Deviations from the von Laue condition: Implications for the on-shell Lagrangian of particles and fluids

Abstract

According to the von Laue condition, the volume integral of the proper pressure inside isolated particles with a fixed structure and finite mass vanishes in the Minkowski limit of general relativity. In this work, we consider a simple illustrative example: nonstandard static global monopoles with finite energy, for which the von Laue condition is satisfied when the proper pressure is integrated over the whole space. We demonstrate, however, that the absolute value of this integral, when calculated up to a finite distance from the center of the global monopole, generally deviates from zero by no more than the energy located outside the specified volume (under the assumption of the dominant energy condition). Furthermore, we find that the maximum deviation from unity of the ratio between the volume averages of the on-shell Lagrangian and the trace of the energy-momentum tensor cannot exceed three times the outer energy fraction. Extending these results to real particles, we demonstrate that these constraints generally hold for finite-mass systems with fixed structure, including stable atomic nuclei, provided the dominant energy condition is satisfied. Specifically, we show that, except in extremely dense environments with energy densities comparable to that of the particles themselves, the volume average of the aforementioned ratio must be extremely close to unity. Finally, we discuss the broader implications of our findings for the form of the on-shell Lagrangian of real fluids, which is often a crucial element for accurately modeling the dynamics of the gravity and matter, especially in scenarios involving nonminimal couplings to other matter fields or gravity. We find that, in general, the ideal gas on-shell Lagrangian provides an accurate approximation of the true on-shell Lagrangian, even for nonideal gases with significant interparticle interactions.

10 pages, 7 figures

References in corpus (28)

• Modified Gravity and Cosmology
• Extended Theories of Gravity
• f(R,T) gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Coupled Quintessence
• Testing General Relativity with Present and Future Astrophysical Observations
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Interacting Quintessence
• f(R,L_m) gravity
• Interacting Dark Matter and Dark Energy
• Forces inside hadrons: pressure, surface tension, mechanical radius, and all that
• Coupling matter in modified $Q$-gravity
• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Further matters in space-time geometry: $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ gravity
• Energy conditions in general relativity and quantum field theory
• $f(R,T_{\mu \nu }{T}^{\mu \nu })$ gravity and Cardassian-like expansion as one of its consequences
• Global topological k-defects
• The pressure distribution and shear forces inside the proton
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• Perfect fluid Lagrangian and its cosmological implications in theories of gravity with nonminimally coupled matter fields
• Structure Formation and Backreaction in Growing Neutrino Quintessence
• Generalised nonminimally gravity-matter coupled theory
• Localized D-dimensional global k-defects
• Merging matter and geometry in the same Lagrangian
• Lagrangian description of cosmic fluids: mapping dark energy into unified dark energy
• On-shell Lagrangian of an ideal gas
• Can gravitational vacuum condensate stars be a dark energy source?
• Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities

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