The Thirukkanesh–Ragel–Malaver Ansatz and the Supernova Remnant HESS J1731-347

The construction of physically realistic analytical solutions of Einstein's field equations remains one of the central problems in relativistic astrophysics. Exact solutions provide important insight into the internal structure, stability, and observable properties of compact stellar objects, including neutron stars, strange quark stars, anisotropic compact stars, and exotic dark-energy-inspired configurations. The Thirukkanesh–Ragel– Malaver (TRM) ansatz has now typically specific mathematical assumption (or metric potential setup) used by within general relativity to find exact, analytical solutions to the Einstein field equations. It is widely used by astrophysicists to model the interior structure of highly dense compact objects, such as strange anisotropic quark stars, neutron stars, and dark energy stars. The TRM approach acts on the radial component of the metric potential. Initially proposed by S. Thirukkanesh and F. C. Ragel (2012) and that was later generalized by Manuel Malaver (2014) who introduced typical adjustable parameter (n) in the metric function, the TRM ansatz serves as an exact mathematical framework for modeling anisotropic stellar interiors, and that has recently gained prominent attention for its ability to explain the incredibly low mass of the compact object within the supernova remnant HESS J1731−347. Discovered by the High Energy Stereoscopic System, HESS J1731−347 contains a compact star whose exceptionally tiny mass has been defying traditional iron-core neutron star formation models. Instead, astrophysicists use the Thirukkanesh–Ragel–Malaver metric ansatz to model the star as a strange quark star. This review shows that the TRM metric potential provides a flexible analytical framework for studying equilibrium configurations as well as physical properties of typically relativistic compact objects.