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

## TL;DR

This paper derives a general analytic formula for black hole shadows in arbitrary rotating spacetimes obtained via the Newman-Janis algorithm, enabling analysis of shadow contours for various black hole solutions.

## Contribution

It provides a new, general method to compute black hole shadows in rotating spacetimes generated by the Newman-Janis algorithm, including novel examples.

## Key findings

- Successfully separated null geodesic equations in NJ-generated spacetimes
- Derived a universal formula for black hole shadow contours
- Validated the formula on known black holes and explored a new example

## 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.