Scattering and absorption of electromagnetic waves by a Schwarzschild black hole

Fabbri, R.

doi:10.1103/physrevd.12.933

Cited by 63 publications

(69 citation statements)

References 18 publications

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“…For small angles, this scattering cross section is the same for the massless scalar and electromagnetic fields, and it is given by [13,14] …”

Section: Arxiv:09053339v1 [Gr-qc] 20 May 2009mentioning

confidence: 99%

“…For Schwarzschild black holes, the phase shifts of the two different physical polarizations are the same, i. e. δ [14]. The differential electromagnetic scattering cross section is [24] …”

Section: Arxiv:09053339v1 [Gr-qc] 20 May 2009mentioning

confidence: 99%

“…Fermion (s = 1/2) scattering by a Schwarzschild black hole was the subject of a recent study [4], in which the authors also elucidated the effect of non-zero field mass. The case of electromagnetic waves (s = 1) was studied analytically by Mashoon [13] and Fabbri [14], and some results were obtained in the low-and high-frequency limits. Gravitational waves (s = 2) were the first to be studied in black hole scattering [15], and are the subject of old [5,16] and new [17,18] works.…”

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Electromagnetic Wave Scattering by Schwarzschild Black Holes

2009

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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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“…For small angles, this scattering cross section is the same for the massless scalar and electromagnetic fields, and it is given by [13,14] …”

Section: Arxiv:09053339v1 [Gr-qc] 20 May 2009mentioning

confidence: 99%

“…For Schwarzschild black holes, the phase shifts of the two different physical polarizations are the same, i. e. δ [14]. The differential electromagnetic scattering cross section is [24] …”

Section: Arxiv:09053339v1 [Gr-qc] 20 May 2009mentioning

confidence: 99%

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confidence: 99%

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Electromagnetic Wave Scattering by Schwarzschild Black Holes

2009

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“…We see that entropy considerations dictate the outcome of physical processes around black holes. The detailed physical mechanism involved has to be explored in the scope of scattering problems in the Schwarzschild space-time, as it has been done in the past by several authors [4][5][6][7], however entropy constrains offer qualitative indications of the results to be expected. The results of [4] already point to an upper limit for the wavelength of an EM wave above which absorption by a black hole strongly decreases, of order R S .…”

Section: Motivationmentioning

confidence: 99%

“…The detailed physical mechanism involved has to be explored in the scope of scattering problems in the Schwarzschild space-time, as it has been done in the past by several authors [4][5][6][7], however entropy constrains offer qualitative indications of the results to be expected. The results of [4] already point to an upper limit for the wavelength of an EM wave above which absorption by a black hole strongly decreases, of order R S . We note that past studies of the interaction between waves and black holes which identify upper critical wavelengths, typically fall within the scope of WKB approximations, where monochromatic waves are assumed to remain as such.…”

Section: Motivationmentioning

confidence: 99%

The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields

Mendoza

Hernández

Rendón

et al. 2009

Entropy

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We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than R s , in the vicinity of R s . As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent 'particle' description fails, and the wave nature becomes apparent.

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