About the coordinate time for photons in Lifshitz Space-times

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 {\bf 73}, 7 (2013)], Olivares et. al. [Astrophys. Space Sci. {\bf 347}, 83-89 (2013)], and Olivares et. al. [arXiv: 1306.5285]. We demonstrate that all asymptotically Lifshitz space-times characterized by a lapse funcion $f(r)$ which tends to one when $r\to \infty$, 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 $r_{+}<r<\infty$, because the proper time results to be independent of the lapse function $f(r)$.

5 pages, 4 figures, accepted for publication on EPJC

References in corpus (1)

• Particles motion on topological Lifshitz black holes in 3+1 dimensions

Cited by in corpus (10)

• Photon spheres in Einstein and Einstein-Gauss-Bonnet theories and circular null geodesics in axially-symmetric spacetimes
• Photons trajectories on a first order scale-dependent static BTZ black hole
• Null paths on a toroidal topological black hole in conformalWeyl gravity
• Scalar field perturbations of a Lifshitz black hole in conformal gravity in three dimensions
• Massive neutral particles on heterotic string theory
• Motion and trajectories of photons in a three-dimensional rotating Hořava AdS black hole
• Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory
• Motion of particles on a $z=2$ Lifshitz black hole in 3+1 dimensions
• Null geodesics in five-dimensional Reissner-Nordström anti-de Sitter black hole
• Kasner-type singularities and solitons with Lifshitz asymptotics