Eur. Phys. J. C (2013) 73: 2587
https://doi.org/10.1140/epjc/s10052-013-2587-3

Regular Article - Theoretical Physics

About the coordinate time for photons in Lifshitz space-times

¹ Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile
² Centro de Astrofísica de Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile
³ Departamento de Ciencias Físicas, Facultad de Ingeniería, Ciencias y Administración, Universidad de La Frontera, Avenida Francisco Salazar 01145, Casilla 54-D, Temuco, Chile
⁴ Departamento de Físicas, Facultad de Ciencias, Universidad de La Serena, Avenida Cisternas 1200, La Serena, Chile

^* e-mail: jose.villanuevalob@uv.cl

Received: 31 July 2013
Published online: 16 October 2013

Abstract

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).