General relativity Definition and 999 Threads

I have the following question considering frame dragging: A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is...

One particular form of the equivalence principle states that The laws of physics for freely falling particles in a gravitational field are locally indistinguishable from those in a uniformly accelerating frame in Minkowski spacetime My question is, does one arrive at this conclusion from a...

Dear All, I am looking for tools and even online platform able to host a study group in physics. My goal would be the creation of a general relativity group. It will be a study group for graduated in physics (then not for amateurs) that for the simple pleasure of science would like to...

One of the founding principles in GR is the principle of general relativity, which loosely states that all coordinate frames (inertial and non-inertial) are equivalent in the sense that the laws of physics are invariant. My question is, does the justification for this come from Einstein's...

TL;DR Why does the Einstein equivalence principle imply that all forms of (non-gravitational) energy source curvature? Now, as understand it, the Einstein equivalence principle (EEP) implies (or at least suggests) that gravity is the manifestation of spacetime curvature, the reason being that...

The Einstein equivalence principle (EEP) states that “The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its position in spacetime.” I’m trying to make sure I’ve understood this correctly. I’m I correct to...

Hi, I am interested in simulating the vacuum field equations, but solving a full boundary value problem rather than the initial value problem. i.e. I might have boundary conditions in all spatial and temporal extents/extremes, rather than just an initial 3D surface. Does anyone know any free...

There are two kind of singularities which are familiar in General Relativity. One of them is the singularity of Black Holes and the other is at the beggining of the universe. I'm confortable with the former singularity --it seems to make sense. But as with the latter, I'm not so confortable...

In almost general case, the space-time metrics looks like: \begin{equation} ds^2 = g_{00}(dx^0)^2 + 2g_{0i}dx^0dx^i + g_{ik}dx^idx^k, \end{equation} where ##i,k = 1 \ldots 3## - are spatial indeces. The spatial distance between points (as determined, for example, by the stationary observer)...

Please don't kill me here...I am really just a curious creature...QFT and GR are mutually incapabatable ergo they cannot both be correct...so best is that one is used for low energy large scale predictions (as per theory) and small scale high energies ( as part theory) ...(BTW I know what the...

In the Feynman Lectures on Physics, Feynman explains the curvature of spacetime by drawing a rectangle in spacetime, see http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18 First waiting 100 sec and then moving 100 feet in height on Earth's surface results in a different situation...

Hi! With the re-release of the textbook "Gravitation" by Misner, Thorne and Wheeler, I was wondering if it is worth buying and if it's outdated. Upon checking the older version at the library, I found that the explanations and visualization techniques in the sections on differential(Riemannian)...

I thought about the geometry of Earth by definition and thought of the implications of 'curved space-time'. I understand a trajectory of a satellite and other objects to be straight geodesics through warped space-time. Would the Earth then therefore be able to described as a straight surface in...

Consider the AdS metric in D+1 dimensions ds^{2}=\frac{L^{2}}{z^{2}}\left(dz^{2}+\eta_{\mu\nu}dx^{\mu}dx^{\nu}\right) I wanted to calculate the Ricci tensor for this metric for D=3. ([\eta_{\mu\nu} is the Minkowski metric in D dimensions) I have found the following Christoffel symbols...

Consider the AdS metric in D+1 dimensions ds^{2}=\frac{L^{2}}{z^{2}}\left(dz^{2}+\eta_{\mu\nu}dx^{\mu}dx^{\nu}\right) I wanted to calculate the Ricci tensor for this metric for D=3. (\eta_{\mu\nu} is the Minkowski metric in D dimensions) I have found the following Christoffel symbols...

Hi guys, A real easy one. Are the following postulates completely true about general relativity as they are pretty amazing to me. 1) Black holes are a solution to his field equations for GR (or are predicted by the theory) 2) His field equations also suggested the universe was expanding 3)...

Hi all, I am reading Bernard Schutz's a first course in general relativity. In Chapter 4 it introduced the energy stress tensor in two ways: 1.) Dust grain 2.) Perfect fluid. The book defined the energy stress tensor for dust grain to be ## p⊗N ##, where ##p## is the 4 momentum for a single...

So, I'm going to learn general relativity but I'm confused in which book I start with Bernard Schutz book seems excellent but I'm more interested in d'Inverno book, And Misner/Throne Book Seems complete but its giant and good for reference, So I think I will go with d'Inverno , but first I need...

I have been wondering what effects a quantum mechanical system would cause in space time. Pick a general state of the system. This would not generaly be in one of the energy eigenstates -rather, it would be on a superposition of energy states. Now, each one of them would cause a different space...

In classical general relativity, gravity is simply a curvature of space-time. But, a quantum field theory for a massless spin-2 graviton has as its classical limit, general relativity. My question is about the topology of space-time in the hypothetical quantum field theory of a massless spin-2...

Does General Relativity predicts that in the early universe vacuum energy was converted into matter? How does it relates to the Inflation Theory by Allan Guth? I'm asking this because I remember reading in a book on GR that there are ways of calculating the total amount of energy in the...

I'm in a graduate course in Physics to obtain a master's degree. I have a major in mathematical physics and my main interests are General Relativity (GR), Quantum Field Theory on Curved Spacetimes (QFTCS), and usual Quantum Field Theory (QFT) itself. My interest is in the fundamental physics...

Hello Maybe my question is dumb but is the bent of space time instant due to gravity? If a mass pops into existence will space time be bent instantly ? Intercations between forces are light speed but gravity is and is not a force depending on pov

Hi, I am seeking to understand better how this well accepted idea: "...according to general relativity, gravity is a manifestation of the geometry of spacetime." (https://en.wikipedia.org/wiki/Loop_quantum_gravity) is compatible with the equally well accepted idea that gravity travels at the...

I'm looking influence of pressure on the general interior Schwarzschild metric (see for example the book by Weinberg, eq. 11.1.11 and 11.1.16. The radial component of the metric (usually called A(r)) depends only on the mass included up to radius r A(r) = \left(1-\frac{ 2G M(r)}{r}\right)^{-1}...

Hello! If energy bends spacetime, then an object moving at high velocity will bend spacetime a lot around it due to its really big kinetic energy. It follows, that an object can become a black hole at extremely high enough velocities. But, since velocity is relative, we can find an observer for...

In special relativity, we know, (proper time)^{2} = - (proper distance)^{2}. But, in Causal Dynamical Triangulations (CDT), they introduce an asymmetry parameter \alpha as, (proper time)^{2} = - \alpha (proper distance)^{2} [Q. 1] Can you please explain me about, why we need to introduce \alpha...

Hey there! My name is Karol and I am 16 years old. I joined the Physics Forums because I have many questions and ideas on how the universe might work. I am interested in General Relativity and Quantum Physics and I often attempt to unify both (finding the world formula :D ). My dreams are to...

Do the field equations themselves constrain the metric tensor? or do they just translate external constraints on the stress-energy tensor into constraints on the metric tensor? another way to ask the question is, if I generated an arbitrary differentiable metric tensor field, would it translate...

it is often stated in texts on general relativity that the theory is diffeomorphism invariant, i.e. if the universe is represented by a manifold ##\mathcal{M}## with metric ##g_{\mu\nu}## and matter fields ##\psi## and ##\phi:\mathcal{M}\rightarrow\mathcal{M}## is a diffeomorphism, then the sets...

Hi Everyone! I have done three years in my undergrad in physics/math and this summer I'm doing a research project in general relativity. I generally use a computer to do my GR computations, but there is a proof that I want to do by hand and I've been having some trouble. I want to show that...

I know two kinds formulas to calculate extrinsic curvature. But I found they do not match. One is from "Calculus: An Intuitive and Physical Approach"##K=\frac{d\phi}{ds}## where ##Δ\phi## is the change in direction and ##Δs## is the change in length. For parametric form curve ##(x(t),y(t))##...

Hi everyone I am reading Sean Carrol's lecture notes on general relativity. link to lecture : https://arxiv.org/abs/gr-qc/9712019 In his lecture he introduced dxμ as the coordinate basis of 1 form and ∂μ as the basis of vectors. I understand why ∂μ could be the basis of the vectors but not for...

Suppose there is a charged particle far enough of any mass so that there is no gravitational interaction between the particle and any other body. The trajectory of the particle in space-time would appear to us like this (we are at the origin of our coordinate system). Consider that at...

(I don't know if this is the right place to post it, but I think the "textbooks" section is'nt. So I'm going to put it here.) I have been self studying S&G relativity for almost eight months, mostly from Weinberg's book on S&G relativity, but also from papers I occasionally find on web and from...

Question Background: I'm considering the Eddington-Robertson-Schiff line element which is given by (ds)^2 = \left( 1 - 2 \left(\frac{\mu}{r}\right) + 2 \left(\frac{\mu^2}{r^2}\right) \right) dt^2 - \left( 1 + 2 \left( \frac{\mu}{r} \right) \right) (dr^2 + r^2 d\theta^2 + r^2 \sin^2{\theta}...

Hello there, I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps. Case 1 Imagine two observers (people with telescopes maybe) in space that are standing thousands of...

As I understand it, in the context of cosmological perturbation theory, one expands the metric tensor around a background metric (in this case Minkowski spacetime) as $$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$$ where ##h_{\mu\nu}## is a metric tensor and ##\kappa <<1##. My question is, how...

Homework Statement To show that ##K=V^uK_u## is conserved along an affinely parameterised geodesic with ##V^u## the tangent vector to some affinely parameterised geodesic and ##K_u## a killing vector field satisfying ##\nabla_a K_b+\nabla_b K_a=0## Homework Equations see above The Attempt at...

Is there any way to travel back in time in reality according to GR? Let me know!

Homework Statement question attached Homework EquationsThe Attempt at a Solution Attempt : Check if ##V^{\alpha}\nabla_{\alpha}V^u=0## Since Minkowski space, connection tensors/christoffel symbols are zero so this reduces to: ##V^{\alpha}\partial_{\alpha}V^u=0## where...

Is it really hard to find a solution of a GR equation maybe two planet system ? Or It could be a different system.I just wonder 1-How much its difficult ( Like can a person calculate those solutions) 2- Whats the boundries (Like we can solve 2 planet system but not 5 etc ? ) 3- Can...

Hi, i got little confused after this conversation in https://www.physicsforums.com/threads/some-questions-about-light-and-relativity.918094/page-2 There was also this conversation: So i want to clear the confusion. As was pointed out to me, in STR mass is defined as m2=E2 - p2, which...

I've been reading Fleisch's "A Student's Guide to Vectors and Tensors" as a self-study, and watched this helpful video also by Fleisch: Suddenly co-vectors and one-forms make more sense than they did when I tried to learn the from Schutz's GR book many years ago. Especially in the video...

General relativity passes test at Milky Way’s central black hole by Ken Croswell For the first time, astronomers use stars orbiting a supermassive black hole to test Einstein's general theory of relativity, finding no sign of a fifth fundamental force. Links: John Batchelor Show...

Hello, I have a mess in interpretation of constants in description of movement in GR. First of all I define Lagrangian ##l=1/2g_{\mu\nu}u^{\mu}u^{\nu}##, and I would like to talk about axial smyetric spacetime (for example Kerr black hole) ##l(r,\theta)##. l is independent from ##t## and...

Currently reading the following document which is a bit of a brain overload at the minute! Im considering Equation (4.61). It is the general relativistic correction due to the Schwarzschild field for a near Earth satellite when the parameters \beta, \;\gamma \equiv 1. However, as you will...

In coordinates given by x^\mu = (ct,x,y,z) the line element is given (ds)^2 = g_{00} (cdt)^2 + 2g_{oi}(cdt\;dx^i) + g_{ij}dx^idx^j, where the g_{\mu\nu} are the components of the metric tensor and latin indices run from 1-3. In the first post-Newtonian approximation the space time metric is...

If we assume I live in Jupiter and there is one year passed in my clock how many years passes in the earth? And how can I use that Equation in the attached?

In Hawking-Ellis Book(1973) "The large scale structure of space-time" p69-p70, they derive the energy-momentum tensor for perfect fluid by lagrangian formulation. They imply if ##D## is a sufficiently small compact region, one can represent a congruence by a diffeomorphism ##\gamma: [a,b]\times...