# Classical and quantum analysis of an Einstein-Scalar solution in $2+1$ dimensions

## TL;DR

This paper explores the classical and quantum characteristics of a new 2+1 dimensional gravity solution coupled with a scalar field, revealing that the spacetime remains quantum singular when probed with quantum particles.

## Contribution

It introduces a new one-parameter generalization of a known solution and analyzes its classical geodesics and quantum singularity properties.

## Key findings

- The solution admits naked singularities with stronger curvature.
- Classical geodesic analysis identifies particle trajectories near the singularity.
- Quantum analysis shows the spacetime remains quantum singular with quantum probes.

## Abstract

The classical and quantum properties of a new solution obtained in $2+1$% -dimensional gravity coupled with a real scalar field is analyzed in detail. The considered new solution is a one-parameter generalization of a previously known solution. We investigate the solution classically by calculating exact null and null circular geodesics which correspond to a typical particle probe of the correspondsing black hole spacetime. The solution admitting naked singularity is investigated within the context of quantum mechanics. The timelike naked singularity is probed with spin-zero and spin-half quantum particles. We show that the curvature singularity in the new solution is stronger and hence in general the spacetime remains quantum singular with respect to a quantum particle probe.