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Register a new userStrong Deflection Limit Lensing Effects in the Minimal Geometric Deformation and Casadio-Fabbri-Mazzacurati Solutions
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Added by
Rogerio Cavalcanti Teixeira
Publication date
2016
fields
Physics
and research's language is
English
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In this paper we apply the strong deflection limit approach to investigate the gravitational lensing phenomena beyond general relativity. This is accomplished by considering the lensing effects related to black hole solutions that emerge out of the domain of Einstein gravity, namely, the ones acquired from the method of geometric deformation and the Casadio-Fabbri-Mazzacurati brane-world black holes. The lensing observables, for those brane-world black hole metrics, are compared with the standard ones for the Schwarzschild case. We prove that brane-world black holes could have significantly different observational signatures, compared to the Schwarzschild black hole, with terms containing the post-Newtonian parameter, for the case of the Casadio-Fabbri-Mazzacurati, and terms with variable brane-world tension, for the method of geometric deformation.
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Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens object [Phys. Rev. D 102, 064060 (2020)]. We examine methods for iterative solutions of the gravitational lens equations in the strong deflection limit. It has been so far unclear whether a convergent series expansion can be provided by the gravitational lens approach based on the geometrical optics for obtaining approximate solutions in the strong deflection limit in terms of a small offset angle. By using the ratio of the lens mass to the lens distance, we discuss a slightly different method for iterative solutions and the behavior of the convergence. Finite distance effects begin at the third order in the iterative method. The iterative solutions in the strong deflection limit are estimated for Sgr $A^{*}$ and M87. These results suggest that only the linear order solution can be relevant with current observations, while the finite distance effects at the third order may be negligible in the Schwarzschild lens model for these astronomical objects.
A perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $(1-b_c/b)$ where $b$ is the impact parameter and $b_c$ is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter $l$ and the asymptotic velocity $v$ of the signal. The BH shadow size were found to decrease slightly as $l$ increase to its critical value, and increase as $v$ decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of $l$ and decrease of $v$ will increase their values.
The gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds $pi$, gravitational lensing can be analytically approximated by the so-called strong deflection limit. In this paper we remove the conventional assumption of sources very far from the black hole, considering the distance of the source as an additional parameter in the lensing problem to be treated exactly. We find expressions for critical curves, caustics and all lensing observables valid for any position of the source up to the horizon. After analyzing the spherically symmetric case we focus on the Kerr black hole, for which we present an analytical 3-dimensional description of the higher order caustic tubes.
The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions. The trace and Weyl anomalies are then employed to probe the MGD in the holographic setup, as a realistic model, playing a prominent role in AdS/CFT.
A modified Hayward black hole is a nonsingular black hole. It is proposed to form when the pressure generated by quantum gravity can stop matters collapse as the matter reaches Planck density. Strong deflection gravitational lensing happening nearby its event horizon might provide some clues of these quantum effects in its central core. We investigate observables of the strong deflection lensing, including angular separations, brightness differences and time delays between its relativistic images, and estimate their values for the supermassive black hole in the Galactic center. We find that it is possible to distinguish the modified Hayward black hole from a Schwarzschild one, but it demands very high resolution beyond current stage.
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