About the coordinate time for photons in Lifshitz space-times
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In this paper we studied the behavior of radial photons from the point of view of the coordinate time in (asymptotically) Lifshitz space-times, and we found a generalization to the result reported in previous works by Cruz et al. (Eur. Phys. J. C 73:7, 2013), Olivares et al. (Astrophys. Space Sci. 347:83–89, 2013), and Olivares et al. (arXiv:1306.5285). We demonstrate that all asymptotically Lifshitz space-times characterized by a lapse function f(r) which tends to one when r→∞, present the same behavior, in the sense that an external observer will see that photons arrive at spatial infinity in a finite coordinate time. Also, we show that radial photons in the proper system cannot determine the presence of the black hole in the region r +<r<∞, because the proper time as a result is independent of the lapse function f(r).
KeywordsBlack Hole Event Horizon Proper Time Coordinate Time Massless Particle
YV is supported by FONDECYT grant 11121148; JRV thanks the UFRO for their hospitality and dedicates this work to JGDVB on his 10th birthday.