# Blackhole in Nonlocal Gravity: Comparing Metric from Newmann-Janis Algorithm with Slowly Rotating Solution

## TL;DR

This paper investigates the effectiveness of the Newman-Janis algorithm in deriving rotating black hole metrics within nonlocal gravity theories, comparing it with solutions obtained through direct perturbative methods.

## Contribution

The study applies the Newman-Janis algorithm to nonlocal gravity to derive rotating black hole metrics and compares these with slowly rotating solutions from field equations.

## Key findings

- Newman-Janis algorithm can be applied to nonlocal gravity for rotating black holes.
- Comparison shows the algorithm's slow rotation limit aligns with perturbative solutions.
- Results highlight the potential and limitations of using Newman-Janis in modified gravity theories.

## Abstract

The strong gravitational field near massive blackhole is an interesting regime to test General Relativity(GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving field equations for rotating blackhole is extremely challenging task for the most modified gravity theories. Though the derivation of Kerr metric of GR is also demanding job, the magical Newmann-Janis algorithm does it without actually solving Einstein equation for rotating blackhole. Due to this notable success of Newmann-Janis algorithm in the case of Kerr metric, it has been being used to obtain rotating blackhole solution in modified gravity theories. In this work, we derive the spacetime metric for the external region of a rotating blackhole in a nonlocal gravity theory using Newmann-Janis algorithm. We also derive metric for a slowly rotating blackhole by perturbatively solving field equations of the theory. We discuss the applicability of Newmann-Janis algorithm to nonlocal gravity by comparing slow rotation limit of the metric obtained through Newmann-Janis algorithm with slowly rotating solution of the field equation.