Studying Generalised Polytropic and Warm Dark Matter in NGC 5055

Abstract Galaxy rotation curves provide a powerful probe of mass distributions in spiral galaxies. We present a general relativistic analysis of NGC 5055 using its observed rotation curve and WISE W1 (3.4 μm) photometry to constrain the stellar mass profile. Adopting a static, spherically symmetric spacetime with anisotropic matter (vanishing radial pressure), we fit a modified exponential azimuthal velocity law to kinematic data, reconstructing metric functions and deriving enclosed mass, energy density, and tangential pressure profiles. The stellar mass underpredicts the total gravitating mass at intermediate-to-large radii, indicating dominant dark matter. The physical viability of the resulting relativistic model is examined through energy conditions, causality constraints, and a generalised polytropic equation of state analysis. Among the candidate equations of state tested — Bose–Einstein condensate, Chaplygin gas, linear fluid, and generalised polytropic — only the generalised polytropic form p = Kργ with γ = 0.91 and K = 4.63 × 10−8 achieves an excellent fit , firmly placing the dark matter of NGC 5055 in the Warm Dark Matter regime. All energy conditions and causality constraints are satisfied, and the halo is stable against gravitational cracking. Sterile neutrinos or gravitinos of keV-scale mass are identified as the most physically motivated particle candidates. Overall, this study demonstrates that combining rotation-curve data with photometric stellar mass estimates within a general relativistic framework provides a consistent and physically viable description of the mass distribution in spiral galaxies such as NGC 5055.