What is the stress energy tensor in general relativity?
In general relativity, the symmetric stress–energy tensor acts as the source of spacetime curvature, and is the current density associated with gauge transformations of gravity which are general curvilinear coordinate transformations. (If there is torsion, then the tensor is no longer symmetric.
Is the stress energy tensor always symmetric?
Symmetry of the stress-energy tensor The stress-energy tensor is a symmetric matrix. If we have a nonzero Ttx, it represents a flux of mass-energy (pt) through a three-surface perpendicular to x. This means that mass is moving in the x direction.
Is a stress tensor a Contravariant?
Well, a tensor is neither covariant nor contravariant, while it can be expressed by its covariant, contravariant, or mixed *components* with respect to any arbitrary coordinate system. …
What is meant by stress tensor?
The Stress Tensor Stress is defined as force per unit area. If we take a cube of material and subject it to an arbitrary load we can measure the stress on it in various directions (figure 4). These measurements will form a second rank tensor; the stress tensor.
What are the units of the stress energy tensor?
Therefore in geometrized units, the stress-energy tensor also has units of distance^-2. This makes sense because the stress-energy tensor can be thought of in the Newtonian limit as a mass density, and mass has units of distance in geometrized units, so mass density is distance/distance^3=distance^-2.
Can stress tensor be non symmetric?
Although the theory generally predicts the stress to be non symmetric, the stress tensor can still be considered as symmetrical in the absence of external fields and when the inertia effects of internal rotations and couple stresses are neglected.
Why stress is a tensor Quora?
What is a stress tensor? – Quora. When a solid is strained by external forces the positions between atoms change and it is in a non-equilibrium state. As a result some internal forces appear. These forces tend to return the strained solid to its equilibrium state.
What is the difference between stress vector and stress tensor?
The stress vector is the force per unit surface. The stress tensor is the matrix {σij(x,t)} and its (i,j)-component is the i-component of the force per unit surface that is exerted at an element of the surface perpendiculart to the direction j.
What is stress tensor in engineering?