How do you find the energy momentum of a tensor?

How do you find the energy momentum of a tensor?

The energy-momentum tensor, Tµν is defined by Tµν = ∂L ∂(∂µφ) ∂νφ−gµνL. We see immediately, using the definition of the canonical momentum, π(x), that T00 is the Hamil- tonian density.

Why is energy momentum tensor symmetric?

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.

What is the relationship between relativistic momentum and energy?

The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc2 relates total energy E to the (total) relativistic mass m (alternatively denoted mrel or mtot ), while E0 = m0c2 relates rest energy E0 to (invariant) rest mass m0.

What are the components of the energy momentum tensor?

These components are given by Eqs. (50)–(53) below. Respectively, they describe: momentum density Γα, stress tensor Tαβ, total energy density E, and density of the total energy flux, Qβ, which approximately equals qβ.

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. …

Is energy momentum tensor symmetric?

The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime.

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.

What is momentum in relativity?

Relativistic momentum p is classical momentum multiplied by the relativistic factor γ. p = γmu, where m is the rest mass of the object, u is its velocity relative to an observer, and the relativistic factor γ=1√1−u2c2 γ = 1 1 − u 2 c 2 . This implies that an object with mass cannot reach the speed of light.

Is the stress tensor covariant?

Which among these forces used in momentum equation is a tensor?

1. Which among these forces used in momentum equation is a tensor? Explanation: Viscous forces are tensors. The other forces given here (Gravitational, viscous and electromagnetic forces) are vectors.

What is the physical meaning of the energy-momentum tensor?

This is the energy-momentum tensor, also known as the stress-energy tensor for the dust. Physical meaning of the energy-momentum tensor Because the stress–energy tensor is of order two, its components can be displayed in 4 × 4 matrix form: As seen previsouly, T tt represents the density of relativistic mass, i.e the energy density.

How is the stress-energy tensor related to general relativity?

General relativity. The stress–energy tensor, sometimes stress–energy–momentum tensor or energy–momentum tensor, is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

Which is the simplest case of energy momentum?

Energy-Momentum Tensor. Incoherent Matter Case. One of the simplest energy-momentum tensors\r is the dust energy momentum tensor. This type of matter field consists of\r noninteracting incoherent matter. The matter field depends on one scalar\r quantity and one vector quantity. These two quantities are as follows:

Is the tensor equation valid in curved spacetime?

Using the ‘comma goes to semi-colon’ rule, we get the following tensor equation, which by the Principle of General Covariance will hold true for any coordinate system, therefore will stay valid in curved spacetime of general relativity.