Deformed Compact Objects

We present solutions for deformed compact astrophysical objects. We begin by presenting the derivation of the Tolman-Oppenheimer-Volkoff equations from a parameterized metric that takes into account the deformation of the star expressed in terms of a parameter \(\mathcal {D}\), which is the ratio between polar and equatorial radii. The stellar structure is solved using the GM1 and MIT bag model equations of state, and the “deformed” Tolman-Oppenheimer-Volkoff equation is numerically integrated for different values of \(\mathcal {D}\). To simplify the analysis, the dimensionality of the problem is reduced to a single radial component, leveraging a direct relationship between \(\mathcal {D}\) and the polar and equatorial directions. This approach allows us to demonstrate the influence of deformation in the star’s mass in a consistent manner. We show that larger values of \(\mathcal {D}>1\), describing prolate objects, yield smaller values of mass and radius, while for smaller values of \(\mathcal {D}<1\), describing oblate objects, larger values for mass and radius are attained. We also show that from the confrontation of our model theoretical predictions with recent observational data on pulsars, it is possible to constrain the values of the parameter \(\mathcal {D}\). Remarkably, the solutions for the two distinct equations of state, when compared to such observational data, yield the same constraints on the deformation parameter.