Preprint Article Version 1 This version is not peer-reviewed

Analysis of the Angular Dependence of Time Delay in Gravitational Lensing

Version 1 : Received: 30 May 2018 / Approved: 31 May 2018 / Online: 31 May 2018 (11:43:05 CEST)

A peer-reviewed article of this Preprint also exists.

Alchera, N.; Bonici, M.; Cardinale, R.; Domi, A.; Maggiore, N.; Righi, C.; Tosi, S. Analysis of the Angular Dependence of Time Delay in Gravitational Lensing. Symmetry 2018, 10, 246. Alchera, N.; Bonici, M.; Cardinale, R.; Domi, A.; Maggiore, N.; Righi, C.; Tosi, S. Analysis of the Angular Dependence of Time Delay in Gravitational Lensing. Symmetry 2018, 10, 246.

Journal reference: Symmetry 2018, 10, 246
DOI: 10.3390/sym10070246

Abstract

We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom of the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in view of softening the known discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.

Subject Areas

gravitational lenses; hubble constant; cosmology

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