# Tagged Questions

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### Boundary term in Einstein-Hilbert action

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting ...
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### Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields? My doubt comes from "The scalar-tensor Theory ...
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### The Einstein-Hilbert Action On-Shell

If one consider the Maxwell action as $$S=-\int \mathrm{d^{4}}x\! \ \frac{1}{4}F_{ab}F^{ab} \,$$ one find the usual Maxwell equation $$\partial_{a}F^{ab}=0$$ Then one can simply arrive the following ...
When taking the EH action, $$S_{EH} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}R$$ and making a small variation in the metric while ignoring boundary terms, we obtain $$\delta S_{EH} = \frac{1}{16\pi ... 1answer 116 views ### Intuition for actions written as integrals over spacetime Right now I'm simply looking for an intuitive explaination of actions that integrate over a 4-volume element, d^4x rather than a parameter say \lambda. More specifically I'm well versed in action ... 1answer 98 views ### Normal to the Hypersurfaces I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ... 1answer 129 views ### Curved spacetime point particle Lagrangian density This is probably trivially related to the question: Action for a point particle in a curved spacetime , but am a bit unsure how to write it as a Lagrangian density. In curved spacetime the action is ... 1answer 71 views ### Why we can set variations for the metric and its derivatives to zero at infinity? This question is the continuation of the following one. I still don't understand why (1) may be set to zero. This refers to the zero value variations of metric and its derivatives on the infinitely ... 3answers 438 views ### Is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations? I know that scaling the action with a non-zero multiplicative constant, or adding a total divergence term to the Lagrangian density do not change the Euler-Lagrange equations, cf. e.g. this ... 1answer 210 views ### Detailing why a scalar gravity theory predicts no bending of light [closed] I want to understand in technical detail why a particular scalar theory for gravity predicts no bending of light. It is left as a question, either in "Gravitation" by Misner, Thorne, and Wheeler, ... 1answer 541 views ### How to find the Stress-Energy tensor? I am a bit at loss about how to proceed to find the stress-energy tensor given some distribution of matter. The Wikipedia page gives some examples, and some (inequivalent) definitions for it: Using ... 1answer 161 views ### Expansion of action in general relativity? I am reading a lot about GR lately (because of thesis), and one thing bothers me, and I'm not finding a direct answer to it. For instance in one article, the author says that they are expanding ... 3answers 545 views ### Action for a point particle in a curved spacetime Is this action for a point particle in a curved spacetime correct?$$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$1answer 423 views ### Lagrangian for Euler Equations in general relativity The stress energy tensor for relativistic dust$$ T_{\mu\nu} = \rho v_\mu v_\nu $$follows from the action$$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu ...
Here is the formula for the stress energy tensor: $$T_{\mu\nu} = - {2\over\sqrt{ |\det g| }}{\delta S_{EM}\over \delta g^{\mu\nu}}$$ (This follows from varying the total action \$S ...