Formalism for testing theories of gravity using lensing by compact objects. III. Braneworld gravity
Abstract
Braneworld gravity is a model that endows physical space with an extra dimension. In the type II RandallSundrum 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 farfield black hole lensing in this model, using invariant quantities to compute all the geometric optics lensing observables: bending angle, image position, magnification, centroid, and time delay. We then make the first analysis of wave optics in braneworld lensing, working in the semiclassical limit. Through quantitative examples 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_{bh} of the dark matter, then roughly ∼3×10^{5}×f_{bh}(M_{•}/10^{18}M_{⊙})^{1} of them lie within our Solar System. These objects, which we call “attolenses,” would produce interference fringes in the energy spectra of gammaray bursts at energies E∼100(M_{•}/10^{18}M_{⊙})^{1}MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the Universe could produce similar interference effects. If they contribute a fraction Ω_{•} of the total energy density, the probability that gammaray bursts are “attolensed” is at least ∼0.1Ω_{•}. If observed, attolensing interference fringes would yield a simple upper limit on M_{•}. Detection of a primordial black hole with M_{•}≲10^{19}M_{⊙} 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.
 Publication:

Physical Review D
 Pub Date:
 May 2006
 DOI:
 10.1103/PhysRevD.73.104032
 arXiv:
 arXiv:grqc/0603061
 Bibcode:
 2006PhRvD..73j4032K
 Keywords:

 04.70.Bw;
 04.50.+h;
 04.80.Cc;
 Classical black holes;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Experimental tests of gravitational theories;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 13 pages, 3 figures