The elastic energy-momentum tensor

1975 ◽  
Vol 5 (3-4) ◽  
pp. 321-335 ◽  
Author(s):  
J. D. Eshelby
Keyword(s):  
Elastic Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor

The pointwise Eshelby force on the interface between a transformed inclusion and its surrounding matrix

2016 ◽  
Vol 23 (2) ◽  
pp. 233-239 ◽  
Author(s):  
Steven D Gavazza ◽  
David M Barnett
Keyword(s):  
Elastic Energy ◽  
Driving Force ◽  
Energy Momentum Tensor ◽  
Normal Component ◽  
Strain Tensor ◽  
Transformation Strain ◽  
Momentum Tensor ◽  
Surrounding Matrix ◽  
Personal Letter ◽  
Thermodynamic Driving Force

Eshelby showed that the pointwise force F on and normal to the interface between a transformed inclusion and its surrounding matrix is the jump in the normal component of the elastic energy-momentum tensor across the interface. Gavazza later showed, using an entirely different approach, that this thermodynamic driving force F has a much simpler form involving only the average of the stress tensors at adjacent points on opposite sides of the interface and the “transformation strain” tensor. The equivalence of and connection between the two formulae was apparently first shown by Eshelby in a personal letter to Gavazza (attached as an appendix to this paper), although the brevity of the letter makes following Eshelby’s proof a little difficult. Here we expand Eshelby’s hitherto unpublished proof of the equivalence of the two expressions in what we believe is a clearer fashion.

scholarly journals Generating elastic solutions of the Einstein field equations from the Schwarzschild vacuum solution

2019 ◽  
Vol 16 (05) ◽  
pp. 1950071
Author(s):  
Irene Brito
Keyword(s):  
Elastic Energy ◽  
Energy Momentum Tensor ◽  
Vacuum Solution ◽  
Momentum Tensor ◽  
Conformal Transformations ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Particular Solutions ◽  
Vacuum Spacetime

The problem of generating solutions of the Einstein field equations with an elastic energy–momentum tensor from the Schwarzschild vacuum solution by means of conformal transformations is analyzed. Applying the formulation of relativistic elasticity, suitable conformal factors are obtained for static and non-static elastic spacetime configurations and particular solutions are presented. This work shows that the technique used here permits generating new elastic matter solutions from a vacuum spacetime.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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