Gravity-sensitive Spectral Indices in Ultracool Dwarfs: Investigating Correlations with Metallicity and Planet Occurrence using SpeX and FIRE Observations

We present a near-infrared spectroscopic analysis (0.9--2.4~$\mu$m) of gravity indices for 56 ultracool dwarfs (M5.5--L0), including exoplanet hosts SPECULOOS-2, SPECULOOS-3, and LHS 3154, with 59 spectra from SpeX and FIRE and literature data for TRAPPIST-1. Using gravity-sensitive spectral features (FeH at 0.99, 1.20, and 1.55~$\mu$m; VO at 1.06~$\mu$m; the H-band continuum; KI at 1.17 and 1.25$\mu$m), we investigate links between gravity classification, metallicity, and planet occurrence. All four planet hosts show intermediate-gravity signatures despite field-age indicators. A volume-corrected logistic regression finds no significant association between gravity class and planet occurrence. Among individual indices, FeH_z (0.99~$\mu$m) is the most promising tracer of planet-hosting status, with a tentative $2\sigma$ correlation that may reflect observational biases. More robustly, FeH_z shows a $3.3\sigma$ anti-correlation with [Fe/H]. A Kruskal--Wallis test finds no metallicity difference across gravity classes, suggesting the FeH_z--[Fe/H] trend is not due to bulk metallicity. We propose this relation reflects the interplay of age, gravity, and composition, with higher-metallicity objects being systematically younger and lower-gravity, reducing FeH absorption. While only hinting at a connection between gravity-sensitive features and planet occurrence among late-M dwarfs, these results highlight the need for caution when using spectral diagnostics to interpret ultracool dwarf planet hosts.