Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm

Abstract

The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency.Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact object whose gravitational field is given by the arbitrary rotating spacetime under consideration. As special cases, we apply our general analytic formula to some known black holes and reproduce the corresponding results for black hole shadow. Finally, we consider a new example and study shadow using our analytic general formula. * rshaikh@iitk.ac.in

Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

“…This metric is featured by the existence of the Carter constant of motion, which implies the separability of the Hamilton-Jacobi equation and null geodesic equations [4]. As we have mentioned previously, the NJA metric (19) also allows for separable null geodesic equations [25]. In addition, the Hamilton-Jacobi equation of the NJA metric is separable when H(r, θ) is an additively separable function.…”

“…In Ref. [25], it has been shown that the general spacetime (19) allows for the separability of the null geodesic equations. However, this does not imply that the Hamilton-Jacobi equation is also separable.…”

“…In Ref. [25], it has been proven that the general stationary and axisymmetric metric generated via NJA allows for completely separable null geodesic equations. In this work, we will study the separability of the Klein-Gordon equation for such a general spacetime derived via NJA (we shall call it NJA metric from now on).…”

Rotating regular black holes in conformal massive gravity

“…2X (r ph ) X(r ph ) − aξ − ∆ (r ph ) η + (ξ − a) 2 = 0. (63) If we eliminate η and solve for ξ evaluated at r = r ph , it follows [74]…”

Rotating black holes with an anisotropic matter field

“…First, we construct a rotating geometry and then obtain matter field satisfying the Einstein equations. For the first step, we employ the Newman-Janis (NJ) algorithm [17,18,19], which has become popular to study the rotational geometry [20,21,22,23,24,25]. This algorithm generates a rotating geometry from a known static one.…”