Gr Definition and 952 Threads

Hi all, I need help understanding the light ray bending in the original GR 1916 paper, Die Grundlagen.... First of all, Einstein states the ##c## is not an invariant in GR. In fact, from (70) and (73), it stems that $$\gamma = \sqrt{ -\frac {g_{44}}{g_{22}} }, $$ where ##\gamma## is ##|c| <= 1##...

Can you approach the GR two body problem through summations of multiple Schwarzschild solutions? Specifically, by using the Schwarzschild metric for each body of mass, then adding the Christoffel symbols together, to arrive at a new geodesic equation. Take point C between bodies A and B...

I'm trying to compute the extrinsic curvature. I have the formula and everything I need to plug into the formula. But I get confused when executing this calculation.. I have that ##ds^2_{interior} = -u(r)dt^2 + (u(r))^{-1} dr^2 + r^2 d\Omega_3^2##. This is a metric describing the interior and...

https://indico.cern.ch/event/977179/ Description The proximity of our Galaxy's center presents a unique opportunity to study a galactic nucleus with orders of magnitude higher spatial resolution than can be brought to bear on any other galaxy. After more than a decade of diffraction-limited...

As per the summary I would like to find a review paper, monograph or book. Google is not find any recent reviews. Post 2018 would be ideal. Thanks for any pointers. Regards Andrew

I think there is nonetheless a difference, and it is in favor of quantum theory. Having the GR equations as an approximation in some appropriate limit is, of course, required by the correspondence principle, as well as simply of empirical viability. In this sense, the same is obligatory as for...

I was surprised to read that the formula for escape velocity — at least for a spherical mass like the Earth — is the same in relativity as it is in classical physics: v_e = (2GM/r)^{1/2} I'm wondering if someone can give me a good source for deriving this. (I assume one takes a radial...

Background and Motivation The stress energy tensor of general relativity, as conventionally defined, has sixteen components. One of those component, conventionally component T00, also called ρ, is mass-energy density, including the E=mc2 conversion for electromagnetic fields. The other...

Two Recent Papers Propose A Simply Tweak To How General Relativity (GR) Is Applied That Purports To Explain All Dark Matter Phenomena Motivated By A Version of GR and Quantum Gravity. The pair of related papers with overlapping text and common authorship (cited below) were published after peer...

Hi, does general relativity have state variables, analogous to current (I), charge (Q), voltage (V), and flux (Φ) in electromagnetism? Thanks.

Hello,. I am looking for another problem book for GR. I have used Problem Book In Relativity and Gravitation by Alan P. Lightman, et al. But first the copy I get is not in a good quality. Some texts are vague. Also, it seems too difficult for me. I only can solve about half of the problems in...

Is the subject of gravitational waves the most difficult one to grasp on the theory of Relativity? Or is it just the math that is very complicated?

I will post the answer here, part of which I do not follow. I do not follow the outer-product part. I know that I should multiply two terms together if they are in the same space. However, in this problem, I do not know how to determin which term belongs to which space. It seems, sometimes...

Hello friends. I have this question about how the Einstein field equations were derived, the assumptions behind them and the possible applications of them. What could their solutions be?Also, how are they used in cosmology and in the big bang theory?What about astrophysics? Thank you very much.

The speed of the ends of the galaxies is higher than what it should be. Current solution: This could be explained by hypothetical "dark matter", which was not found up to now, or by a MOND theory (MOdified Newtonian Dynamics). Can this be explained instead with rotational frame-dragging...

As history is Newton considered infinite speeds of his gravitational force as unphysical, out of which Einstein constructed relativity. In special relativity moving faster than c induces an imaginary space-time and is hence ruled out. My question is regardin towards GR, in which Gödel showed...

I'm reading 'A Most Incomprehensible Thing: Notes towards a very gentle introduction to the mathematics of relativity' by Collier and came across the following paragraph in the chapter on tensors: I'm a bit skeptical about the "useful but not essential" part, but I'd still like to get the...

Apologies in advance if this is a naive question. From what I've understood, it's not particularly meaningful to talk about gravity as a force, since it induces the same acceleration (classically speaking) in everything. Whatever device or accelerometer we use, every component of that too will...

on page 269 it's written in the second edition of Schutz's textbook that ##(10.69)p_c/\rho_c=\beta (2-5\beta)^{-1}##. Demanding that this be less than ##1/7## gives: ##(10.70) 0<\beta < 1/6## Now, if I am not mistaken on page 268 in equation (10.57) the condition should be ##p_c/\rho_c >1/7##...

Prove that the stress-energy tensor is given by the functional derivative of the action with respect to ##\delta g^{\mu \nu}## $$T_{\mu \nu} = \frac{-2}{\sqrt{-g}} \frac{\delta S}{\delta g^{\mu \nu}}$$ Tong suggests (around 25:30) we could get the desired tensor by performing a...

I have a question about the history of cosmology, hope its okay to ask here. Who was the first person since Einstein's Gr to point out a singularity in cosmology? I know Freidman talked of an expanding universe and Lematire a primeval atom. But were there any explicit mentions of the density of...

I think it can do more than the wave only events we know of (superposition, entanglement, and tunneling). If the quantum field doesn't care about spatial distance, does that mean every unobserved quantum wave is already everywhere throughout the quantum field? Does it explain spooky action at a...

I was reading chapter 3 of Carroll's book up to page 100, where he mentions that the coefficients of Christoffel symbol in flat spacetime vanish in cartesian coordinates but not in curvilinear coordinate systems. I was thinking on why this happens. My logic tells me that these coefficients...

Hi all, I have ran into some confusion about the equivalence principle; perhaps I should state what I understand and then proceed to ask questions. It is my understanding that the equivalence principle states that spacetimes are locally Minkowski, and so the rules of SR apply in that locality...

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} =...

My attempt was to first rewrite ##S_M## slightly to make it more clear where ##g_{\mu\nu}## appears $$S_M = \int d^4x \sqrt{-g} (g^{\mu\nu} \nabla_\mu\phi\nabla_\nu\phi-\frac{1}{2}m^2\phi^2).$$ Now we can apply the variation: $$\begin{align*} \delta S_M &= \int d^4x (\delta\sqrt{-g})...

I had a discussion with an engineer about forces and accelerations in the context of general relativity. My contention (which I confirmed in these forums some time ago) was that in GR, the real force and real acceleration at the Earth’s surface is upward, not downward. He contended that in...

It's been 2 years since the SR book was released. Any news on when the GR book is going to be released?

A gear A has 50 teeth and another B has 10 teeth, how many times does the small gear rotate around the big one? I thought 5 but its 6! Note: The gear is curved like 360 degrees.

I am self-studying GR, using principally Carroll’s textbook and Alex Maloney’s online lectures, and nice book by a guy called Herbert Roseman. I am a bit confused by alternative ways of expressing the metric and it would be most helpful if someone could clarify J Basically, I am perplexed by...

Hi Folks, I am finishing up my last year in undergrad (physics with a math minor) and am searching for potential grad schools. My areas of interest are pretty much exclusively in Gravitation (specially theoretical study of general relativity) and Physics Education Research, with a bit of...

If in the early Universe the matter density was density so large causing an intense gravity field, was the time at that epoch running much more slowly compared to the actual time according to the GR? If so then, would any reference frame in the early Universe see the light apparently traveling...

A central feature of classical GR that it is background independent and operates via a curvature in space-time. As I understand it, this is not true of the other Standard Model forces which are consistent with special relativity and operate in Minkowski space, in which forces are transmitted via...

Hello World, I have understood the following: in SR, time intervals and space intervals (distances, lengths) are relative and inertial reference frame dependent. Space and time is not absolute anymore. However, acceleration is still absolute: different inertial frames see the same acceleration...

I know this question sounds stupid but somehow i need confirmation I guess. Is it necessary to learn GR and SR to study cosmology ?

The exact formula for gravitational time dilation is T_d = exp(m\phi / mc^2). (We usually cancel out the ms, but I want to show this as a ratio of energies.) Since m\phi is the potential energy, this says that the rates or frequencies of things in GR depend exponentially on their energy. On the...

You may be familiar with how you can express a vector field as a linear combination of basis vectors like so: X = Xi∂i Now, I know that normally, the basis vectors ∂i can be derived by taking the derivatives of the position vector for the coordinate system with respect to all the axes like...

Dear all, I'm having a small issue with the notion of Lie-derivatives after rereading Carroll's notes https://arxiv.org/abs/gr-qc/9712019 page 135 onward. The Lie derivative of a tensor T w.r.t. a vector field V is defined in eqn.(5.18) via a diffeomorphism ##\phi##. In this definition, both...

Is General Relativity applicable in problems involving tidal gravity? For example if a system being analyzed is large enough where tidal gravity effects become apparent - suppose two distantly separated hovering observers see a freefalling object change velocity - are general relativity...

Taking the time derivative of the energy density of the energy momentum tensor should equal to the spatial derivatives or divergence of the momentum density components. How do the units work out though? shouldn't a time derivative of the energy density be in kg/xt^3 and the spatial derivative of...

How does GR predict the Earth's orbit around the sun? Newtonian mechanics predict a gravitational force that is a function of the two masses. Is the geodesic path of the Earth a function of both the sun's and Earth's curvature of space?

I can see that by the tensor transformation law of the Kronecker delta that ##\frac{\partial x^a}{\partial x^b}=\delta^a_b## And thus coordinates must be independent of each other. But is there a more straightforward and fundamental reason why we don’t consider dependent coordinates? Is it...

Let’s say to the average Astronomer conducting research; generalizing the research to “astronomy” ; which would be more useful for the “average” Astronomer on a day to day basis: Quantum Mechanics or General Relativity? Obviously most are, but which so more? Which would be referred to more?

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 was just looking for recommendations for textbooks for an Undergraduate (Senior) Level course in General Relativity. I want to prepare for this "Intro" GR course i'll be taking in January by self-learning what i can beforehand in summer, does anyone have any good, first hand recommendations...

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...

Hi, folks. Several years ago I made a YouTube video with a new demonstration of GR for a general audience ("How Gravity Makes Things Fall"). It won a pretty prestigious physics award. I still get comments and questions on it. One today stumped me: "How do we account for potential energy if...

I was studying linearized GR where we make the following coordinate transformation ## \tilde{x}^{a} = x^{a} + \epsilon y^{a}(x) ## This coordinate transformation is then meant to imply ## g_{ab}(x) = \tilde{g}_{ab}(x) + \epsilon \mathcal{L}_{Y} g_{ab} ## Would anyone be kind enough to explain...

This is a rather offbeat question, but I was wondering just the same. Imagine a spiral galaxy. Imagine a space surrounding that galaxy, somewhat larger. Imagine that this space surrounding the galaxy were to rotate somewhat with the galaxy, as a whole, stiff like a bike wheel. (Side note...

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...