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Motion of particles on a z=2 Lifshitz black hole background in 3+1 dimensions |
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| Authors: | Marco Olivares Yerko Vásquez J R Villanueva Felipe Moncada |
| Institution: | 1. Instituto de Física, Pontificia Universidad Católica de Valparaíso, Av. Universidad 330, Curauma, Valparaíso, Chile 2. Departamento de Física, Facultad de Ciencias, Universidad de La Serena, Av. Cisternas 1200, La Serena, Chile 3. Departamento de Ciencias Físicas, Facultad de Ingeniería y Ciencias, Universidad de La Frontera, Av. Francisco Salazar 01145, Casilla 54-D, Temuco, Chile 4. Instituto de Física y Astronomía, Universidad de Valpara íso, Gran Breta?a 1111, Playa Ancha, Valparaíso, Chile 5. Centro de Astrofísica de Valparaíso, Gran Breta?a 1111, Playa Ancha, Valparaíso, Chile |
| Abstract: | The object of study is the geodesic structure of a \(z=2\) Lifshitz black hole in 3+1 space–time dimensions, which is an exact solution to the Einstein-scalar-Maxwell theory. The motion of massless and massive particles in this background is researched using the standard Lagrangian procedure. Analytical expressions are obtained for radial and angular motions of the test particles, where the polar trajectories are given in terms of the \(\wp \) -Weierstraß elliptic function. It will be demonstrated that an external observer can see that photons with radial motion arrive at spatial infinity in a finite coordinate time. For particles with non-vanished angular momentum, the motion is studied on the invariant plane \(\phi = \pi /2\) and, it is shown that bounded orbits are not allowed for this space–time on this plane. These results are consistent with other recent studies on Lifshitz black holes. |
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