Math @ Duke

Publications [#244002] of Arlie O. Petters
Papers Published
 Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects: Static, spherically symmetric case,
Physical Review D, vol. 72 no. 10
(2005),
pp. 104006, ISSN 15507998 [0511019], [doi]
(last updated on 2018/10/21)
Abstract: We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weakdeflection limit. In this paper we present the formalism for computing corrections to lensing observables for static, spherically symmetric gravity theories in which the corrections to the weakdeflection limit can be expanded as a Taylor series in one parameter, namely, the gravitational radius of the lens object. We take care to derive coordinateindependent expressions and compute quantities that are directly observable. We compute series expansions for the observables that are accurate to second order in the ratio ε= •/ E of the angle subtended by the lens's gravitational radius to the weakdeflection Einstein radius, which scales with mass as ε M•1/2. The positions, magnifications, and time delays of the individual images have corrections at both first and second order in ε, as does the differential time delay between the two images. Interestingly, we find that the firstorder corrections to the total magnification and centroid position vanish in all gravity theories that agree with general relativity in the weakdeflection limit, but they can remain nonzero in modified theories that disagree with general relativity in the weakdeflection limit. For the ReissnerNordström metric and a related metric from heterotic string theory, our formalism reveals an intriguing connection between lensing observables and the condition for having a naked singularity, which could provide an observational method for testing the existence of such objects. We apply our formalism to the galactic black hole and predict that the corrections to the image positions are at the level of 10μarcs (microarcseconds), while the correction to the time delay is a few hundredths of a second. These corrections would be measurable today if a pulsar were found to be lensed by the galactic black hole, and they should be readily detectable with planned missions like MAXIM. © 2005 The American Physical Society.


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