# Questions tagged [stress-energy-momentum-tensor]

A rank-2 tensor in relativity, which expresses the flux of energy-momentum along timelike and spacelike axes. Also known as the energy-momentum tensor. In the Einstein field equations, it is the source of gravitational fields.

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### How does one add matter coupling terms to the linearized Lagrangian for General Relativity?

In Spacetime and Geometry, Dr. Carroll provides a Lagrangian for Einstein's equations in vacuum assuming that the metric can be written in the form $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$. The ...
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### How to prove symmetry of stress tensor using torque equation? [closed]

** You have to write the angular momentum equation i.e. Torque = (Moment of Inertia)x(Angular Acceleration) for an infinitesimally small 3D element (about any axis of your choice). Finally, you have ...
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### 4-momentum through a spacelike-othogonal hypersurface for a perfect fluid in special relativity

My understanding of the stress-energy tensor in special relativity (or in general relativity), is that it gives you the flux density of 4-momentum flowing through an oriented 3D hypersurface. So at ...
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### Special Relativity: Interpretation of the partial derivate of Stress-Energy Tensor

This question is based on Carroll's book Spacetime and Geometry, specifically from page 33 to page 36. In the upper mentioned section we define the Stress-Energy Tensor as: The flux of the four ...
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### How to calculate the attractive force in a gravitational field in General Relativity?

I believe that a gravitational field has energy, as Weinburg wrote in his textbook Gravitation and Cosmology, on page 171: "... ... the gravitational field does carry energy and momentum." ...
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### Proving an Identity “easily” as written by author, in GR electromagnetism [closed]

The last day and, some days before, I found myself incapable of proving an Equation, while the author said it was "easily" deducted (Chapter 6, Page 127, 3+1 Ideal Magnetohydrodynamics- Ćric ...
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### Solutions to Einstein Field Equations where $T_{\mu \nu} = 0$

My Level/Background: I have just completed my first year of undergrad. In high school, I completed AP Physics C Mechanics and Electricity and Magnetism. In my first year of undergrad, I completed a ...
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### Are energy and momentum imposed by purely geometrical properties of spacetime?

If we defined spacetime as a purely geometrical (not physical) structure of the kind that is in general relativity (a 4-dimensional Lorentzian manifold), would it automatically have properties that ...
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### Reasonable ways to couple matter with metric

In general relativity without matter, the equation of motion of the metric field is described by the Hilbert's action or the Einstein tensor $G$. It's natural to lead to this conclusion once one ...
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### Energy density of gravitational field [duplicate]

Can we define the energy density of gravity field? If so, what is the formula, and the newtonian approximation? In newtonian mechanics, we can easily obtain the gravitational potential energy. But if ...
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### Help on Hamiltonian tensor equations in Einstein's original General Relativity papers

Studying Einstein's original Die Grundlage der allgemeinen RelativitĆ¤tstheorie published in 1916's Annalen Der Physik, I came across Equations 47b) regarding the gravity contribution to the stress-...
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### Help on electromagnetic tensor equations in Einstein's original General Relativity papers

Studying Einstein's original Die Grundlage der allgemeinen RelativitĆ¤tstheorie published in 1916's Annalen Der Physik, I came across Equations 66) and 66a) regarding the electromagnetic contribution ...
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### Can a stress-energy tensor induce signature changes on the metric?

Suppose we use the signature of a Riemannian manifold $$\eta^{\mu\nu}=\operatorname{diag}(+,+,+,+)$$ as the starting point to describe a 4d Euclidean version of general relativity. Alternatively one ...
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### Does Energy-momentum tensor from Polyakov action have anything to do with the energy and momentum of the string?

I'm a bit confused with the idea of EMT from the Polyakov action. The EMT is derived by variation of the action with respect to the metric which provide the constraint to the theory, $T_{ab}=0$. ...
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