Strong gravitational lensing in a squashed Kaluza-Klein black hole spacetime

Abstract

We investigate the strong gravitational lensing in a Kaluza-Klein black hole with squashed horizons. We find the size of the extra dimension imprints in the radius of the photon sphere, the deflection angle, the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.

Strong gravitational lensing in a squashed Kaluza-Klein Gödel black hole

“…(2)- (3), we plot the variations of the coefficientsā andb in the deflection angle (30) with the parameters j and ρ 0 . As j tends to zero, these quantities reduce to those in the squashed Kaluza-Klein black hole in the cosmological background without rotation [17]. Moreover, we can see that for fixed j, both of the coefficientsā andb increase with the size of the extra dimension ρ 0 , which are similar to those in the usual squashed Kaluza-Klein black hole spacetime.…”

“…The equations (15) and (16) are more complex than those in the usual spherical symmetric black hole spacetime. As the Gödel parameter j → 0, we find that the function H(ρ) → 0, which yields that the impact parameter (15) and the photon sphere equation (16) reduce to those in the usual neutral squashed Kaluza-Klein black hole spacetime [17]. The radius of the photon sphere is the largest real root of Eq.…”

“…In Fig. (4), We present the deflection angle α(θ) evaluated at u = u ps +0.003, which shows that the larger parameters j and ρ 0 lead to the bigger deflection angle α(θ) for the light propagated in the squashed Kaluza-Klein Gödel black hole spacetime [17]. Comparing with those in the Schwarzschild black hole spacetime, we could extract information about both the rotation of the cosmological background and the size of the extra dimension by using strong field gravitational lensing.…”

“…As done in the usual squashed Kaluza-Klein black hole spacetime [17], here we set L ψ = 0, which implies that the total angular momentum J of the photo is equal to the constant L φ . In doing so, one can get the effective potential for the photon passing close to the black hole…”

“…It is shown that the relativistic images can provide us not only some important signatures about black holes in the Universe, but also profound verification of alternative theories of gravity in their strong field regime. Thus, the strong gravitational lensing by black holes has been studied extensively in various theories of gravity [5][6][7][8][9][10][11][14][15][16][17]. Most studies of the strong gravitational lensing are focused on black holes immersed in the rather idealized isotropic homogeneous Universe.…”