Mechanical Equilibrium in the Magnetized Quark--Hadron Mixed Phase: A Covariant Generalization of the Gibbs Condition

TL;DR

This paper develops a covariant framework for mechanical equilibrium at the quark-hadron interface in magnetic fields, generalizing the classical Gibbs condition to account for anisotropic pressures.

Contribution

It introduces a relativistic thin-shell formalism to describe the quark-hadron boundary, replacing scalar pressure balance with generalized Young-Laplace conditions.

Findings

Provides a covariant description of equilibrium at the interface

Replaces scalar pressure balance with generalized Young-Laplace conditions

Accounts for magnetic-field-induced pressure anisotropy

Abstract

We formulate a covariant mechanical equilibrium condition for the quark-hadron mixed phase boundary in the presence of a magnetic-field-induced pressure anisotropy. Using the \emph{relativistic thin-shell} formalism to describe the quark-hadron boundary, we interpret conservation of stress-energy across the interface as a set of generalized Young--Laplace conditions which characterize the geometry of the interface. In a comoving stationary frame, this provides a covariant description of mechanical equilibrium at the interface, which serves as a replacement for the scalar pressure-balance condition used in the isotropic Gibbs construction.