# Behavior of vacuum and naked singularity under smooth gauge function in Lyra geometry

## TL;DR

This paper explores how smooth gauge functions in Lyra geometry influence the nature of vacuum and naked singularities, revealing conditions under which singularities become naked and analyzing their physical implications.

## Contribution

It introduces a method to modulate singularity divergence in Lyra geometry using smooth gauge functions, leading to the formation of naked singularities under specific conditions.

## Key findings

- Naked singularities can form under certain gauge functions in Lyra geometry.
- No spaceship with finite acceleration can reach the naked singularity.
- The gauge function's role in controlling singularity behavior is elucidated.

## Abstract

Lyra geometry is a conformal geometry originated from Weyl geometry. In this article, we derive the exterior field equation under spherically symmetric gauge function $x^0(r)$ and metric in Lyra geometry. When we impose a specific form of the gauge function $x^0(r)$, the radial differential equation of the metric component $g_{00}$ will possess an irregular singular point(ISP) at $r=0$. Moreover, we apply the method of dominant balance and then get the asymptotic behavior of the new spacetime solution. The significance of this work is that we could use a series of smooth gauge functions $x^0(r)$ to modulate the degree of divergence of the singularity at $r=0$ and the singularity will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of spacetime in Lyra geometry and find out that no spaceship with finite integrated acceleration could arrive at this singularity at $r=0$. The physical meaning of gauge function and integrability is also discussed.