A Slowly-Rotating Extension of the Tolman IV Solution: A Hartle-Thorne Approach

Abstract We present a complete Hartle-Thorne slow-rotation analysis of the Tolman IV stellar model by applying the Hartle-Thorne formalism to an exact isotropic interior solution of Einstein's equations. This unified framework provides a self-consistent description of the static structure, frame-dragging, quadrupole deformation, and surface redshift of the configuration. Using high precision numerical integration of the first and second-order Hartle-Thorne equations, we compute the moment of inertia I, dimensionless spin parameter J/M², quadrupole moment Q, and the angular redshift distribution across the physically admissible parameter space. For the fiducial model \(a=0.002, R=12 km\), we obtain M=1.854, I=117.9, bar{I}=I/M³approx18.5, and spin parameters 0.14leqχleq0.43 for rotation rates f=200-600 Hz, all within the slow-rotation regime. The purely static configurations span a surface redshift range of 0.13 lesssim z_s lesssim 0.36. The full set of rotating configurations, including those with higher compactness up to $M/R approx 0.44$ and subject to mathcal{O}\(Omega²\) rotational corrections, extends the observable surface redshift to an upper range of z_s lesssim 0.65. This higher range is achieved by combining the maximum static redshift with the rotational enhancement, ensuring consistency with NICER constraints. The Tolman IV configurations satisfy the Buchdahl bound (M/R < 4/9) and fall within mass-radius ranges comparable to those inferred from NICER observations of PSR J0030+0451 and PSR J0740+6620. Furthermore, the rotating Tolman IV model follows the universal I-Love-Q relations of neutron stars while exhibiting distinct regular features that deviate from the Kerr geometry. These results establish the Hartle-Thorne rotating Tolman IV stellar model as a mathematically consistent relativistic benchmark model in the strong-gravity regime. This work provides a complete Hartle-Thorne rotational analysis of the Tolman IV exact isotropic stellar interior, including the full set of rotational observables and an explicit I-Love-Q mapping for this model.