Abstract
We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the ‘photon-sphere’ and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass.
Highlights
Can address the extension to the rotating case
We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the fivedimensional solution
In view of the fuzz-ball proposal [25,26,27,28,29,30,31], according to which the microstates of BHs should be represented by smooth horizonless geometries, we focus on BH geometries or singular metrics with the latter lifting to a regular six-dimensional JMaRT geometry [24]
Summary
We describe the general solution of Einstein-Maxwell theory with three Killing symmetries in five dimensions and Lagrangian. Solutions along the blue wedge/wing-like surfaces outside the middle rectangle represents over-rotating geometries where rs2ing(θ) < r+2 < 0. Mind that both the singularity and the horizon, outside the central BH region, are generally hidden behind a smooth cap characterized by the vanishing of a space-like (rather than time-like) Killing vector.. For the special BPS case Q = M (BMPV solution) they have been thoroughly explored in [34] It is not in the interest of this work to study the geodesic structure of the more general CCLP geometries, which has been tackled in [35, 36]. For 2 < M, this is an event horizon and the BH is known as the BMPV BH after Breckenridge, Myers, Peet and Vafa [37]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
