1,567 research outputs found
Static self-gravitating elastic bodies in Einstein gravity
We prove that given a stress-free elastic body there exists, for sufficiently
small values of the gravitational constant, a unique static solution of the
Einstein equations coupled to the equations of relativistic elasticity. The
solution constructed is a small deformation of the relaxed configuration. This
result yields the first proof of existence of static solutions of the Einstein
equations without symmetries.Comment: 29 pages. Updated to conform with published version, typos fixe
Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
We consider a problem of quantitative static elastography, the estimation of
the Lam\'e parameters from internal displacement field data. This problem is
formulated as a nonlinear operator equation. To solve this equation, we
investigate the Landweber iteration both analytically and numerically. The main
result of this paper is the verification of a nonlinearity condition in an
infinite dimensional Hilbert space context. This condition guarantees
convergence of iterative regularization methods. Furthermore, numerical
examples for recovery of the Lam\'e parameters from displacement data
simulating a static elastography experiment are presented.Comment: 29 page
Self-gravitating elastic bodies
Extended objects in GR are often modelled using distributional solutions of
the Einstein equations with point-like sources, or as the limit of
infinitesimally small "test" objects. In this note, I will consider models of
finite self-gravitating extended objects, which make it possible to give a
rigorous treatment of the initial value problem for (finite) extended objects.Comment: 16 pages. Based on a talk given at the 2013 WE-Heraeus seminar on
"Equations of motion in relativistic gravity
- …