Gr Definition and 952 Threads

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...

Hi everyone! I'm trying to make a list of recommended books (introductory and advanced). So far, what I was able to search are the following: Particle Physics: - Griffiths: Introduction to Elementary Particles - Thomson: Modern Particle Physics - Nachtmann: Elementary Particle Physics -...

Hello! I am reading about spherical geometry and for a static system and based on the metric, ##p_0## and ##p_\phi## are constant of motion. I am not sure I understand in which sense are they constant? The energy of a particle measured by an observer depends on the metric (so on its position) in...

There is something that has been bothering me for some time about binding energy (and respective mass difference) but I was not sure how to formulate the question. Now it feels like I can ask it meaningfully enough. In GR energy produces gravity just like mass. But how potential energy is...

We were shown the answer to this question as a worked example: A photon is emitted from a radius ##r_2## and travels radially inward to ##r_1## until it's reflected by a fixed mirror and travels back to ##r_2##. Calculate the time taken for the photon to travel in and back, according to a...

I know we do not have a version of QFT (?) in which we can dynamically solve for the QFT and the background spacetime at once. What we can do is where if we come up with a QFT whose expectation value of the stress-energy tensor doesn't match the fixed background spacetime geometry via the...

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)...

Hello! I am reading A first course in General Relativity by Schutz and at a point he proves that for a weak gravitational field and assuming ##\Lambda = 0## we have ##\Box \bar{h}^{\mu \nu} = -16\pi T^{\mu \nu}##. Leaving the notations aside, he says that for a weak gravitational field (and...

I have always been wondering whether GR is generally, see what I did there :), more important in terms of science than special relativity.

I would like to ask rather general question. Can a binding energy of some QM process at the same time be binding energy of gravity? I am just trying to find overlap between QM and GR and I have thought about this question but I'm not sure how to tackle it.

Homework Statement From pages 10--11 in "A First Course in General Relativity" (Second Edition) by Bernard Schutz: Given $$\Delta\overline{s}^2 = \phi\left(\textbf{v}\right)\Delta s^2,$$ where ##\Delta \overline{s}^2## is the interval measured between two events in frame ##O'##, which is...

Back in the 1960s, Richard Feynman worked on quantum gravity for a few years, and most of his notes are collected in the 'Feynman Lectures on Gravitation'. His approach was that of a particle physicist applying the principles of QED to GR, notably the concept of gravitons mediating the force of...

First of all, I'm new here, so hello everyone! Apologies if this is posted in the wrong thread, I recently started getting into high-ish physics in general, so I'm coming from a low-ish background in the way of math- a couple courses of calculus (single variable covering the basics of the...

Hi everyone! Please what are the conditions necessary for space and time to be nonholonomic?

Hello everyone, I have recently developed interest in what I reckoned the most difficult field of Physics- general relativity, I am also desiring to do a PhD in the field. But first I need to write journal articles in this field. I am lost as to what topic to write on, how to write and publish...

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...

In a thread that is now closed in the QM sub-forum someone wrote: Isn't spacetime supposed to be fixed, "it just is", not changing or evolving? To which I replied: These days we know the core of GR - its simply this - no prior geometry (it's dynamical) which is the exact opposite of 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

For example, the curvature due to a mass; does that curvature continue passing from within to outside the mass's light cone? If so, is the mass subject to the external curvature? If not, does the curvature have a discontinuity at the light cone surface?

Hi everyone, I am reading Sean Carroll's note on gr and he mentioned metric compatibility. When ∇g=0 we say the metric is compatible. However from another online material, the lecturer argues ∇ of a tensor is still a tensor, and given that ∇g vanish in locally flat coordinate and this is a...

Hi Everyone, I am a physics undergraduate students who intended to study General Relativity. I have planned to purchase or borrow one of the following books： 1.A first course in General Relativity by Schutz 2.Space time and Geometry by Carroll (I have heard that it is an advance textbook rather...

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...

Homework Statement How to show that lie deriviaitve of metric vanish ##(L_v g)_{uv}=0## <=> metric is independent of this coordinate, for example if ##v=\partial_z## then ##g_{uv} ## is independent of ##z## (and vice versa) 2. Relevant equation I am wanting to show this for the levi-civita...

Homework Statement Question attached. Homework Equations 3. The Attempt at a Solution [/B] I'm not really sure how to work with what is given in the question without introducing my knowledge on lie derivatives. We have: ##(L_ug)_{uv} =...

I was reading the wikipedia page on the twin paradox (https://en.m.wikipedia.org/wiki/Twin_paradox). It says: The mechanism for the advancing of the stay-at-home twin's clock is gravitational time dilation. When an observer finds that inertially moving objects are being accelerated with...

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, We know that for lightlike paths, there are circular geodesics at ##r = 3GM## in Schwarzschild geometry. Suppose an observer flashes his flashlight at ##r=3GM## and after some time the light reappears from the other side of the black hole. The time he measures is ##6 \pi GM##. I...

Physicists try to unite Quantum Mechanics and General Relativity. QM deals with three forces in nature (i.e., strong, weak , electromagnetism), while GR deals with geometry of space. How can one unite 3 forces and geometry? If one thinks of gravity as a force (not geometry), would one have a...

If dolphins thought the universe was just a really big ocean, and if they had come up with the theory of general relativity, how would the fact that certain particles radiate faster than light through water shape their version of the theory? Would it be essentially the same with the human...

Hello there, I am learning GR and in the cosmology chapter, we are using the metric $$ ds^2 = - dt^2 + a^2(t) \left[ \frac{dr^2}{1 - \kappa r^2} + r^2 d \Omega \right]. $$ Suppose now that ##U^\mu = (1,0,0,0)## and the energy momentum tensor is $$ T_{\mu \nu} = (\rho + p)U_\mu U_\nu + p g_{\mu...

In his book Gravitation and cosmology, Weinberg derives the perihelion precession of Mercury in the Robertson expansion. The final formula is \Delta\phi =\frac{6\pi M G}{L} \frac{2+2\gamma-\beta}{3} The second term is one for GR (β=γ=1). I have two questions regarding this formula: 1. The...

Homework Statement Question attached Homework Equations The Attempt at a Solution part a) ##ds^2=\frac{R^2}{z^2}(-dt^2+dy^2+dx^2+dz^2)## part b) it is clear there is a conserved quantity associated with ##t,y,x## From Euler-Lagrange equations ## \dot{t}=k ## , k a constant ; similar for...

Hello! I read this definition of vectors in my GR book: "To each point p in spacetime we associate the set of all possible vectors located at that point; this set is known as the tangent space at p, or ##T_p##". This means that each point in space time is viewed as the origin for the 4...

if GR is correct about spacetime (expanding of space) then i think time travel in back (back to the past) is impossible... suppose before 2 billion years ago (from now) the total space (volume) of universe was "X" so, it's clear that the space (volume) of the present universe must be greater...

Hello All! 1. Homework Statement Action, where there are Yang-Mills field and Scalar field Lagrangians (as I know, so let me know if it is not), is given as $$S=\int \sqrt -g \left[ \frac {M_p^2} {2} R + F\left( Z \right) + \frac {\bar \kappa} {384} \left( \epsilon^{\alpha \beta \lambda...

It is said that GR in the weak field limit it produces Newtons familiar law, so why can't GR produce other formulas for "strong field" which I guess it means at short distances.

Hello everyone. I was reading Einsteins 1916 original paper on GR, the "The foundation of the general theory of relativity". There are some derivation that he did but I didn't quite understand. It would be nice if someone can give me some direction or some guidance on it. Here is the link to...

1. Problem ##g_{uv}'=g_{uv}+\nabla_v C_u+\nabla_u C_v## If ##g_{uv}' ## is given by ##ds^2=dx^2+2\epsilon f'(y) dx dy + dy^2## And ##g_{uv}## is given by ##ds^2=dx^2+dy^2##, Show that ## C_u=2\epsilon(f(y),0)##? Homework Equations Since we are in flatspace we have ##g_{uv}'=g_{uv}+\partial_v...

Hi. I was trying to translate the divergence theorem and the Green's theorem to tensor notation that we use in Relativity. For the divergence theorem, it was easy (please tell me if I'm wrong in the below derivation). I'm using the standard electromagnetic tensor ##F_{\mu \nu}## in place of the...

So, most Relativity textbooks (although some famous, like Weinberg's don't) show us that a vector ##V## is properly written as $$V^\mu(x) \frac{\partial}{\partial x^\mu}$$ where ##V^\mu(x)## are its components at the point ##x## and the "base" in which the vector is written in is the operator...

I am trying to solve the following problem but have gotten stuck. Consider a massive particle moving in the radial direction above the Earth, not necessarily on a geodesic, with instantaneous velocity v = dr/dt Both θ and φ can be taken as constant. Calculate the components of the...

In GR. What's the worldline of a quantum particle before and after it undergoes state reduction (before and after Born rule applied)?

Have members of the community had the experience of being taught GR both from a mathematical and physics perspective? I am a trained mathematician ( whatever that means - I still struggle with integral equations :) ) but I have always been drawn to applied mathematical physics subjects and much...

This isn't homework, nor is it an exercise problem; merely a question about a diagram. Re: B.Schutz book "A First Course in General Relativity" 2nd Edition, (Asian print version), page 5, Figure 1.1 "A spacetime diagram in natural units". From section 1.4 Spacetime diagrams: A world line is...

is spacetime Lorentz invariant like the quantum vacuum? They say the quantum vacuum is Lorentz invariant.. you can't locate it at any place.. but if spacetime manifold is also Lorentz invariant and you can't locate it at any place.. how come the Earth can curve the spacetime around the Earth...

First I don't have extensive knowledge about gravity beyond General Relativity, so please forgive my ignorance about this subject. I have confusion about the relation between GR and QM and I just want a general picture so that I can connect the dots. My questions: 1- Why do we need quantum...

General Relativity is just geometry with 20 numbers corresponding to Weyl and Ricci curvature. It's possible to write software that can let you input say the mass or stress energy or whether it's Sitter or de Sitter space and other variables.. then it can input the corresponding 3D graphic...