Derives a factorized leading term for the strong deflection angle near degenerate photon spheres using local expansion of the effective potential and Weyl tensor measures.
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Gravitational lensing in the strong field limit
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abstract
We provide an analytic method to discriminate among different types of black holes on the ground of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighbourhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild, Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the coefficients characterizing these metrics and find that different collapsed objects are characterized by different strong field limits. The strong field limit coefficients are directly connected to the observables, such as the position and the magnification of the relativistic images. As a concrete example, we consider the black hole at the centre of our galaxy and estimate the optical resolution needed to investigate its strong field behaviour through its relativistic images.
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gr-qc 9representative citing papers
A conformal isothermal reformulation of optical geometry converts the Gauss-Bonnet area term for weak deflection into boundary integrals evaluated on a flat reference ray, reproducing known finite-distance results for Schwarzschild, Reissner-Nordström, and Kottler spacetimes.
In dRGT massive gravity, static spherically symmetric black holes exhibit zero, one, or two photon spheres whose topological charges and stability patterns differ from Einstein gravity and from horizonless compact objects.
A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.
Corotating point sources on accretion disks near black holes distort the relative magnification factor distribution, modulating caustics and encoding accretion flow kinematics via time-delayed images.
For a cubic-plus-quartic curvature EFT, photon-sphere and strong-lensing observables shift at first order in the couplings, but the impact-parameter formula is dimensionally wrong and the gravitational-wave QNM prediction is unproven.
Higher-curvature corrections induce polarization-dependent effective metrics for photons that shift photon spheres, alter eikonal quasinormal modes, and modify deflection angles in static spherically symmetric backgrounds.
Perturbative f(R,G) corrections shift the photon-sphere radius and shadow size, with the Gauss-Bonnet term dominating over mixed curvature contributions.
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Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity
Perturbative f(R,G) corrections shift the photon-sphere radius and shadow size, with the Gauss-Bonnet term dominating over mixed curvature contributions.