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Hydrostatic Newton-Cartan membranes.
Domingo Gallegos1, Carlos Málaga1
1Universidad Nacional Autónoma de México, Facultad de Ciencias, Investigación Científica C.U. S/N, 04510 Mexico City, Ciudad de México, Mexico.
Physical Review. E
|May 16, 2026
Summary
This study applies the Newton-Cartan framework to hydrostatic membranes, deriving equilibrium constraints and constitutive relations. It presents the Young-Laplace equation for membranes in spacetime with vorticity, offering analytic and numerical solutions.
Area of Science:
- Theoretical Physics
- Fluid Dynamics
- Continuum Mechanics
Background:
- Membrane theory is crucial for understanding various physical phenomena.
- Newton-Cartan geometry provides a framework for studying gravity and spacetime.
- Hydrostatic equilibrium is a fundamental concept in fluid mechanics.
Purpose of the Study:
- To apply the Newton-Cartan framework to study codimension-1 membranes in hydrostatic equilibrium.
- To derive the equilibrium partition function and constitutive relations for these membranes.
- To investigate the Young-Laplace equation for membranes in a specific spacetime geometry.
Main Methods:
- Utilizing the Newton-Cartan framework for membrane analysis.
- Calculating the equilibrium partition function at second-order hydrodynamic expansion.
- Deriving equilibrium constraints and constitutive relations.
- Applying the Young-Laplace equation to two-dimensional axisymmetric closed membranes.
Main Results:
- The equilibrium partition function at second order was determined.
- Equilibrium constraints and constitutive relations were established.
- The Young-Laplace equation was presented for membranes in a flat 3D spacetime with constant ambient vorticity.
- Numerical and analytic solutions to the Young-Laplace equation were explored.
Conclusions:
- The Newton-Cartan framework offers a robust approach to studying hydrostatic membranes.
- The derived constitutive relations and Young-Laplace equation provide insights into membrane behavior.
- The study contributes to understanding membrane physics in curved spacetime contexts.
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