Time delay of light signals in an energy-dependent spacetime metric

In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts ($z<<1$) smaller time delays than in the generic Lorentz Invariance Violating case.Comment: 5 pages. This version contains two new references with respect to the published versio

Resonance of Gravitational Axions-like Particles

The motion of gravitational axion-like particles (ALP) around a Kerr black hole is analyzed, paying attention to resonance and distribution of spectral radiation. We first discuss the computation of $\sqrt{g}{\tilde R}_{\mu \nu \rho \rho \sigma}R^{\mu \nu \rho \sigma}$ and its implications with Pontryagin's theorem and a detailed analysis of Teukolsky's master equation is done. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when $\omega \gtrsim \mu$ where $\mu$ is the mass of the ALP. A skew-normal distribution can approximate the energy distribution, and we can calculate the mean lifetime of the resonance for black holes with masses between 100 to 1000 $M_{\odot}$. This range corresponds to a duration between $10^{-1}$s and $10^{41}$s, the observation range used in LIGO data.Comment: 23 page