Photon spheres in Einstein and Einstein-Gauss-Bonnet theories and circular null geodesics in axially-symmetric spacetimes

In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically symmetric black holes. As applications of these results we give a universal upper bound for the real part of quasinormal modes in the WKB limit and a universal lower bound for the position of the first relativistic image in the strong lensing regime produced by these type of black holes. For the axially-symmetric case, we also make some general comments (independent of the underlying gravitational theory) on the relation between circular null geodesics and the fastest way to circle a black hole.Comment: In this post-publisher version two typos were corrected: the signature of the metric in eq.(1) and a factor in eq.(102). We thanks Gary Gibbons and Chris Pope for bringing to our attention these typo

About the coordinate time for photons in Lifshitz Space-times

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 $r\rightarrow \infty$, 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 $f(r)$.Comment: 5 pages, 4 figures, accepted for publication on EPJ

Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

Properties of the motion of electrically charged particles in the background of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is presented in this paper. Radial and angular motion are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analysed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys. Rev. D 85: 024033, 2012), Olivares & Villanueva (Eur. Phys. J. C 73: 2659, 2013) and Blaga (Automat. Comp. Appl. Math. 22, 41 (2013); Serb. Astron. J. 190, 41 (2015)) for time-like geodesics.Comment: 11 pages, 12 figure

A Jacobian elliptic single-field inflation

In the scenario of single-field inflation, this field is done in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analysed using the Hamilton-Jacobi approach and then, the main results are contrasted with the recent measurements obtained from the Planck 2015 data.Comment: 7 pages, 5 figure

Massive neutral particles on heterotic string theory

The motion of massive particles in the background of a charged black hole in heterotic string theory, which is characterized by a parameter $\alpha$, is studied in detail in this paper. Since it is possible to write this space-time in the Einstein frame, we perform a quantitative analysis of the time-like geodesics by means of the standard Lagrange procedure. Thus, we obtain and solve a set of differential equations and then we describe the orbits in terms of the elliptic $\wp$-Weierstra{\ss} function. Also, by making an elementary derivation developed by Cornbleet (Am. J. Phys. \textbf{61} 7, (1993) 650 - 651) we obtain the correction to the angle of advance of perihelion to first order in $\alpha$, and thus, by comparing with Mercury's data we give an estimation for the value of this parameter, which yields an {\it heterotic solar charge} $Q_{\odot}\simeq 0.728\,[\textrm{Km}]= 0.493\, M_{\odot}$. Therefore, in addition to the study on null geodesics performed by Fernando (Phys. Rev. D {\bf 85}, (2012) 024033), this work completes the geodesic structure for this class of space-time.Comment: 12 pages, 8 figures. Accepted for publication on EPJ