# General relaivity Definition and 137 Discussions

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1. ### I How strong is dark energy relative to gravity in the voids?

Assuming dark energy is fairly, uniformly distributed through out the cosmos, how strong is it, or how much energy is associate with it, out in the deepest, emptiest voids in space? I'm specificlaly refering to the great voids in between the great walls of galaxy clusters. I'm making the...
2. ### B If gravity was a force wouldn't going back in time cause us to float?

This might sound as a dumb and silly question but if you think about it, it makes sense. If we wrongly assume that gravity is a force just like any other, and given the fact that time is closely related to gravity and that gravitational time dilation is a thing, wouldn't reverse time travel...
3. ### I Spacetimes, metrics and symmetries in the theory of relativity?

I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970) In the paper, the authors describe "spacetimes without symmetries". When I mentioned that, one of my friends said that no spacetime predicted or included in the theory of relativity...
4. ### Help with formatting math

I'm not aware of the mathcode here, so forgive me for not posting my work straight away. I simply need to ascertain what code first displays equations. $a$ a a
5. ### A Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor

Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units? Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR? If so, What...
6. ### A Pseudoscience video on General Relativity gains a lot of popularity

Here is the video: [link deleted by moderators] His basic idea is to take the spacetime interval and add a 5th term for the 5th dimension he is describing so it looks like: $$\Delta S^2 = c^2\Delta t^2 + c^2\Delta w^2 - \Delta x^2 - \Delta y^2 - \Delta z^2$$ where w is the difference in time...
7. ### I Orbital precession unit

Hi, I've just calculated the orbital precession for the earth using the sigma formula of general relativity. $$\sigma=\frac{24 \pi^{3} R^{2}}{T^{2} c^{2}\left(1-e^{2}\right)}=\frac{24\pi^3×1.5×10^{11}}{3×10^7×3×10^8(1-0.0034^2)}=0.012$$ What is the unit of the result? Degrees per century or...
8. ### I What would an observer inside of a collapsing shell observe?

What does and observer inside of a collapsing shell observe? Lets say we have a shell of matter collapsing to a black hole. What would observers near the center see? How would the rest of the universe appear when, The shell is approaching the Schwarzschild radius? After the shell passes the...
9. ### A The scale of an extra dimension

Any help to understand how the authors of this paper Fine Tuning Problem of the Cosmological Constant in a Generalized Randall-Sundrum Model calculted this size of the extra dimension Equ. (3.8) from the scale factor defined by Equ. (3.3) ? Specifically, this paragraph after Equ. (3.8) -...

25. ### Help with variation of the 3-dimensional ##\sigma##-model action

Consider the following action $$S=\int\mathrm{d}^3x\sqrt{h}\left[R^{(3)}-\frac{1}{4}\mathrm{Tr}\left(\chi^{-1}\chi_{,i}\chi^{-1}\chi^{,i}\right)\right]$$ where ##h## is the determinant of the 3-dimensional metric tensor ##h_{ij}## and ##R## is the Ricci scalar. I want to get the equations of...
26. ### I What if Einstein equivalence principle is proven wrong one day?

What would be the consequences of such thing? How it will affect physics theories and the world?
27. ### Help with a calculation about gravitational waves

An exact gravitational plane wave solution to Einstein's field equation has the line metric $$\mathrm{d}s^2=-2\mathrm{d}u\mathrm{d}v+a^2(u)\mathrm{d}^2x+b^2(u)\mathrm{d}^2y.$$ I have calculated the non-vanishing Christoffel symbols and Ricci curvature components and used the vacuum Einstein...
28. ### Relativity I want to learn special relativity. More details below

I want to learn special relativity.I have read a tiny bit of 2nd edition of Spacetime Physics: Introduction to Special Relativity and am liking it. Is it a good book? I also want problems to solve. I tried Special Relativity: For the Enthusiastic Beginner but found it to difficult. Does anyone...
29. ### A How Randall-Sundrum model has solved the hierarchy problem?

I'm trying to understand how the RS model solved the hierarchy problem from this mass relation $$M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$ Equ. 16 in their paper: https://arxiv.org/abs/hep-ph/9905221 With k as large as the Planck scale, the exponential will be so small and...
30. ### A Deriving an action from a metric

Hello! The paper I study is related to string theory and modified gravity theories topics. As they say in page 5 “The four-dimensional effective theory now follows by substituting Eq. (13) into the original action, Eq. (4)” I wonder how did they drive a 4- dimensional effective metric...
31. ### Help with Kaluza Klein Christoffel symbols

If I want to calculate ##\tilde{\Gamma}^\lambda_{\mu 5}##, I will write \begin{align} \tilde{\Gamma}^\lambda_{\mu 5} & = \frac{1}{2} \tilde{g}^{\lambda X} \left(\partial_\mu \tilde{g}_{5 X} + \partial_5 \tilde{g}_{\mu X} - \partial_X \tilde{g}_{\mu 5}\right) \\ & =\frac{1}{2}...
32. ### Relativity Exercises in Math of GR

I have been reading the book Spacetime and Geometry by Sean Carroll, especially Ch. 2 Manifolds and Ch. 3 Curvature. I'm just wondering are there any lecture notes or books with lots of practice problems (with solutions or at least answers the better) that is suitable for physicist? To give an...
33. ### I Position vector in a curved space time

It is said that: It is not possible to write a position vector in a curved space time. What is the reason? How can one describe a general vector in a curved space time? Can you please suggest a good textbook or an article which explains this aspect?

40. ### A Induced metric for Riemann hypersurface

We know in Lorentzian signature spacetime, in the case of timelike or spacelike hypersurfaces ##\Sigma## with \begin{align} n^\alpha n_\alpha=\epsilon=\pm1 \end{align} where ##\epsilon=1## for timelike and ##-1## for spacelike. We can define a tensor ## h_{\alpha\beta}## on ##\Sigma## by...
41. ### Star collapse in general relativity — pressure as a function of star radius

What I've done is using the TOV equations and I what I found at the end is: ##e^{[\frac{-8}{3}\pi G\rho]r^2+[\frac{16}{9}(G\pi\rho)^{2}]r^4}-\rho=P(r)## so I am sure that this is not right, if someone can help me knowing it I really apricate it :)
42. ### I General Relativity - bending spacetime - gravity - Question

Hi everybody I saw quite a nice Youtube vid about general relativity and how gravity bends spacetime and therefor redirects angular momentum into the center of gravity. I thought the first time I begun to understand the concept but immediatly the questions poped up. The video basically says...
43. ### A How do I obtain a normal vector of a bubble wall?

So say I have a bubble embedded in a spacetime with metric: $$ds^2 = -dt^2 + a(t) ( dr^2 + r^2 d\Omega^2_2)$$ how do I compute the normal vector if I assume the wall of the bubble the metric represents follows a time-like trajectory, for any ##a(t)##? Since we are interested in dynamical...
44. ### I Speed of light not an invariant in GR

Hi all, I need help understanding the light ray bending in the original GR 1916 paper, Die Grundlagen.... First of all, Einstein states the ##c## is not an invariant in GR. In fact, from (70) and (73), it stems that $$\gamma = \sqrt{ -\frac {g_{44}}{g_{22}} },$$ where ##\gamma## is ##|c| <= 1##...
45. ### B Seek correct visualization of curvature of spacetime (1s+1t) in 3d

Via web search found https://www.physicsforums.com/threads/what-dimension-does-space-time-curve-in.852103/ Read it and watched two videos mentioned: I understand we cannot perceive 5D ;-), so extrinsic visualization of maximum of 2D intrinsic curvature is possible. So time+1d space is all we...
46. ### I Gravity transition directly at the underside of a "shell planet"

I'm watching the Stanford University Lecture series: Einsten's General Theory of Relativity presented by Leonard Susskind (who incidentally has to be one of the greatest educators I've ever watched). Whilst deriving the basic divergence equations relating acceleration, mass density, and...
47. G

### A Metric Ansatz For Unifying All Forces In 11D?

The ansatz for the 5D metric is $$G_{\mu \nu}= g_{\mu \nu}+ \phi A_{\mu} A_{\nu},$$ $$G_{5\nu} = \phi A_{\nu},$$ $$G_{55} = \phi.$$ This information was extremely enlightening for me, but what's the analogous...
48. ### Equation of motion in curved spacetime

1) We know that for a given Killing vector ##K^\mu## the quantity ##g_{\mu\nu}K^\mu \dot q^\nu## is conserved along the geodesic ##q^k##, ##k\in\{t,r,x,y\}## . Therefore we find, with the three given Killing vectors ##\delta^t_0, \delta^x_0## and ##\delta^y_0## the conserved quantities Q^t :=...
49. ### I Spacetime distance between spacelike related events

Hi, in general relativity I'm aware of the spacetime 'distance' between two timelike related events is maximized by the free falling timelike path (zero proper acceleration) joining them. Consider now a couple of events belonging to a spacelike hypersurface (AFAIK it is an hypersurface with...
50. ### A Help on some equations in Einstein's original papers

Studying Einstein's original Die Grundlage der allgemeinen Relativitätstheorie, published in 1916's Annalen Der Physik, I came across some equations which I couldn't verify after doing the computations hinted at. The first are equations 47b) regarding the gravity contribution to the...