Retrolensing by a wormhole at deflection anglesπand3π

Abstract

The deflection angle of a light ray can be arbitrarily large near a light sphere. The timesymmetrical shape of light curves of a pair of light rays reflected by a light sphere of a lens object does not depend on the details of the lens object. We consider retrolensing light curves of sunlight with deflection angles π and 3π by an Ellis wormhole, which is the simplest MorrisThorne wormhole. If an Ellis wormhole with a throat parameter a = 10 11 km is 100 pc away from an observer and if the Ellis wormhole, the observer, and the sun are aligned perfectly in this order, the apparent magnitudes of a pair of light rays with deflection angles π and 3π become 11 and 18, respectively. The two pairs of light rays make a superposed light curve with two separable peaks and they break down time symmetry of a retrolensing light curve. The observation of the two separated peaks of the light curves gives us information on the details of the lens object. If the observer can also separate the pair of the images with the deflection angle π into a double image, he or she can say whether the retrolensing is caused by an Ellis wormhole or a Schwarzschild black hole. * tsukamoto@rikkyo.ac.jp

Gravitational lensing by a Horndeski black hole

“…[10], in order to approximate the deflection angle α. As x 0 approaches x m this angle diverges logarithmically, and it can be approximated in the form [10,11] α(x 0 ) = −a 1 log…”

“…The first step in calculating the integral I (x 0 ) that determines the deflection angle α in Eq. (11) Finally, after some calculations (see [11] for the details), the strong deflection limit coefficients take the form…”

“…We follow the method described in Ref. [11], which is in turn an improvement to the one developed in Ref. [10], in order to approximate the deflection angle α.…”

“…Let us apply the general procedure [11], valid for any spherically symmetric and asymptotically flat geometry with a photon sphere, for obtaining the strong deflection limit coefficients c 1 and c 2 appearing in Eq. (15).…”

“…This method, consisting in a logarithmic approximation of the deflection angle for light rays deflecting close to the photon sphere, was introduced for the Schwarzschild black hole [4][5][6][7][8], extended to the Reissner-Nordström geometry [9], and generalized to arbitrary spherically symmetric and asymptotically flat spacetimes [10]. It has been recently improved by simplifying the form to perform the calculations [11]. Within this limit, one can analytically obtain the positions, the magnifications, and the time delays of the relativistic images.…”