Gr Definition and 937 Threads

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...

The Schwarzschild solution of the Einstein Equation of GR is said to be the only time-independent matter-free solution of that equation. In this usage, does “matter-free solution” mean without matter everywhere except at the singularity of the solution? I thought that the only solutions of the...

Hello I have been going through the cosmology chapter in Choquet Bruhats GR and Einstein equations and in definition 3.1 of chapter 5 she defines the sectional curvature with a Riemann( X, Y;X, Y) (X and Y two vectors) I don't understand this notation, regarding the use of the semi colon, is it...

I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange. GR cannot accommodate a non-symmetric momentum tensor...

So I just learned that in general relativity Magnatic and Electric fields are dependent on the observer. What are some consequences as a result?

Homework Statement Hi I am looking at the attached as part of the derivation and am stuck on how we go from 18 to 19 [/B]Homework Equations Above below The Attempt at a Solution [/B] I'm pretty stuck. Lambda is small and not sin so can't see why one would expand out sine in a Taylor...

Hi all! Happy New year! I will select my supervisor soon but i want to involve in the field that uses QM or GR frequently I love physics and i want to apply physics to explain astrophysical phenomenon. I know that Compact objects and Astrochemistry use such physics but i wonder to know more...

Homework Statement I am trying to follow my lecture notes, attached below, an argument to the number of degrees of freedom from the number of constraints of he Einstein field equations The bit I a man stuck on is the second thumbnail, and the deduction that he righ hand side of 5.18 only has...

In GR Mass is said to curve spacetime which is the explanation for Gravity versus Newtonian physics where it is explained as all matter attracts each other. My question is how does curved spacetime cause objects traveling at different velocities to follow different paths? If gravity was only due...

In his GR youtube talk ( , starting 24:30), Susskind shows that a light photon on straight path in a stationary frame has a curved path in an accelerated frame. Concluding, as did also Einstein, that gravity deflects photons. But exactly the same argument applies to massless particles. Meaning...

hi! Do you know about a good book that introduces relativistic quantum mechanics with one-forms (diferential forms) like the book a first course of general relativity of Schutz does?

In recently closed thread titled Conservation of energy in GR, 4-velocity of popped up baseball along geodestic ##(u^0(r),u^1(r),0,0)## where ##x^1=r,x^2=\theta,x^3=\phi##, is derived. In SR, 4-momentum of ball is ##m(u^0,u^1,0,0)## in contravariant component and ##m(u_0,u_1,0,0)## in covariant...

I would like to understand better about the conservation of energy in GR. Let us think of infinitesimal vacuum volume dr\ sin\theta d\theta d\phi around the star in center. Light emitted from the star hit the bottom surface, r, of the volume. Say violet light photons hit the area 1 photon/1...

For the purposes of distance measurement, time measurement of signals, and so on, can we approximate the distance across the Milky Way as an extended inertial reference frame? Or is that way out of bounds? (I mean obviously there are massive bodies that already prohibit that, I suspect, but say...

https://universe-review.ca/I02-24-inflation2.png https://courses.lumenlearning.com/astronomy/chapter/the-inflationary-universe/ http://abyss.uoregon.edu/~js/ast123/lectures/lec18.html Hello. The diagrams I've linked to are comparisons between the Standard Hot Big Bang and Inflationary...

Homework Statement This is a continuation of this problem. I will rewrite it here too: The Lagrangian density for the ##h=h^{00}## term of the Einstein gravity tensor can be simplified to: $$L=-\frac{1}{2}h\Box h + (M_p)^ah^2\Box h - (M_p)^b h T$$ The equations of motion following from this...

Homework Statement A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence What should the dimensions of the garden be if the area is...

Hi all, I’d like to ask why do we need to modify the General Relativity with theories like F(R) modified gravity ? Thanx

I decided to go deep in physics theories such as QFT, general QM and Special/General Relativity. Would it be better to spend a lot of time, say, 1+ year, learning through the most complete math books or just use books that mix math and physics to learn the necessary and suficient math and go to...

Hello, I was wondering if somebody could help me by suggesting a concrete topic in GR for my master's dissertation. My background is from Mathematics, but I have followed first year masters program courses in Theoretical Physics, including one on General Relativity based on Schutz's book...

It has occurred to me that there's a pretty simple thought experiment, and was wondering if any proposed theory of quantum gravity can "handle" it. Imagine a completely empty universe with just 2 hydrogen atoms. They are set up to orbit the common center of mass, being attracted to each other by...

Hi there I'm studying GR and I am confused about coordinate transformations. In my understanding, if I want to study a rotating reference system this is what I do. In my inertial system the object trajectory is described by $$ x = r\cos(\theta - \omega t)\\ y = r\sin(\theta - \omega t) $$...

I have a question regarding the interactions of electromagnetic fields. Say you have two superconducting electromagnets A and B. The properties of the magnets are known such that you can tell precisely how quickly it takes each one to produce it's full strength magnetic field and how long it...

1. The problem statement, all variables and given/known I don't understand the proof of the following theorem: Theorem 3.1.1 Let ##g_{ab}## be a metric. Then there exists a unique derivative operator ##\nabla_a## satisfying ##\nabla_a\,g_{bc}=0## 2. Homework Equations After some manipulations...

I am making this thread to discuss interesting open questions in Gravity and Cosmology with people working in these or even relevant area. Anyone who is working in these (and relevant) areas, please identify yourself here and we will begin and hopefully people will catch on and contribute.

It had previously been verified within our own galaxy. http://uopnews.port.ac.uk/2018/06/22/einstein-proved-right-in-another-galaxy/

Homework Statement part d) from the following question please Homework EquationsThe Attempt at a Solution [/B] sol attached So I see that the idea is that it is a maximum so to set ##\dot{r}=0## and then the maximum value is dependent on some values of J and K, to get the equation. But...

Homework Statement I would like to ask about parts c) and d) , the graph sketching bits. 2. Homework Equations ##V(r) = ( \frac{J^2}{r^2}+\epsilon)(r-\frac{1}{r}) ## where the value of ## \epsilon ## is set according to whether time-like or null etc. The Attempt at a Solution Q1)for...

*This question is beyond my education, but if you need to post graduate level math, feel free to, and if it requires changing this to A level, be my guest* So in SR, we assume that time dilation does not depend on acceleration, but only instantaneous speed. But in first learning about the...

Hi Can I just confirm that when we associate a T-L KvF with energy it should be the form ##\dot{t}^2## and not ##\dot{t}##, since I have seen a mix of the notation amongst notes/books, well with just one example using just ##\dot{t}##, I suspect it must be the ## \dot{t}^2 ## , since...

Homework Statement question attached- I am stuck on some of the reasoning as to why we set ##B(r=0)=0## please not as described in the attempt I am interested in the concepts and have not posted my solution to A, nor any solutions not relevant to the concepts I am trying to understand...

Hi All. On Tuesday I have to present my research proposal for my undergrad research. I intend to model our solar system using general relativity and compare and contrast my results with observations. Attached is my paper that I had to submit to my adviser. He suggested that I talk about some...

Homework Statement attached: I am stuck on question 2, and give my working to question 1 - the ##B(r) ## part I am fine with the ##A(r)## part which clearly is the same in both regions seen by looking at ##G_{rr}## , and attempt, however I assume I have gone wrong in 1 please see below for...

Based on what I’ve read here, I really have to absolutely kill linear algebra. Maybe some abstract algebra, too. And based on all this talk of manifolds, I’m guessing some topology and differential geometry is in order. Those of you who know GR, can you offer a math subject prescription so I...

As far as I can tell QM has several interpretations, but GR doesn't have such a diversity, am I correct? Why is that? Will a theory of QGR suffer also from the disease of QM and will yield several interpretations?

Hi So we write ##g_{ab}g^{ac}=\delta^{(4)c}_b ##, but this simply means to replace ##b## with ##c## or vice versa, so, why don't we write ##\delta_{bc}##? Thanks i.e. the affect is not to replace and raise/lower, it is simply to replace, so I'm a bit confused by the notation...

Hi I've done a masters taught module in GR and from what I've learned these are two of some of the most important significance of needing a Riemannian Geometry: 1) If we consider the Lagrangian of a freely-falling particle given by ##L= \int ds \sqrt{g_{uv}\dot{dx^u}\dot{dx^v}} ## and find the...

In STR we measure motion relative to a observer, and the he is rest respect to him. We make coordinates relative to "a rest frame" , that is the observer. In GTR ,all motion are calculated from which frame?

This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...

In another thread Peter Donis mentioned there may be a way to define energy properly GR. I always thought it highly problematical because you don't have time transnational symmetry so Nother can be applied. John Baez wrote an interesting article about it...

In Special Relativity, acceleration at high speeds causes time dilation and length contraction. Is it fair to restate this as; Acceleration at high speeds causes curvature of spacetime? In General Relativity, curvature of spacetime causes acceleration. Acceleration at high speeds causes...

Hi! I will soon begin my third year at the theoretical physics program. I have done a bunch of classical & Lagrangian mechanics, SP, atomic physics, electromagnetism, and basic particle physics. Is it a good idea to study general relativity and quantum field theory with this knowledge, what...

Recently I watched a video on Gravity according to General Relativity. The video shows that the Earth rises up to catch the apple, what does this mean? It also shows the time axis being curved as the apple falls. Doesn't this mean that with enough time falling, the time axis will curve into a...

[Moderator's note: spin off from previous thread.] Have you read Ohanian? He uses an entirely different approach much more in line with the Standard model type of equations and Lagrangian's, and shows how - first you get from an analogy with EM the linearised gravitational equations then how...

In special relativity, an object moving at higher speed experiences time dilation, length contraction, and mass increase, compared to an object moving at slower speed. In general relativity, for an object in stronger gravitational field (i.e., with higher acceleration due to gravity), time runs...

I get asked a lot of questions like "what is the gravitational field due to xyz curved spacetime" ... and I don't think the concepts match well the way the querant is thinking. However, I was wondering if there is a sort-of way to get to something like that. I would normally think of a...

When we talk about energy scales, we often hear that we need new theories of gravity and particle physics when we hit the barrier that is the Planck scale. In particle physics we've only probed up to about 13TeV, which is way WAY below that level. It's easy for us to designate the energy to...

I'd like this issue clarified I understand that a full nonpertubative quantization of a yang mills gauge theory in 4D is unavailable. is Dirac quantization of classical theory of gravity e.g GR rewritten Ashtekar Variables Variables or some variation of the idea, a viable approach to a...

Homework Statement I am stuck on finding ##W^u## Homework Equations [/B] I have computed the christoffel symbols via comparing the Euler-Lagrange equations to the form expected from geodesic equation. geodesic equation: ##\ddot{x^a}+\Gamma^a_{bc}\dot{x^b}\dot{x^c}=0## covariantly constant...

Homework Statement Homework Equations above The Attempt at a Solution I'm totally stuck as to how to get to started , how to use the hint to decompose a vector given a preferred spacetime direction. All I know is that any tensor can be decomposed into a anti symmetric and a symmetric...