Abstract
The motion of photons around black holes determines the shape of shadow and match the ringdown properties of a perturbed black hole. Observations of shadows and ringdown waveforms will reveal the nature of black holes. In this paper, we study the motion of photons in a general parametrized metric beyond the Kerr hypothesis. We investigated the radius and frequency of the photon circular orbits on the equatorial plane and obtained fitted formula with varied parameters. The Lyapunov exponent which connects to the decay rate of the ringdown amplitude is also calculated. We also analyzed the shape of shadow with full parameters of the generally axisymmetric metric. Our results imply the potential constraint on black hole parameters by combining the Event Horizon Telescope and gravitational wave observations in the future.
Highlights
One of the main problems of gravity theories is to test the theory in strong field regime with high accuracy
We want to know how the shadows of KRZ metric can reproduce the ones from exact metrics, so we calculate the shadows with the Kerr–Sen (KS) and Einstein Dilaton
In the present work we have studied the photon motion in the equatorial plane around the generally axisymmetric black hole which is described by the parametrized KRZ metric
Summary
One of the main problems of gravity theories is to test the theory in strong field regime with high accuracy. The new parameters of solutions within modified or alternative theories of gravity representing the deflections from Kerr spacetime may mimic the effects of the spin parameter of the Kerr black holes [22,23,24]. Several ways of parametrization of the spacetime describing the rotating black hole have been proposed by different authors [29,30,31]. -called KRZ metric was proposed by Konoplya et al [30] where they have suggested parametrization of the spacetime of rotating black hole. We plan to study shadow of the black holes described by the parametric spacetime metric proposed in [30].
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