General relativity Definition and 999 Threads

I have been learning gr on YouTube for the last few months. Most of the videos and the book I have focus on high level understanding. I can do all of the tensor calculus proofs. However simple questions like how you set up a velocity vector or measure proper time in schwarzschild are beyond me...

I just need to compare my results of the Ricci and Riemann Tensors of FRW metric, but only considering the spatial coordinates.

Why in general relativity do we need the physics of perfect fluids?

Spacetime is a differential manifold and at each point is attached a Minkowski spacetime. There the laws of physics are the usual ones without gravity. Gravity is the curvature of spacetime. To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is...

Hello, this is my first thread. Robert Wald, in General Relativity, equation (4.2.8) says : E = – pa va where E is the energy of a particle, pa the energy-momentum 4-vector and va the 4-velocity of the particle. How can I see this is compatible with the common energy-momentum-relation E2 – p2 =...

In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...

Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...

What mathematical topics do I need to know to start studying general relativity? From which textbooks can I learn them? I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and...

I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...

According to Wikipedia, the definition of the Riemann Tensor can be taken as ##R^{\rho}_{\sigma \mu \nu} = dx^{\rho}[\nabla_{\mu},\nabla_{\nu}]\partial_{\sigma}##. Note that I dropped the Lie Bracket term and used the commutator since I'm looking at calculating this w.r.t. the basis. I...

Hi, In general relativity, gravitation is not anymore a Force but a deformation of space time. I would like to know what's becomes the 3 law of Newton for gravity that action equal reaction ? When a apple fall on the earth, does "the force" is exactly the same as the one applied on Earth ...

Following are not strictly physics questions. But cool questions to discuss. We need to add dark energy to our cosmological model if we strictly follow GR. This lead to some beliefs that GR is an effective theory. (1)Do you believe that GR is the fundamental theory? If GR is an effective...

Hi everybody. I recently started to learn GR from a very begginer level. I would like to share with you some lines of discussion, to understand your approach to some specific topics which for me are key to better understand the whole story. If a put an accelerometer on the floor it reads 9.8...

So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...

When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...

Hello! I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism. This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$ I don't see how ##g^{\mu\nu}\to...

This thought surprisingly came from thinking about the definition of temperature and the symmetry breaking that separated time from temperature. Which led to thoughts about symmetry breaking that separated QM from GR. Which led to to the symmetry breaking that separated dark energy from baryonic...

In both Wald and Carroll, a type (k,l) tensor has k dual vectors and l vectors, yet a (1,0) tensor is a vector and a (0,1) tensor is a dual vector. I must be missing something simple. Please explain.

Recently I have seen a number of General Relativity visualisations that show spacetime flowing towards any mass, similar to water flowing into a sink hole. ScienceClic's video is an example. That model is also used in the "waterfall model" to explain the event horizon of a black hole, as the...

In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ] Since Einstein equation is G = 8πGT, I am...

Is energy really not conserved in a constantly expanding universe?

I recently noticed that "General Relativity: The Essentials" by Carlo Rovelli has been published. Based on the description, table of contents, and the Amazon reviews, it seems to me that it might be a spiritual successor to Dirac's "General Theory of Relativity." Is that an accurate assessment...

Hi all, I am currently trying to prove formula 21 from the attached paper. My work is as follows: If anyone can point out where I went wrong I would greatly appreciate it! Thanks.

Hello all, I have a question on a pivotal concept of GR that I've never managed to fully grasp. In what coordinate system is the Einstein's Field Equation set up and solved? I've always assumed it's an Euclidean 4D space, whose metric is irrelevant because we are dealing with scalar...

From the section[5.1] of 'Homogeneity and Isotropy' from General Relativity by Robert M. Wald (pages 91-92, edition 1984) whatever I have understood is that - ##\Sigma_t## is a spacelike hypersurface for some fixed time ##t##. The hypersurface is homogeneous. The metric of whole space is ##g##...

In Minkowski space, with line element $$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$ (and ##c = 1##) we take spacelike trajectories to have ##ds^2 > 0##, null trajectories to have ##ds^2 = 0##, and timelike trajectories to have ##ds^2 < 0##. This makes sense given our definition of the line element...

By definition of the vector potential we may write \nabla \times A =B at least in flat space. Does this relation hold in curved space? I am particularly interested if we can still write this in a spatially flat Friedmann-Robertson-Walker background with metric ds^2=dt^2-a^2(dx^2+dy^2+dz^2) and...

Hello everyone, I have a hard time to conceptualize the case of a moving black hole. We know from SR that time slows down for moving objects; but time dilation at the event horizon is already equal (tends) to zero. It seems that it can create some sort of conflict for the black hole movement...

Hi all, What I notice is that there's a significant difference in style between the GR texts and the other textbooks. In particular, GR texts very much try hard to read like a math textbooks, emphasizing theorems and abstract definitions, which I'm not sure are practically useful (though...

I'm not sure how to approach this question. So I start off with the fact the path taken is space-like, $$ds^2>0$$ Input the Schwarzschild metric, $$−(1−\frac{2GM}{r})dt^2+(1−\frac{2GM}{r})^{−1}dr^2>0$$ Where I assume the mass doesn't move in angular direction. How should I continue?

I want to learn General Relativity so I am looking for a good beginners book with low amounts of math and clear explanations. Any suggestions?

hello it is well known that gravitationl force is actually a fictitious force generally speaking,are fictitious forces still necessary in general relativity ? the fictitious forces which we experience on a bus or on a car can also be understood as due to the spacetime distortion ?

Edward G. Timoshenko PhD, MSc, EurPhys, CPhys MInstP, CChem MRSC Web site: https://www.EdTim.live Bio: 2011- Researcher, TEdQz Research after an early retirement from UCD 2005 - 2011 Senior Lecturer in Physical Chemistry, School of Chemistry and Chemical Biology, UCD 1997 College Lecturer...

I found an interesting list of "must-read" papers in the field of general relativity compiled by Emanuele Berti: https://pages.jh.edu/eberti2/posts/must-read-paper-list/ Are there any notable exceptions, or other "classic" papers that - in your view - every relativist ought to have read?

Let's say I want to describe a massive box in spacetime as described by the Einstein Field Equations. If one were to construct a metric in cartesian coordinates from the Minkowski metric, would it be reasonable to use a piecewise Stress-Energy Tensor to find our metric? (For example, having...

Hi, I would like to ask for some clarification about the physics involved in the gravitational waves detection using interferometers. Starting from this thread Light speed and the LIGO experiment I'm aware of the two ends of an arm of the interferometer (e.g. LIGO) can be taken as the...

I have seen the "Hafele-Keating with the plane as reference frame?" thread (https://www.physicsforums.com/threads/hafele-keating-with-the-plane-as-reference-frame.767913/ ), but the replies do not seem to explain (to me anyway) what when taking a plane as a reference frame, balances the slowing...

I'm having trouble with Rovelli's new book, partly because the info in it is pretty condensed, but also because his subjects are often very different from those in other books on GR like the one by Schutz. For one thing, he never uses the term "manifold", but talks about frame fields, which seem...

Which is the mathematical procedure to obtain ##\delta r = \frac{GM}{3c^2}## from ##\nabla^2 V = R_{00} = 4\pi G\rho## where ##\nabla^2 V## is volume contraction of a spherical mass of density ##\rho## and ##R_{00}## is the 00 component of Ricci tensor ##R_{ij}##?

Hello everyone - The gravitational force near the edge of the galaxy at point A (see attached image) can be calculated by assuming that all the galactic mass is located in the center of the galaxy. - In order to calculate the gravitational force in the middle of the galaxy (point B) we take...

General relativity tells us that an object in free-fall is actually inertial, following a geodesic through curved spacetime, and not accelerating. Instead, it's objects like us, on the surface of a large body, that are accelerating upwards. Maxwell's equations also tell us that accelerated...

Let us consider a hypothetical scenario, where we are able to translate any mass at a constant speed of 10m/s w.r.t to a given frame of reference. For simplicity, we are going to assume that the object is at rest initially. Case 1 - Now, consider 2 points A and B at a distance of 10m, and our...

Let us denote the events in spacetime before the trip has started by subscript 1 and those after the trip is over by subscript 2. So before the trip has begun, the coordinates in spacetime for A and B are ##A = (t_{A_1},x,y,z)## and ##B = (t_{B_1},x,y,z) = (t_{A_1},x,y,z)##. After the trip is...

Hi, starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be. In GR we take as definition of inertial frame (aka inertial coordinate system or inertial...

The equivalence principle states that a person stood on Earth would experience “gravity” the same as if he was in an elevator in space traveling at 1g. I get this. but when Einstein was first exploring this, I read he came to the realisation that a person free falling on Earth (if in a vacuum)...

From "standard" formula we have that the gravity acceleration a = GM/r^2 and that the Schwarzschild radius rs = 2 GM / c^2 Is it possible to compute the gravity acceleration at Schwarzschild radius putting r = rs? In this case we will have a = c^4 / (4GM) This mean that a very very...

I was reading Einstein's 1911 paper named "On the Influence of Gravitation on the Propagation of Light" when stated the formula for frequencies measured by observers at different fixed positions (heights) on Earth surface. One observer is at the origin of some coordinate system and measures a...

Why momenergy has magnitude equal to the mass? > The mom-energy of a particle is a 4-vector: Its magnitude is proportional to its mass, it points in the direction of the particle's spacetime displacement, and it is reckoned using the proper time for that displacement. How are these properties...

Assumptions 1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way. 2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...

Hello everyone, in equation 3.86 of this online version of Carroll´s lecture notes on general relativity (https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html) the covariant derviative of the Riemann tensor is simply given by the partial derivative, the terms carrying the...