General relativity Definition and 999 Threads

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 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...

Has anyone heard of papers describing Brans-Dicke vacuum cosmology solutions? I'd be interested to know if the following calculations make sense. I assumed a constant mass density vacuum with equation of state ##p=-\rho##. I then plugged this equation of state into the Brans-Dicke equations...

Hi, starting from this very interesting thread I'm still a bit confused about the conclusions. The main point, as far as I can understand, is all about conditions for a quadrilateral to be considered a parallelogram. My first basic doubt is: the concept of 'parallel' applies just to geodesic...

Hello everyone! It seems I can't solve this exercise and I don't know where I fail. By inserting the metric on the lefthand side of I. and employing the chain rule, the equation eventually reads (confirmed by my notes from the tutorial): $$m\frac{\mathrm{d}p_\delta}{\mathrm{d}t} =...

If an astronaut travels to a 10 ly distant star with a speed very close to light speed, then he will measure a distance to his star much smaller than 10 ly (length contraction) so his time for reaching the star will be smaller than 10 years, let's say 1 year. Then, without delay, he returns back...

Let me begin by stating that I'm aware of the fact that this is a metric of de Sitter spacetime, aka I know the solution, my problem is getting there. My idea/approach so far: in the coordinates ##(u,v)## the metric is given by $$g_{\mu\nu}= \begin{pmatrix}1 & 0\\ 0 & -u^2\end{pmatrix}.$$ The...

In this paper by Carlip, a comparison is made between electromagnetic and gravitational aberration. For the latter case, he takes as a study subject the Kinnersley’s “photon rocket”, an exact solution which is known to have the strange property of not producing any gravitational waves, even...

I always was confused on how objects fall on Earth due to curvature of space. All I see everywhere is a flat stretched piece of fabric and balls going round and round the central massive ball. But that does not explain anything, how objects actually fall. Finally I saw this video where it...

Let us say that we have a stellar object so its total velocity is defined as $$ v_{tot} = v_{pec} + V_{rec}$$ Where $$V_{rec} = H_0r$$ and $$V(z) = \frac{cz}{1+z}[1+\frac{1}{2}(1-q_0)z - \frac{1}{6}(1-q_0-3q_0^2+j_0)z^2]$$ for small z.So my first question is what is the $z$ value here? Is...

One obvious difference is that gravity is more general, because there are alternative theories of gravity that differ from general relativity. In this sense general relativity can be thought of as a subset of gravity. But I am interested in a different type of difference. I am interested in a...

I'm a bit confused about the notation used in the exercise statement, but if I'm not misunderstanding we have $$\begin{align*}(\psi^+_1)^{-1}:\begin{array}{rcl} \{\lambda^1,\lambda^2\in [a,b]\mid (\lambda^1)^2+(\lambda^2)^2<1\}&\longrightarrow& \{\pm x_1>0\}\subset \mathbb{S}^2\\...

Attempt: I don't know what they mean by effective Lagrangian. I am aware there is something called 'the lagrangian' that goes as L=g_ab * dx^a/dk * dx^b/dk, but i don't see how this gives me any of the chrostoffel symbols... cheers

I am very new to such ideas but was wondering if there is any connection to what I am asking. Taking two events, let's say at opposite ends of the globe. Would even A, only have a potential on event B, if light could travel between these event in the given time frame of these event occurring...

Hello. I've recently been reading this paper... https://arxiv.org/pdf/gr-qc/0001099.pdf ...in the hope that I can begin to understand some the role of the energy conditions in General Relativity. But I'm not making much progress and so I've turned to this paper...

"their scalar product is..." why?

If you’re traveling at the speed of light TOWARDS a mirror, will you be able to see yourself?

In Newtonian gravity, non-rest mass contributions to gravitational effects are ignored and for many purposes (e.g. low precision solar system astronomy, N-body approximations of galaxy or galaxy cluster dynamics), the other contributions that enter Einstein's field equations through the...

T = (x+\frac{1}{\alpha}) sinh(\alpha t) X = (x+\frac{1}{\alpha}) cosh(\alpha t) - \frac{1}{\alpha} Objective is to show that ds^2 = -(1 +\alpha x)^2 dt^2 + dx^2 via finding dT and dX and inserting them into ds^2 = -dT^2 + dX^2 Incorrect attempt #1: dT= (dx+\frac{1}{\alpha})...

Summary: At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough...

I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad $$. Expressing the first term in the equation as $$ (P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r} $$ I obtained the...

The Friedman Equations is based on the cosmological principle, which states that the universe at sufficiently large scale is homogeneous and isotropic. But what if, as an hypothesis, the universe was anisotropic and the clustering of masses are aligned to an arbitrary axis (axial pole), how...

According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...

This thread is supposed to be about finding flaws in General Relativity, but the way these people talk they sound like they have no real knowledge of GR. I was just curious if any of you guys could explain further.

My name is Martin Scholtz and I am a postdoc researcher at the Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic. I'm working mainly in the area of gravitational physics, but I am interested in different topics as well, see tags...

Hi, I'm worried I've got a grave misunderstanding. Also, throughout this post, a prime mark (') will indicate the transformed versions of my tensor, coordinates, etc. I'm going to define a tensor. $$T^\mu_\nu \partial_\mu \otimes dx^\nu$$ Now I'd like to investigate how the tensor transforms...

Have there been any recent developments in the attempt to unify the standard model of quantum theory with General Relativity? It appears the no progress has been made recently in string theory or loop quantum gravity.

If Earth's motion about the sun is described by General Relativity why was Eddington's experiment with the bending of starlight needed to confirm the theory? In other words, don't we see enough common phenomena in our every day experiences to confirm GR without verifying subtle phenomena such as...

I know that it would vary depending on the type of research a specific astronomer would be doing ( Astrophysics/Cosmology research versus an Astronomer researching exoplanets ) ; but in your opinion, “how much” or “how well” should an Astronomer with a graduate degree in Astronomy know General...

From Thomas Moore A General Relativity Workbook I have the geodesic equation as, $$ 0=\frac{d}{d \tau} (g_{\alpha \beta} \frac{dx^\beta}{d \tau}) - \frac{1}{2} \partial_\alpha g_{\mu\nu} \frac{dx^\mu}{d \tau} \frac{dx^\nu}{d \tau} $$ as well as $$ 0= \frac{d^2x^\gamma}{d \tau^2} +...

I am reading the following paper on the basic physics of a binary black hole merger: https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf Imagine two black holes orbiting each other until a point they merge. As you can see in Figure 1, the wave period is decreasing and thus the frequency...

i am far from an expert in Special and General Relativity, however, my attempts to learn from this forum are hampered by the large volume of posts involving common misconceptions and lack of understanding of the material. while the members of the forums patiently [usually] help our novice and...

Just wondering if I'm going to be in over my head here, as I'm not sure what to expect. A notoriously "difficult" professor as my school is teaching a senior level undergraduate course "Introduction to General Relativity Physical consequences of Einstein's equations, including the principle of...

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