Relativisitic non-pascalian fluid as a density contribution

Abstract Understanding the role of pressure anisotropy and dissipation is crucial for modelling compact objects’ internal structure and observable properties. In this work, we reinterpret local pressure anisotropy in relativistic stellar structures as an additional contribution to the energy density. This perspective enables the formulation of anisotropic equations of state for self-gravitating systems by incorporating anisotropy as a fundamental component. We demonstrate that this approach yields more realistic stellar models that satisfy key physical constraints, including mass-radius relationships and stability conditions. Our results are compared with observational data, particularly the inferred compactness of pulsars PSR J0740+6620 and PSR J0030+0451, showing that both anisotropic and isotropic models can describe these objects. Additionally, we examine the influence of dissipation – such as temperature gradients – on radial pressure, demonstrating that it can be modelled similarly to anisotropy. This interpretation allows the transformation of dissipative anisotropic models into equivalent non-dissipative isotropic configurations.