}$ (right). The results are presented for three values of the maximum multipole number, $\ell_{\text{max}}=5,10,20$.
• Figure 2: Ratio of the total emitted power of the electromagnetic field to that of the minimally coupled scalar field in SdS spacetime with $M^2 \Lambda = 15^{-1}$.
• Figure 3: Ratio of the total emitted power of the electromagnetic field to that of the conformally coupled scalar field in SdS spacetime with $M^2 \Lambda = 15^{-1}$.
• Figure 4: Ratio of the total emitted power of the electromagnetic field to that of the scalar field in Schwarzschild spacetime.
• Figure 5: Relative contributions of the $\lambda= I$ and $\lambda=I\!I$ photon polarizations to the total emitted power.