Gravitational Capture Cross-Section of Particles by Schwarzschild-Tangherlini Black Holes

Round 1

Reviewer 1 Report

In the refereeing paper, the authors study the capture cross-section of massless and massive classical particles by the higher-dimensional (D>4) Schwarzschild-Tangherlini black hole. Though being rather academic and technically simple, this topic is still of sufficient interest. However, it seems that the authors are completely unaware of many previous papers in which geodesics in the Schwarzschild-Tangherlini space-time were studied and where many of their results have been already obtained, especially regarding massless particles, and in a more general form. For brevity, I present here archive references only: gr-qc/9405067, 0804.4112, 1002.0121, 1104.3285, 1208.0168,`1402.6823, 1707.07125, 1909.07298, 2008.00179. Regarding 1707.07125, let me note that the black-hole shadow and the capture of massless particles by a black hole represent the same mathematical problem with the same result for the area of the shadow and the capture cross-section, it is only physical interpretation of the result obtained that is different. Thus, I suppose that the authors have to study these papers, cite them and explain which of their own results are new. So, the paper needs major revision.

Author Response

We would like to thank the Referee for his/her comments that
surely improved the quality of the paper. Indeed, in previous original
version of the manuscript we had left several very relevant
references and some of them are indicated by the Referee as unmentioned. We
have looked through that papers and found majority of them very relevant to
our research performed. Most of them are about the capture of massless particle
(photon) by the Schwarzschild-Tangherlini black holes. In the
paper we presented extended results on the capture of photon by
the Schwarzschild-Tangherlini black hole by including the angle between the radial  coordinate and propagation direction of photon to escape from (be
captured by) the black hole. Moreover, we studied the capture of
massive particle by the Schwarzschild-Tangherlini black hole for the non-relativistic and relativistic particles.

Since the recommended references are mainly about the topics and
the formalism, we included new paragraph in Introduction of the
paper, by giving brief details on each of them. Moreover, in order
to explain the topic comprehensively, we included a few more additional
references. We think that the revised version of the manuscript
addresses the point raised by Referee and we hope that the paper
can now be considered suitable for publication in the Universe journal.

Reviewer 2 Report

Authors elucidate in details the capture cross section of massless and massive test particles in the gravitational field of the Schwarzschild-Tangherlini black hole. The main result of the paper is the calculation of the capture cross section of test relativistic and non-relativistic particles in the higher dimensions and demonstration that an extra dimension weakens the gravitational attraction of black hole. Respectively, in the higher dimensions the radii of all characteristic circular orbits decrease in comparison with the standard 4 dimensional space-time. Additionally, it is demonstrated that in higher dimensions there is no stable and bounded circular orbits. All these results are new and interesting. This paper, in spite of some formal presentation, may be interesting for a wide scientific community in view of the fundamental importance of the physical properties of the enigmatic black holes. The manuscript is well organized, clearly written and may be published as it is. I recommend to publish this paper in Universe.

Author Response

Dear Reviewer,

Thank you very much for your positive report and your kind recommendation to publish our paper in the Unverse journal.

Best wishes,

The authors

Round 2

Reviewer 1 Report

No more comments, the paper can be accepted now.