Relativistic elastic shells: material support and cavity geometry
Abstract
We derive the source moments that determine the leading tidal field and rotational clock shift inside a finite-thickness relativistic elastic shell. In weak gravity and slow rotation, these moments depend on the elastic response of the material and its two free vacuum faces. Two choices of elastic moduli, each causal near relaxation, give opposite signs for both observables. Both shells have oblate faces and gain rotational mass. The tide depends on differential flattening, bulk deformation, and rotational stress and energy; the central clock shift measures a distinct inverse-radius moment. A single constitutive action determines the material support and response. Nonnegative isotropic pressure cannot support a static spherical shell of positive-density matter with two free vacuum faces, whereas tangential elastic stress admits equilibria near relaxation. For sufficiently weak gravity these equilibria obey the dominant energy condition and have subluminal sound speeds. Their static cavities are locally flat, with clocks redshifted relative to infinity. At leading weak-gravity order, static redshift and linear frame dragging probe the same inverse-radius mass moment. Energy estimates establish radial linear stability and exclude exponentially growing odd-parity modes for weakly gravitating spherical equilibria. Nonlinear compression can nevertheless produce unbounded gradients while the material remains causal. Nonspherical even-parity and rotating stability, together with quantitative bounds at finite rotation, remain open. The cavity observables distinguish material responses that surface shape and total mass alone do not determine.
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BibTeX
@misc{le2026relativistic,
title = {{Relativistic elastic shells: material support and cavity geometry}},
author = {An T. Le},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.25417},
eprint = {2605.25417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25417},
}
RIS
TY - UNPB
TI - Relativistic elastic shells: material support and cavity geometry
AU - An T. Le
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2605.25417
UR - https://arxiv.org/abs/2605.25417
AB - We derive the source moments that determine the leading tidal field and rotational clock shift inside a finite-thickness relativistic elastic shell. In weak gravity and slow rotation, these moments depend on the elastic response of the material and its two free vacuum faces. Two choices of elastic moduli, each causal near relaxation, give opposite signs for both observables. Both shells have oblate faces and gain rotational mass. The tide depends on differential flattening, bulk deformation, and rotational stress and energy; the central clock shift measures a distinct inverse-radius moment. A single constitutive action determines the material support and response. Nonnegative isotropic pressure cannot support a static spherical shell of positive-density matter with two free vacuum faces, whereas tangential elastic stress admits equilibria near relaxation. For sufficiently weak gravity these equilibria obey the dominant energy condition and have subluminal sound speeds. Their static cavities are locally flat, with clocks redshifted relative to infinity. At leading weak-gravity order, static redshift and linear frame dragging probe the same inverse-radius mass moment. Energy estimates establish radial linear stability and exclude exponentially growing odd-parity modes for weakly gravitating spherical equilibria. Nonlinear compression can nevertheless produce unbounded gradients while the material remains causal. Nonspherical even-parity and rotating stability, together with quantitative bounds at finite rotation, remain open. The cavity observables distinguish material responses that surface shape and total mass alone do not determine.
ER -