Thermodynamics: A Thermodynamic Extension of the Aichmayr Metric

In this paper, we present a thermodynamically extended form of the Aichmayr metric—a singularity-free modification of the Schwarzschild solution that incorporates real-world damping effects. By coupling local entropy density \( S(r) \) and energy flux \( \frac{dQ}{dt} \) directly into the metric structure, we define a dynamic modulation factor that adjusts the curvature of spacetime in response to thermal and informational states. We derive the full line element and propose an extended energy-momentum tensor including thermodynamic contributions. A numerical approximation of the Ricci tensor component \( R_{tt}(r) \) reveals a finite, structured curvature field modulated by entropy saturation and heat flow, avoiding divergences typically associated with classical gravitational collapse. This framework opens the door to modeling heat-coupled gravitational systems, entropy-regulated collapse dynamics, and real-time spacetime feedback via physical sensor data. The proposed metric represents a step toward thermodynamic-geometric unification and may have implications for black hole interiors, quantum gravity models, and future experimental tests.