# Spinning Strings, Black Holes and Stable Closed Timelike Geodesics

## TL;DR

This paper investigates the existence and stability of closed timelike curves in a spacetime combining a Schwarzschild black hole with a spinning string, revealing conditions that allow such curves to exist.

## Contribution

It demonstrates how a spinning string deforms black hole spacetime to enable stable closed timelike geodesics, expanding understanding of causality violations in such geometries.

## Key findings

- Closed timelike geodesics exist in the combined spacetime.
- Spinning string deformation permits stable closed timelike curves.
- The spacetime remains stable under linear perturbations.

## Abstract

The existence and stability under linear perturbation of closed timelike curves in the spacetime associated to Schwarzschild black hole pierced by a spinning string are studied. Due to the superposition of the black hole, we find that the spinning string spacetime is deformed in such a way to allow the existence of closed timelike geodesics.