Slowly rotating condensate dark stars beyond the mean-field approximation

Abstract We investigate rotational properties and universal relations of slowly rotating Bose–Einstein condensate dark stars in the context of General Relativity, both at the mean-field level and when the leading beyond-mean-field Lee–Huang–Yang correction is retained self-consistently. Adopting the polytropic $$n=1$$ n = 1 equation of state appropriate to a dilute, self-interacting Bose gas, parameterised by the boson mass m and the s -wave scattering length $$a_s$$ a s , we integrate the Tolman–Oppenheimer–Volkoff equations together with Hartle’s dipole equation for the frame-dragging angular velocity, and we compute the moment of inertia, the gravito-electric tidal Love number and the dimensionless tidal deformability. The resulting equilibrium sequences yield gravitational masses in the 1– $$2\,M_{\odot }$$ 2 M ⊙ range with radii of 10– $$20\,\textrm{km}$$ 20 km , squarely within the window presently probed by NICER and the LIGO-Virgo-KAGRA network. We observe that the LHY term produces a measurable reduction of the dimensionless moment of inertia at fixed compactness, whilst the I- $$\Lambda $$ Λ universal relation is preserved to within a few per cent. We supply polynomial fits for the I- $$\Lambda $$ Λ and I- C relations, and show that the LHY footprint is large enough to serve as a clean diagnostic of beyond-mean-field quantum physics in a putative dark star population, complementing existing dark matter constraints from pulsar masses and from the equation-of-state interpretation of the unusually light compact remnant HESS J1731-347.