Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity

TL;DR

This paper develops an analytical formalism for black hole lensing in braneworld gravity, highlighting wave optics as a key observational tool to detect or constrain extra-dimensional effects through interference fringes in gamma-ray spectra.

Contribution

It introduces the first comprehensive analysis of wave optics in braneworld black hole lensing, providing a method to detect extra-dimensional effects via interference fringes in gamma-ray observations.

Findings

Wave optics can reveal braneworld effects in black hole lensing.

Primordial braneworld black holes could produce observable interference fringes.

Detection of fringes could constrain black hole mass and test gravity theories.

Abstract

Braneworld gravity is a model that endows physical space with an extra dimension. In the type II Randall-Sundrum braneworld gravity model, the extra dimension modifies the spacetime geometry around black holes, and changes predictions for the formation and survival of primordial black holes. We develop a comprehensive analytical formalism for far-field black hole lensing in this model, using invariant quantities to compute all geometric optics lensing observables. We then make the first analysis of wave optics in braneworld lensing, working in the semi-classical limit. We show that wave optics offers the only realistic way to observe braneworld effects in black hole lensing. We point out that if primordial braneworld black holes exist, have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which we call "attolenses," would produce interference fringes in the energy spectra of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the universe could produce similar interference effects; the probability for "attolensing" may be non-negligible. If interference fringes were observed, the fringe spacing would yield a simple upper limit on M. Detection of a primordial black hole with M <~ 1e-19 Msun would challenge general relativity and favor the braneworld model. Further work on lensing tests of braneworld gravity must proceed into the physical optics regime, which awaits a description of the full spacetime geometry around braneworld black holes.