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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Does spacetime curvature increase when an attractor's potential energy is converted to kinetic energy?

Imagine an asymptotically flat spacetime with nothing but two stars at a certain distance. They fall into each other and form one big star, so their potential energy is converted to kinetic energy. ...
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96 views

Shawyer EM Drive — Momentum Conservation Violation

I have been following the developments around the Shawyer EM drive for about 2 years now as NASA and other parties test it out in various environments. To preface, I would very much like to see the EM ...
2
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20 views

What component of the stress–energy tensor contains the kinetic energy of heat? [duplicate]

As I understand it, the component $T_{00}$ of the stress-energy tensor contains the energy density (which equals the mass density), $T_{0i}$ are the impulse flows (intuitively speaking, the ...
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51 views

Prove that $T_{00}$, $T_{10}$, $T_{01}$, and $T_{11}$ are all $L/(4\pi x^2)$ at $(ct, x, 0, 0)$ for star of constant luminosity $L$

We have a star of constant luminosity $L$. We want to prove that the components $T_{00}$, $T_{10}$, $T_{01}$ and $T_{11}$ are all the same for the event $(ct,x,0,0)$ and they are all $L/(4\pi x^2)$. ...
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60 views

What is the value of the variation stress energy tensor?

If we are living in a portion of space-time where the metric is very close to flat space and we know that the stress energy tensor is negligible at this portion of space-time is it ok to assume that ...
3
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1answer
49 views

Interpretation of a term in the Maxwell stress tensor

With no magnetism, the $xx$ component of the Maxwell stress tensor $T$ is $$T_{xx} = \frac{1}{2}(E_x^2 - E_y^2 - E_z^2)$$ I can see why there should be a $+E_x^2$ term, but intuitively I don't see why ...
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58 views

From Noether's theorem to canonical Energy-Momentum tensor using translations

In this text that I am reading it says that the transformation $\delta \phi(x)$ is a symmetry if the Lagrangian changes by a total derivative: $$\delta \mathcal{L}= \partial_{\mu}F^{\mu} . $$ From ...
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194 views

Energy-Momentum Tensor for Electromagnetism in Curved Space

$\newcommand{\l}{\mathcal L} \newcommand{\g}{\sqrt{-g}}$$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$I want to calculate the energy-momentum tensor in curved free space by functional ...
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35 views

Normal of a null surface and null junction conditions in general relativity

I am trying to use the null junction formalism in general relativity (as explained in eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.3763&rep=rep1&type=pdf, "Junctions and thin ...
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47 views

Can the stress energy tensor have nonzero value in a vacuum region?

In general relativity, when solving for the schwartzchild solution, we set $T=0$. 1) Is it possible for the stress energy tensor to have nonzero value in a vacuum region? 2) Is the stress $T=0$ in ...
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82 views

Why does a certain covariant derivative of the stress-energy tensor vanish due to diffeomorphism invariance?

In Polchinski's string theory volume 1, at chap 1.2, after equation 1.2.22, he says $$\nabla_{a}T^{ab}=0$$ as a consequence of diffeomorphism invariance. But I cannot derive it. My derivation is ...
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2answers
94 views

Is the stress energy tensor continuous at the interface between an object and vacuum?

The stress energy tensor has (as I understand) zero value in the region where there is no matter and non-zero value where there is matter. Suppose there is one matter object in space, now how does the ...
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1answer
64 views

Stress-energy tensor on spacetime satisfying Klein-Gordon equation

Consider the stress-energy-momentum tensor $$T_{\alpha \beta}=(\nabla_\alpha \phi )\nabla_\beta \phi -\frac{1}{2}g_{\alpha \beta}((\nabla^\nu \phi ) \nabla_{\nu} \phi +m^2 \phi^2$$ where the ...
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52 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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49 views

Non-local gravitational energy tensor

The well-known derivation of the Landau-Lifshitz gravitational energy pseudotensor, relies on several requirements: 1) that it be constructed entirely from the metric tensor 2) that it be index ...
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1answer
60 views

What is the metric of a constant electromagnetic (pure electric or pure magnetic) field?

For example, imagine a magnetic field $B_x$ directing in $\hat{x}$ direction filling all the space. What is its associated metric field? I can construct the electromagnetic stress-energy tensor for ...
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31 views

Do anyone know a good software that where I can easily find the metric from the stress-energy tensor? [duplicate]

I'm using SageMath but the obtainment of the metric from the stress-energy tensor is not trivial, i.e., it is not implemented in a predefined function. Do anyone know a good software that where I can ...
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2answers
63 views

Explosion in a sphere and the Gravitational field outside

Take a hollow sphere and conduct a process on the inside, which transfers mass into kinetic energy (e.g. we let a big nuclear bomb detonate or something like that). For simplicity, assume that this ...
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20 views

How does the energy-momentum tensor transform under parity in 2D CFT?

I'm trying to get that if parity is conserved, the two represenations of Virasoro algebra which we get from $L_n$'s and $\bar{L}_n$'s starting from dilatation invariant Wightman theory have the same ...
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37 views

Symmetry of the Gravitational Stress Energy pseudo tensor

Recently, I have been reading on the Gravitational Stress-Energy pseudo tensor. It says in Wikipedia that one of the conditions for a suitable GSE pseudo tensor is that it has to be symmetric about ...
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39 views

Entropy of the boundary and stress-energy tensor in the bulk

The importance of this result cannot be understated: Positivity, monotonicity and convexity of relative entropy in the boundary is implied by the positivity of the stress-energy density tensor in the ...
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1answer
24 views

Meaning of these terms for stress fields?

I'm from a math & comp sci background and I'm currently looking at facture theory which deals with stress fields. Can someone explain to me what the following terms represent in the context of a ...
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1answer
43 views

The significance of the pressure term within the momentum-energy tensor [duplicate]

EDIT: this question is based around my notion regarding the possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$, The answer below resolves the question and I have deleted ...
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197 views

Intuitive understanding of the elements in the stress-energy tensor

There is an image in the Wikipedia about the stress-energy tensor: I have a rough understanding of the stress tensor: you imagine cutting out a tiny cube from the fluid and form a matrix out of the ...
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74 views

The divergence of the Stress Energy Tensor

I have been studying general relativity and I have often seen in textbooks that the divergence of the stress energy tensor is zero. $$T^{\mu\nu}_{;\nu} = 0$$ but is it possible to contract and ...
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54 views

Converging light

Imagine that we emit a light pulse. As is the nature of light, it will expand. However, light is affected by gravitational fields and light has its own. Therefore, will the light converge given ...
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1answer
63 views

What is the gravitational effect inside a electromagnetic shield due to an external electromagnetic field?

I am new in General Relativity. I know that electromagnetic field (or, the electromagnetic energy tensor, $T^{ik}=1/4\pi[1/4F_{mn}F^{mn}g^{ik}-F^i_lF^{lk}]$) can affect gravitation. Now if we take a ...
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1answer
57 views

Derivation of the energy-momentum tensor for an imperfect fluid

In chapter 7 of the "Physical Foundations of Cosmology" Mukhanov uses this energy-momentum tensor for an imperfect fluid: $T^\mu_\nu = (\rho + p)u^\mu u_\nu - p\delta^\mu_\nu - \eta(P^\mu_\gamma ...
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1answer
80 views

Deriving the energy-momentum tensor conservation equation in complex coordinates, Polchinski 2.4.2

I am trying to derive equation (2.4.2) in Polchinski's string theory textbook, $$\overline \partial T_{zz}=\partial T_{\overline z \overline z} = 0 \tag{2.4.2}.$$ Using the conservation equation, ...
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68 views

Why can we not choose the stress tensor in a CFT to be identically symmetric?

The stress tensor for a conformal field theory (or any quantum field theory) can be derived from the action $S$ by the functional derivative $$T^{\mu \nu} ~=~ -\frac{2}{\sqrt{|g|}}\frac{\delta ...
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36 views

Calculate energy-density of known plasma in microwave?

Let's assume I want to create a plasma in a regular household microwave similar to this home-made experiment. Although I am dealing with a small amount of mass, I assume that the addition of microwave ...
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125 views

Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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39 views

electroweak field contribution to the space curvature in GR

i've just found out that EM stress energy tensor along with gravitational stress energy contribute to the curvature of space. So, does the electroweak field also contribute to the curvature of space? ...
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Does this identity that applies to the metric tensor also apply to the stress-energy tensor?

Okay so if the $g_{00}$ component of the metric is $-c^2$ and $g_{11}=g_{22}=g_{33}$ and all the other other components are zero, the question is simple, would similar identities apply to the ...
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1answer
77 views

In general, can a Lagrangian density depend on space-time explicitly?

In an exercise on classical field theories, I'm trying to derive the general formula of the Energy-momentum tensor. According to the formula in the lecture notes, this tensor includes a term of minus ...
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1answer
40 views

What observation(s)--if any--confirm that the types & concentrations of energy, which are influenced by gravity, are the same ones that cause gravity?

General relativity allows various forms of energy to participate in the gravitational force. What observation(s)--if any--confirm general relativity's notion that the various types & ...
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1answer
68 views

Real-world evidence that non-massive entities (or even: antiparticles), and their behaviors, are sources of gravity?

The theory of general relativity tells us that non-massive entities, and their behaviors, are possible sources of gravity. Mass isn't needed, the theory says. What's the real-world evidence that ...
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384 views

Negative pressure, tension, and energy conditions

We have lots of common everyday experience with positive pressure, the canonical example is a gas. But other examples of positive pressure are easy to imagine: for instance, a solid that gets ...
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1answer
107 views

How can I use Einstein's field equations to find the metric tensor? [duplicate]

I have watched and read a lot on the topic of General Relativity and the geometry behind it. I am confident that I can derive an approximation of the the stress-energy-momentum tensor with just the ...
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3answers
183 views

Is every spacetime metric physically realizable?

Is every spacetime metric physically realizable? I know that given any spacetime metric, you could work out a stress-energy tensor for each position that would result in that metric. However, I also ...
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82 views

Time dilation as an effect of energy density

Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation? i.e. Higher energy density==>Slower rate of time?
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63 views

Will a stress-energy tensor have the same identities as it's metric?

Say I have a metric tensor where $$g_{00} = -c^{2}\ and $$ $$g_{01}=g_{02}=g_{03}=0$$ and $$g_{12}=g_{13}=g_{23}$$ and $$g_{11}=g_{22}=g_{33}$$ My question is straightforward: would the same or ...
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150 views

What is the meaning of Einstein's field equation in terms of source and its effects on curvature?

The Einstein's Field Equation is $$R_{\mu\nu}-(1/2)g_{\mu\nu}R=-8\pi T_{\mu\nu},$$ where the left hand side is the curvature term and the right hand side is the source term (see, Hartle). Now, in the ...
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1answer
80 views

Hamiltonian density of classical Klein-Gordon field

I am working my way through Peskin and Schroeder section 2.2 and trying to show that $T^{00}$ is equivalent to the expression $\frac{1}{2}\pi^2-\frac{1}{2}(\nabla \phi)^2-\frac{1}{2}m^2\phi^2$ in ...
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1answer
71 views

Computation of $T^{\mu\nu}$ from Lagrangian density $\mathscr{L} $

I am trying to understand how upper and lower indices are connected when computing the energy-momentum tensor. In particular, I found the simple problem where the Lagrangian density is given as ...
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1answer
85 views

Different forms of the Einstein field equation

I am working my way through the wonderfully written introduction "General relativity for mathematicians" by Sachs & Wu. I am indeed a mathematics student and find this book to be well suited to ...
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1answer
41 views

Stress Energy tensor for non-relativistic particle [closed]

I am trying to write down the elements of stress-energy tensor for a point particle moving with non-relativistic velocity $v$. I have written : $ T_{00} = mc\delta(\vec{r} -\vec{r}') $ and $ T_{0i} ...
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1answer
55 views

Energy-Momentum Tensor with mixed indices

I know that $T_{\mu\nu}$ is the Energy-Momentum Tensor and $T=g^{\mu\nu}T_{\mu\nu}$, but does anyone know what $T^{\nu}_{\mu}$ is and how its calculated?
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1answer
577 views

Why does the Ricci tensor vanishes in Schwarzschild metric? [duplicate]

If the Schwarzschild metric is suppose to describe the behaviour of a spherical object in flat space, so the Schwarzschild is different from the flat metric because it describes curved space so why ...
2
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1answer
120 views

Doubt regarding stress-energy tensor definition

I'm having some trouble understanding the following definition of the stress energy tensor: $T^{\mu\nu}$ is the flux of four-momentum $p^{\mu}$ across a surface of constant $x^{\nu}$. Here's an ...