  Detailed magnetic field structure of the dense core SL42 (CrA-E) in the
Corona Australis molecular cloud complex was investigated based on
near-infrared polarimetric observations of background stars to measure
dichroically polarized light produced by magnetically aligned dust grains. The
magnetic fields in and around SL42 were mapped using 206 stars and curved
magnetic fields were identified. On the basis of simple hourglass (parabolic)
magnetic field modeling, the magnetic axis of the core on the plane of sky was
estimated to be $40^{\circ} \pm 3^{\circ}$. The plane-of-sky magnetic field
strength of SL42 was found to be $22.4 \pm 13.9$ $\mu$G. Taking into account
the effects of thermal/turbulent pressure and the plane-of-sky magnetic field
component, the critical mass of SL42 was obtained to be $M_{\rm cr} = 21.2 \pm
6.6$ M$_{\odot}$, which is close to the observed core mass of $M_{\rm core}
\approx 20$ M$_{\odot}$. We thus conclude that SL42 is in a condition close to
the critical state if the magnetic fields lie near the plane of the sky. Since
there is a very low luminosity object (VeLLO) toward the center of SL42, it is
unlikely this core is in a highly subcritical condition (i.e., magnetic
inclination angle significantly deviated from the plane of sky). The core
probably started to collapse from a nearly kinematically critical state. In
addition to the hourglass magnetic field modeling, the Inoue \& Fukui (2013)
mechanism may explain the origin of the curved magnetic fields in the SL42
region.
