General relativity Definition and 999 Threads

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...

In the test of General Relativity by perihelion motion of mercury, the stress-energy tensor is set to 0 in Schwarzschild solution. Then, is the curvature caused by solar mass, or by the 0 stress-energy? Or, do we consider solar mass as the gravitating mass? Or the 0 stress-energy the gravitating...

This video explains gravity in a way I haven't encountered before (regardless of how irritating the presenter may be). Nevertheless, I find it hard to believe that a squirrel falls from a tree to the ground due to gravitational time dilation between its head and its feet. The amount is so...

We are discussing the introduction to Einstein field equation, so he start talk about the linearity in Newtonian gravity and the non linearity in GR. But there is somethings I am missing: > " (...) in GR the gravitational field couples to itself (...) A nice way to think about this is provided...

Off the back of a recently closed thread where there was some discussion about the gravitational field of an infinite flat slab, I decided to have a play at investigating that. I've found a few interesting things. It's fairly straightforward to solve for this situation. You use Cartesian-esque...

Hello, What I understood from multiple answers on different threads is that the effect of the time dilation is too small to explain the galaxy rotation curve. I was advised to do some calculations in order to see it myself. And this is what I would like to do but I need some help. - What is...

I know that general relativity fails in singularities like the center of a black hole or the big bang. GR also fails at fundamental particle levels like electrons, protons and neutrons etc. I.e. GR cannot explain interactions of various fundamental particles?? (Am I correct?) But these does...

I was going over the Einstein-Hilbert action derivation of the Einstein field equations and came across a term that does not seem to be explicitly defined. That term is the Langragian for the matter fields. What exactly is matter in General relativity in the context of the Lagrangian? Here is...

Disclaimer - I am not an expert by any means so this might be as much about confirming my understanding as an inquiry from the general public... as such, it might be fairly conversational as I attempt to clearly communicate my thoughts and understanding. Please excuse this. If gravity is the...

Hello. I have a question about the law of energy conservation in GR. As time is inhmogeneous, we don't have energy-momentum 4-vector which would be preserved during system's dynamical change. It is only possible to define 4-vector locally. And next, the problem regarding how to sum this vectors...

Summary:: I am looking for a good introductory book about general relativity at undergraduate level. I am looking for a good introductory book about general relativity at undergraduate level.

I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what...

I am trying to understand a thought experiment I just posed, which is: if an observer is traveling near the speed of light, and sends out two photons; one in the direction of travel and one in the opposite direction, how does general relativity account for time dilation? The photon "in front"...

Trying to understand how Einstein predicted the appearance of stars during the solar eclipse around the turn of the 20th century (the first experimental confirmation of General Relativity, I believe). My impression, which is not physically correct, is that the sun attracts the photons as they...

General relativity. Curvature of spacetime: ok. time dilation: ok. What about space? Curvature is intrinsic and given by complex equations. But could we definitely say is there more space between 2 points along curved space through the star than would be through flat space (no star there) or...

i'm trying to find what sort of 2-d geometry this system is in, I've been given the line element 𝑑𝑠2=−sin𝜃cos𝜃sin𝜙cos𝜙[𝑑𝜃2+𝑑𝜙2]+(sin2𝜃sin2𝜙+cos2𝜃cos2𝜙)𝑑𝜃𝑑𝜙 where 0≤𝜙<2𝜋 and 0≤𝜃<𝜋/2 Im just not sure where to start. I've tried converting the coordinates to cartesian to see if it yields a...

When parallel transporting a vector along a straight line on flat space, does the connection (when calculating the covariant derivative) always equal zero? Do things change at all when using an arbitrary connection, rather than Christoffel symbols?

Is there a relationship between the Lagrangian ‘hill diagram’ and the spacetime curvature embedment graphs? The Lagrangian map shows effective potential, which deals with centrifugal force. As centrifugal force is a fictitious force (and gravity is as well), I would assume the underlying...

Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks

Einstein's theory describes gravity as a curvature of spacetime. As such, everything is affected by it. This includes light, which has no mass, as was made clear for the first time during the famous 1919 solar eclipse. In the standard model, the cause of gravity is supposed to be gravitons...

Helo, The Lagrangian in general relativity is written in the following form: \begin {aligned} \mathcal {L} & = \frac {1} {2} g ^ {\mu \nu} \nabla \mu \phi \nabla \nu \phi-V (\phi) \\ & = R + \dfrac {16 \pi G} {c ^ {4}} \mathcal {L} _ {\mathcal {M}} \end {aligned} with ## g ^ {\mu \nu}: ## the...

Background and Motivation The stress energy tensor of general relativity, as conventionally defined, has sixteen components. One of those component, conventionally component T00, also called ρ, is mass-energy density, including the E=mc2 conversion for electromagnetic fields. The other...

HI, I'm curios about the analytic derivation of Mercury perihelion precession starting from EFE - Einstein Field Equation (or simply just from Schwarzschild solution of the EFE). Can you advise me about some source or online material to learn it ? Thanks.

I haven't gone to movie theaters in 6 months. So I have to be content with online movies, and reading sci fi models, and maybe writing a short story or two. If a flying ship could travel thousands of miles per second, it can't suddenly turn 90 degrees because of inertia, the occupants would be...

Hey there.Have you read about the alternative theories proposed by other scientists to General Relativity?So far General Relativity still stays the most accurate.But if we could generalise it?Perhaps try with some new maths like complex differentiable manifolds or Lie groups or another...

Actually I know there would be some permutations used here. I know how to calculate the symbols but estimating is quite a new thing to me

"The dual space is the space of all linear maps from the original vector space to the real numbers." Spacetime and Geometry by Carroll. Dual space can be anything that maps a vector space (including matrix and all other vector spaces) to real numbers. So why do we picked only a vector as a...

Prof Wetterich has proposed that atoms are shrinking rather than the Universe is expanding. Here is a 2013 Nature News article describing his theory: https://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379 Here is his 2013 paper "A Universe without expansion"...

Good day, I'm starting my master in physics, and it's time for me to choose my courses. I will take one or two of the following three courses, which are: Statistical Physics, QFT and General relativity. Now, I'm finding it very hard to decide as on the one hand, I'm interested in QFT and...

Hi, can i use a light clock made out of mirrors a distance appart to measure whether there is length contraction in different regions of spacetime? If the clock speeds up then the distance between the mirrors decreased. If the clock slows down the distance between mirrors increased.

Hi. I have tried David Tong's note on QFT. I think it works well for me and lead me into QFT. Now I am confident to read Peskin's book. Now I am trying to learning GR. I planned to try David Tong's lectures on GR first and then read Sean Carroll's book. But I am not sure this plan now. I got...

My attempt: Realize we can work in whatever coordinate system we want, therefore we might as well work in the rest frame of the fluid. In this case ##u^a=(c,\vec{0})##. The conservation law reads ##\nabla^a T_{ab}=0##. Let us pick the Levi-Civita connection so that we don't have to worry about...

As far as I understand it general relativity does not explain the origin of the inertial mass ##m_i## in Newton's law of motion ##\vec{F}=m_i\ d\vec{v}/dt## but rather it simply applies the concept to curved spacetime. For example if we have a particle with inertial mass ##m_i## and charge...

Consider a mass ##M## that generates a curvature of the space-time and an observer ##O##, fixed and positioned at such a great distance from ##M## that the time ##t## of its clock is not affected by ##M##. Suppose that the observer ##O##, in his polar coordinates reference system centred at...

The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by $$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$ Faraday's law of induction for the induced EMF ##V_c## in a coil...

There are some universe models where ##\Lambda < 0##. In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time? Such that, ##\Lambda <...

It seems that there are two distinct gravitational cases to consider: a) Object with no external contact with any type of stuff (e.g., a person in free-fall in a vacuum) b) Object WITH external contact (e.g., a person standing on the ground) I've enjoyed reading and listening to various...

Given a one parameter family of geodesics, the variation vector field is a Jacobi field. Mathematically this means that the field, ##J##, satisfies the differential equation ## ∇_{V}∇_{V}J =- R(V,J,)V## where ##V## is the tangent vector field and ##R## is the curvature tensor and ##∇## is the...

Hey there, I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ##{ g...

James Clerk Maxwell deduced that the unit of mass has the dimensions of (L^3)(T^-2). But he assumed Newton's Law. What would it be under general relativity?

Hello everyone, Heisenberg's uncertainty principle tells us that we cannot measure the position and the momentum of a particle to infinite accuracy. My question is, can we use general relativity to overcome this difficulty? From what I know, any mass can curve spacetime even if it was small, and...

Hi. What are the math courses should I take in order to understand the mathematics involved in a book such as Sean Carroll in general relativity. Thanks

I am trying to study "religiously" the book by Sachs and Wu, but I am finding the Exercises very much of a challenge. Does anyone know if there exists a source for solutions one can consult when stuck?

If anybody has studied the book: A First course in String Theory - Barton Zweibach - 2nd edition This statement is present in 6th chapter of book on pg 110

Well I became interested in String theory before my high school. Now I am in ginal year of my BS in Physics. I am working on a project in string theory.

Why does the constraint: $$R_{ijkl}=K(g_{ik} g_{jl} - g_{il}g_{jk})$$ Imply that the resulting space is maximally symmetric? The GR book I'm using takes this relation more or less as a definition, what is the idea behind here?

I'm going through the "Advanced Lectures on General Relativity" by G. Compère and got stuck with solving one set of conditions on the subject of asymptotic flatness. Let ##(M,g)## be ##4##-dimensional spacetime and ##(u,r,x^A)## be a chart such that the coordinate expression of ##g## is in Bondi...

I have been at this exercise for the past two days now, and I finally decided to get some help. I am learning General Relativity using Carrolls Spacetime and Geometry on my own, so I can't really ask a tutor or something. I think I have a solution, but I am really unsure about it and I found 6...

Summary:: I want to learn special and general relativity I am curious what is the best way to learn special and general relativity. https://www.coursera.org/learn/einstein-relativity/home/info I started this course but it seems relativity easy so far. Only on week 2. Being easy is not bad I...

I was reading an article about the misconceptions in cosmological horizons and I wanted to clarify an idea. https://arxiv.org/abs/astro-ph/0310808 In cosmological perspective, is there a global inertial reference frame (maybe CMB) ? Or all inertial frames are defined locally and there is no...