Hydrodynamic Approach to Macroscopic Gravity: Thermodynamic Equilibrium via Viscous Dissipation and Quaternion Tensors

Gravity is usually thought of as a force that pulls things together, or in modern physics, as a curve in the fabric of space and time created by massive objects. For centuries, scientists have used geometry to describe how planets orbit and how stars collapse, treating space as a smooth, bending stage. However, when these geometric models are applied to the very center of a spinning planet or a star, the mathematics often breaks down. The equations predict that density becomes infinite and the structure of space itself tears apart at the poles of rotation, creating a mathematical dead end known as a singularity. This leaves a gap in our understanding of how massive bodies maintain their shape and stability over time without imploding into a single point.

A new study by independent researcher Jung Soo Kim proposes a different way to look at this problem. Instead of viewing gravity purely as a geometric curve, the paper suggests treating the gravitational field as a flowing fluid made of vacuum energy. This approach borrows from the physics of liquids and gases, specifically the equations that describe how honey or water moves and resists flow. By modeling the universe's gravitational field as a continuous, viscous fluid, the researcher aims to solve the long-standing problems of infinite density and mathematical breakdowns that occur in traditional models of rotating celestial bodies.

The core of this work is a shift in perspective. Traditional models often treat planets as solid points or simple geometric shapes, which leads to errors when calculating rotation at the poles. To fix this, the study introduces a mathematical tool called a quaternion tensor. In simple terms, this is a way of describing rotation that does not get stuck or confused at the poles, unlike older methods that fail when an object spins on a specific axis. This allows the model to calculate the spin of a planet smoothly from the equator all the way to the poles without the numbers crashing or becoming undefined.

Beyond just fixing the rotation math, the paper addresses the issue of why planets do not collapse under their own weight. In standard models, gravity pulls everything inward, which can lead to a runaway effect where matter is crushed into an infinitely small point. The new framework adds a counter-force: a pressure gradient that pushes outward, similar to how air pressure inside a balloon keeps it from collapsing. By combining this outward pressure with a model where the density of the planet changes gradually from the center to the surface, the study shows that the planet can maintain a stable, spherical shape. This prevents the "implosion" that happens in other simulations, ensuring the planet stays a solid, stable sphere rather than shrinking into a singularity.

The final piece of the puzzle involves the energy generated by the fluid motion of the planet. If a fluid spins without any resistance, the energy of that spin can grow uncontrollably, leading to chaos. The study introduces a concept called viscous dissipation, which acts like friction within the fluid. This friction slowly turns the excess spinning energy into heat, calming the turbulence. This process ensures that the system settles into a state of thermodynamic equilibrium, where the energy flowing in is balanced by the energy flowing out. The result is a stable, permanent state where the planet's gravitational field is calm and predictable, rather than chaotic or explosive.

The researcher tested these ideas using computer simulations designed to mimic the behavior of fluids in space. These simulations confirmed that the new equations successfully prevent the mathematical errors that usually occur at the poles of rotation. They also showed that the pressure and friction terms work together to stop the density from becoming infinite, keeping the simulated planet stable. The study concludes that this hydrodynamic approach provides a way to calculate the gravity of large planetary systems without the errors of infinite density or broken geometry. While the work is currently a theoretical framework supported by computer models, it offers a fresh path for understanding how massive objects in the universe hold themselves together, potentially changing how scientists simulate the mechanics of stars and planets in the future.