# Noncommutative black hole in the Finslerian spacetime

## TL;DR

This paper explores how noncommutative Schwarzschild black holes behave in Finslerian spacetime, revealing changes in horizon structure, temperature, and stability influenced by Finslerian and noncommutative parameters.

## Contribution

It introduces a detailed analysis of noncommutative black holes within Finslerian spacetime, highlighting the impact of Finslerian parameters on black hole horizons, temperature, and stability, which is a novel approach.

## Key findings

- Black holes can have two, one, or no horizons depending on parameters.
- Minimal mass varies with Finslerian parameter, while minimal horizon remains fixed.
- A stable black hole remnant is predicted, with properties determined by Finslerian and noncommutative parameters.

## Abstract

We study the behavior of the noncommutative radiating Schwarzschild black hole in the Finslerian spacetime. The investigation shows that black hole possesses either (i) two horizons, or (ii) a single horizon, or (iii) no horizon corresponding to a minimal mass. We obtain that the minimal mass significantly changes with the Finslerian parameter, keeping minimal horizon remain unchanged. It turns out that under Finslerian spacetime, the maximum temperature before cooling down to absolute zero varies with Finslerian parameter. We then study the stability of the black hole by analyzing the specific heat and free energy. The energy conditions, their violation limit also scrutinized. Our findings suggest a stable black hole remnant, whose mass and size are uniquely determined in terms of the Finslerian parameter $\overline{Ric}$ and noncommutative parameter $\theta$. The physical relevance of these results are discussed in a brief.