Defocusing gravitational microlensing

Abstract. Holz & Wheeler (2002) have recently proposed that a Schwarzschild black hole may act as a retro-lens which, if illuminated by a powerful light source, deflects light ray paths to large bending angles and a series of luminous arcs (or rings in the case of aligned objects) centered on the black hole may form. Obviously, the most convenient geometry to get retrolensing images would be that of a very bright star close to a massive black hole, say the putative ∼4 × 10 6 M black hole at the galactic center. Recent observations of the galactic center region in the K-band have revealed the presence of a very bright main sequence star (labelled S2) with mass ∼15 M orbiting at close distance (130−1900 AU) from Sgr A * . The relatively vicinity of S2 to the central massive black hole may offer a unique laboratory to test the formation of retro-lensing images. The next generation of space-based telescopes in the K-band (like NGST) may have high enough limiting magnitude necessary to observe such retro-lensing images.

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“…2 A somehow related idea has been proposed by Capozziello et al (1997) who considered the effect of defocusing gravitational lensing.…”

Section: Discussionmentioning

confidence: 99%

The black hole at the galactic center as a possible retro-lens for the S2 orbiting star

Paolis

Geralico

Ingrosso

et al. 2003

A&A

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“… This constant K can be determined. At the point of closest approach to the mass (call this point r = r 0 ), the radius is at a minimum, that is d r /dφ= 0, so it follows that Thus, the path is defined by It can be easily seen that substituting u = 1/ r followed by differentiation gives the well‐known second‐order equation as (Capozziello et al 1997) …”

Section: Light Paths In a Schwarzschild Systemmentioning

confidence: 99%

“…It can be easily seen that substituting u = 1/r followed by differentiation gives the well known second order equation as (Capozziello et al (1997))…”

Section: Kinematical Approachmentioning

confidence: 99%

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

Walters

Forbes

Jarvis

2010

Monthly Notices of the Royal Astronomical Society

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This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first‐order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer‐plane caustic patterns for multiple masses.

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“…We have: (58) which reproduces, as expected, the scalar-tensor case (42). In other words, scalartensor theories can be recovered in a first order approximation of a general theory where gravity and non-minimal couplings are any (compare (57) with (46)). This fact agrees with the above considerations where Lagrangians of physical interactions are stochastic functions with local gauge invariance properties [12].…”

Section: The General Casementioning

confidence: 99%

Conformal aspects of the Palatini approach in Extended Theories of Gravity

et al. 2006

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The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account in gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of the Palatini approach which allows to distinguish between spacetime structure and geodesic structure. These facts are relevant at least at cosmological scales, while at small scale (i.e. in the spacetime regions relevant for observations) the conformal factor is slowly varying and its effects are not relevant. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frame are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.

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Defocusing gravitational microlensing

Cited by 5 publications

References 29 publications

The black hole at the galactic center as a possible retro-lens for the S2 orbiting star

The black hole at the galactic center as a possible retro-lens for the S2 orbiting star

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

Conformal aspects of the Palatini approach in Extended Theories of Gravity

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