Analytical formulas for gravitational lensing

Amore, Paolo; Arceo, Santiago

doi:10.1103/physrevd.73.083004

Cited by 45 publications

(85 citation statements)

References 32 publications

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“…As pointed out in [26] in the Schwarzschild case, the 1/b expansion for the deflection angle does not reproduce the photon sphere singularity of the Schwarzschild metric, which is achieved using the exact GR expression in terms of elliptic function given in (8.14), but it represents nevertheless an improvement respect to the 0P N order. Expanding the RN metric in M/ρ 1 up to the third order, the 2P N approximation gives…”

Section: Post Newtonian Contributions In Classical Grmentioning

confidence: 99%

“…This has been studied quite carefully in the literature, especially in the limit of strong lensing [26,27]. The 1/b n h expansion has been shown to appear quite naturally in the post-Newtonian approach applied to the Einstein integral for light deflection.…”

Section: /B N Contributions To the Deflectionmentioning

confidence: 99%

“…In these cases the expression of the renormalized f Z form factor takes the form 25) while the W form factor is slightly lengthier 26) 3 Cross sections for photons, massive fermions and scalars…”

Section: Jhep07(2015)160mentioning

confidence: 99%

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Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions

Corianò

Costantini

Dell’Atti

et al. 2015

J. High Energ. Phys.

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We extend a previous phenomenological analysis of photon lensing in an external gravitational background to the case of a massless neutrino, and propose a method to incorporate radiative effects in the classical lens equations of neutrinos and photons. The study is performed for a Schwarzschild metric, generated by a point-like source, and expanded in the Newtonian potential at first order. We use a semiclassical approach, where the perturbative corrections to neutrino scattering, evaluated at one-loop in the Standard Model, are compared with the Einstein formula for the deflection using an impact parameter formulation. For this purpose, we use the renormalized expression of the graviton/fermion/fermion vertex presented in previous studies. We show the agreement between the classical and the semiclassical formulations, for values of the impact parameter b h of the neutrinos of the order of b h ∼ 20, measured in units of the Schwarzschild radius. The analysis is then extended with the inclusion of the post Newtonian corrections in the external gravity field, showing that this extension finds application in the case of the scattering of a neutrino/photon off a primordial black hole. The energy dependence of the deflection, generated by the quantum corrections, is then combined with the standard formulation of the classical lens equations. We illustrate our approach by detailed numerical studies, using as a reference both the thin lens and the Virbhadra-Ellis lens.

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Section: Post Newtonian Contributions In Classical Grmentioning

confidence: 99%

Section: /B N Contributions To the Deflectionmentioning

confidence: 99%

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Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions

Corianò

Costantini

Dell’Atti

et al. 2015

J. High Energ. Phys.

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“…The method provides several advantages over other well established methods in the literature: first of all, to the best of our knowledge our method is the only nonperturbative method which allows to obtain fully analytical results and for which the exponential convergence of the series is proved ( [6,7,8]); secondly, previous work done in [6,7,8], where the method was used to calculate the period (and not the solution) has shown that our method can be used for a quite large of class of potentials, even in cases where the exact result cannot be obtained; finally it is easy to calculate higher order contributions (never involving special functions) with our method.…”

Section: Discussionmentioning

confidence: 99%

“…While other techniques are been developed in the literature to deal with this problem, see for example [1,2], we wish to present a novel method which was recently devised by one of us [6,7,8] and which allows one to calculate accurate analytical solutions for a classical oscillator, described by Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

Development of accurate solutions for a classical oscillator

Amore

Sanchez

2007

Journal of Sound and Vibration

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Electroweak corrections to photon scattering, polarization and lensing in a gravitational background and the near horizon limit

Corianò

Rose

Maglio

et al. 2015

J. High Energ. Phys.

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We investigate the semiclassical approach to the lensing of photons in a spherically symmetric gravitational background, starting from Born level and include in our analysis the radiative corrections obtained from the electroweak theory for the graviton/photon/photon vertex. In this approach, the cross section is related to the angular variation of the impact parameter (b), which is then solved for b as a function of the angle of deflection, and measured in horizon units (b h ≡ b/(2GM )). Exact numerical solutions for the angular deflection are presented. The numerical analysis shows that perturbation theory in a weak background agrees with the classical Einstein formula for the deflection already at distances of the order of 20 horizon units (∼ 20 b h ) and it is optimal in the description both of very strong and weak lensings. We show that the electroweak corrections to the cross section are sizeable, becoming very significant for high energy gamma rays. Our analysis covers in energy most of the photon spectrum, from the cosmic microwave background up to very high energy gamma rays, and scatterings with any value of the photon impact parameter. We also study the helicity-flip photon amplitude, which is of O(α 2 ) in the weak coupling α, and its massless fermion limit, which involves the exchange of a conformal anomaly pole. The corresponding cross section is proportional to the Born level result and brings to a simple renormalization of Einsten's formula.

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Analytical formulas for gravitational lensing

Cited by 45 publications

References 32 publications

Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions

Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions

Development of accurate solutions for a classical oscillator

Electroweak corrections to photon scattering, polarization and lensing in a gravitational background and the near horizon limit

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