# Tunneling of Massive Vector Particles from Dilaton Black Holes in $(2+1)$ Dimensions

## TL;DR

This paper investigates the Hawking radiation of massive vector particles from (2+1)-dimensional dilaton black holes, deriving tunneling probabilities and temperatures, and recovering known results in specific limits.

## Contribution

It extends the tunneling method to massive vector particles in dilaton black hole backgrounds, including static charged and spinning neutral cases, and connects to BTZ black holes.

## Key findings

- Calculated tunneling probabilities and Hawking temperatures for massive bosons.
- Recovered BTZ black hole temperature in a specific dilaton coupling limit.
- Demonstrated the applicability of WKB and Hamilton-Jacobi methods to these black holes.

## Abstract

In this paper, we have studied the Hawking radiation of massive spin-$1$ particles from the black holes in $(2+1)$ dimensions with non- trivial dilaton fields. We consider two special varities of these black holes one is static charged and other is spinning electrically neutral. By applying the standard method of $WKB$ approximation and Hamilton- Jacobi ansatz we have shown the tunneling probability and Hawking temperature of massive bosons accordingly. In the certain limit of the dilaton coupling for spinning neutral case we have recovered the Hawking temperature of the $BTZ$ black holes as well.