Electromagnetic Wave Scattering by Schwarzschild Black Holes

Abstract

We analyze the scattering of a planar monochromatic electromagnetic wave incident upon a Schwarzschild black hole. We obtain accurate numerical results from the partial wave method for the electromagnetic scattering cross section, and show that they are in excellent agreement with analytical approximations. The scattering of electromagnetic waves is compared with the scattering of scalar, spinor and gravitational waves. We present a unified picture of the scattering of all massless fields for the first time.PACS numbers: 04.40.-b, 04.70.-s, 11.80.-m Black holes are thought to be efficient catalysts for the liberation of rest-mass energy. As such, black holes are implicated in the most energetic phenomena in the known universe (e.g. gamma ray bursts). On the other hand, after a turbulent youth, many black holes settle into a quiescent old age. Some estimates suggest there may be up to a billion quiescent stellar-mass black holes within our galaxy [1]. Their existence may be inferred from, for example, the transient lensing of background sources; a handful of events have so far been observed [2]. A possibility for future consideration is that quiescent black holes may be indirectly identified from the 'fingerprint' they leave on radiation that impinges upon them.Over the last four decades, some clues about the properties of any such 'fingerprint' have been uncovered. For example, a time-dependent perturbation incident upon a black hole will excite characteristic damped ringing in response. The frequencies and decay rates of the ringing are linked to the well-studied quasinormal mode spectrum [3]. Black holes illuminated by long-lasting planar radiation will create interference patterns, and rotating black holes will create distinctive polarization patterns [4]. Both effects depend strongly on the ratio of horizon size to wavelength. Hence, it is conceivable that future gravitational-wave detectors may be able to identify the fingerprint from rapid and distinctive variations across a narrow frequency band. Nevertheless, inferring the presence of quiescent black holes from such clues must remain a challenge for future decades.Scattering by black holes is of foundational interest in both black hole physics [5] and scattering theory [6]. Many authors have studied the simplest timeindependent scenario, in which a black hole is subject to a long-lasting, monochromatic beam of radiation. Here, the key dimensionless quantity is the ratio r h /λ where r h is the horizon size of the black hole, and λ is the wavelength of the incident wave. The interference pattern depends also on the spin s of the perturbing field, with s = 0, 1/2, 1 and 2 corresponding to scalar, neutrino, electromagnetic and gravitational fields, respectively.To the best of our knowledge, the first paper outlining a calculation of wave scattering cross section in the spacetime of a black hole was published by Matzner [7] in the late sixties. Since then, planar wave scattering from black holes has received much attention, especially in Schwarzschild and...

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