  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.
