T-model field equations: the general solution

TL;DR

This paper derives the general solutions for T-model perfect fluid spacetimes with specific symmetry properties, providing methods to integrate the field equations without explicit integration.

Contribution

It introduces new methods to solve the T-model field equations and presents the complete general solution without requiring integral calculations.

Findings

Derived the general solution for T-model field equations.

Developed methods to integrate the equations analytically.

Provided explicit solutions without integral computation.

Abstract

We analyze the field equations for the perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient that is tangent to the fluid flow (T-models). We propose several methods to integrate the field equations and we present the general solution without the need to calculate any integral.