General relativity Definition and 999 Threads

I'm trying to do past exam papers in GR but there are some things I don't yet feel comfortable with, so even though I can do some parts of the question I would be very happy if you could check my solution. Thank you! 1. Homework Statement Spacetime is stationary := there exists a coord chart...

(precursor: I have not formally studied GR) I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case? Am I correct in thinking that the constant was determined by Cavendish and was for the classical theory of gravitation? So, my...

i opine that the universe is not 3 dimensional at all. its not build up of 3 coordinates at all. it is because, we humans could see 3 dimensions it doesn't mean the space metric is of 3 dimensions. suppose there's a super being living on an Earth like planet of some other galaxy whose viewing...

Hello to all members! I heard on a documentary about general relativity and singularities that "energy is locally never negative". However, I was not able to get grasp the meaning of this term. Could someone explain to me the meaning of this term in the framework of general relativity. I really...

Suppose two masses are connected via a really strong spring, where one of the masses undergo an acceleration towards a relativistic speed, by say a rocket that leaves the scene soon after. When in isolation, (the two masses), they exhibit a sinusoidal oscillation to and fro. What is the...

I'm working through Wald's "General Relativity" right now. My questions are actually about the math, but I figure that a few of you that frequent this part of the forums may have read this book and so will be in a good position to answer my questions. I have two questions: 1) Wald first defines...

Apologies if this question has been asked already. I've been given resources to help me understand, but it's been hard for me to wrap my head around the answer and, for that matter, it is difficult to understand a text when you have to look up every other word (an exaggeration, but you know ...

Assume we drill a hole through the Earth - through the center towards the other side. Then we use a telescope, point it through the hole and observe stars on the other side of the earth. The telescope experiences a constant acceleration from Earth's gravitation. Accelerated movements have an...

Sorry for the amateurish setup that follows. Here's my thought experiment. Consider a 2-dimensional universe on the Cartesian plane. Earth is located at point (0,0). There is a binary system {A,B} oscillating around (1,1). To simplify, assume that the oscillation is 1-dimensional and occurs on...

Currently I'm in the last year of the Physics course and I'm interested in working on some undergraduate research project. At first I was suggested to work with statistical physics, but I believe I would prefer working with General Relativity. From the point of view of background I do have a...

What is general relativity all about. I don't know anything about it. I am an undergrad.

Conserved quantities in GR deal with ##p_\mu## not ##p^\mu## and while in Minkowski spacetime its easy to see what each of the components mean (since the metric is so simple) in general relativity I think its not and its starting to confuse me. Why exactly is ##-p_0## the energy in general...

If I know the density curvature parameter for today $$ \Omega_{k,0} = \frac{-c^{2}k}{R_{0}H_{0}} $$ then is it possible to surmise what it would be, say, during the matter dominated era $$ \Omega_{k,t} = \frac{-c^{2}k}{R(t)H(t)}$$ ?

suppose the AdS_3 metric is given by $$ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2$$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications as n=1 case? Thanks in advance.

If I am asked to show that the tt-component of the Einstein equation for the static metric ##ds^2 = (1-2\phi(r)) dt^2 - (1+2\phi(r)) dr^2 - r^2(d\theta^2 + sin^2(\theta) d\phi^2)##, where ##|\phi(r)| \ll1## reduces to the Newton's equation, what exactly am I supposed to prove?

Hello! I want to learn about the mathematics of General Relativity, about Topology and Differential Geometry in general. I am looking for a book that has applications in physics. But, most importantly, i want a book that offers geometrical intuition(graphs and illustrations are a huge plus) but...

Hi all, I need some help- I was reading Carroll's GR book, and on pages 71-71 he discusses the metric in curved spacetime. I have a few questions regarding this section: (1) He says In our discussion of path lengths in special relativity we (somewhat handwavingly) introduced the line element...

I'm having a bit of trouble understanding the nature of tensors (which is pretty central to the gen rel course I'm currently taking). I understand that the order (or rank) of a tensor is the dimensionality of the array required to describe it's components, i.e. a 0 rank tensor is a scalar, a 1...

Introduction If Quantum Mechanics is more fundamental than General Relativity as most Physicists believe, and Quantum Mechanics is described using Hilbert Spaces wouldn't finding a compatible version of General Relativity that operates within the confines of a Hilbert Space be of utmost...

I'm looking for a demonstration of the equation governing the evolution of the scalar field: ## \Box \phi = \frac{1}{\sqrt{g}} \frac{ \partial}{\partial x^{\mu}} \sqrt(g)g^{(\mu)(\nu)} \frac{\partial}{\partial x^{\nu}} \phi=0## I used the lagrangian for a scalar field: ## L = \nabla_{\mu}\phi...

In the book I'm reading, there is a discussion about how a person inside a "box" falling in a gravitation field would see himself as compared to someone on the ground. It is as follows "While the guy is asleep, put him in a spacious box elaborately furnished inside to look exactly like his...

It is known that light beam bends near massive body and the object sendind deflected the beam is seen in shifted position. Now about spacetime curvature. As I undestand the things are like that: http://i11.pixs.ru/storage/3/3/4/pic2png_7037348_21446334.png The question is why are geodesics...

Is there a simple geometric interpretation of the Einstein tensor ? I know about its algebraic definitions ( i.e. via contraction of Riemann's double dual, as a combination of Ricci tensor and Ricci scalar etc etc ), but I am finding it hard to actually understand it geometrically...

My goal is to develop an intuitive understanding of the math underlying general relativity and ultimately be able to take a book like Wald or Carroll and, as someone on these forums commented once, “be able to casually read it while sipping my morning coffee and listening to the news.” :) So...

I had the following question how are the Schwarchzild metric that describes a spherically symmetric matter distribution (such as a star) be compatible with the FRW metric that describes the 'overall universe' that the star resides in/is part of its matter distribution? Then we say that FRW...

Hi all, I've just been made offers to two different institutions - one to study General Relativity and Early Universe Cosmology, and one to study particle physics phenomenology and dark matter at PhD level, and I'm having a hard time choosing! Relativity and Cosmology is Queen Mary University...

I'm a 16 year old whose summer goal is two understand general relativity, but I'm lost on what math to have to understand it, I understand topological spaces and a topological manifold. but then it becomes more complicated math, and I know I simply don't understand because of the mathematics.

The question is to resolve a logical conflict. GR says as we fall into a black hole, an outside observer will see that event come to a stand still as if the falling object is hovering at the horizon. This stand still extends to infinite time. Unfortunately, I've read and hear the term...

haushofer submitted a new PF Insights post The Revival of Newton-Cartan Theory Continue reading the Original PF Insights Post.

nikkkom submitted a new PF Insights post A Brief on the Expansion of the Universe Continue reading the Original PF Insights Post.

Let a mass oscillate with relativistic acceleration (sinusoidal) by means which are irrelevant. What does the gravitational field look like a distance R away?

How will be the gravitational effect of an object which is accelerated until reaching 1.5 times of its inertial mass? (According to space and satellites of this object)

according to the general relativity, if someone stayed on Earth and another person was traveling near the speed of light, time will go slower for who's traveling faster. but we all know that the universe has no center, so no frame of reference, then if we consider the person moving to be at...

Homework Statement As the title says, I need to show this. A conformal transformation is made by changing the metric: ##g_{\mu\nu}\mapsto\omega(x)^{2}g_{\mu\nu}=\tilde{g}_{\mu\nu}## Homework Equations The Weyl tensor is given in four dimensions as: ##...

Homework Statement I'm doing a project on the redshift from a star system (I chose a binomial system because why not). I might be going a little overboard using topology to calculate redshift, but whatever. First off, can I just treat a binomial system as the superposition of 2 sources which...

Hello! Good morning to all forum members! I am studying general relativity through the wonderful book: "General Relativity: An Introduction for Physicists" by M.P. Hobson (Cambridge University Press) (2006). My question is about Riemannian manifolds and local cartesian coordinates (Chapter 02 -...

How does movement of the creator of gravity field( mass or energy density) affect the magnetude of exerted gravitational field ! Is there any relation at all ?

If gravity is the warping of space, how does it work on Earth for us? Imagine a trampoline (the most common example for describing gravity) when a bowling ball is kept on a trampoline the weight of the ball forces the trampoline to stretch, but on our planet the gravity works downward on the...

Hello. I have 2 books in General Relativity: MTW Gravitation and Bernard Schutz First Course in General Relativity. I studied Calculus I, II, and have a basic understanding of Linear Algebra(did not studied extensively). I want to learn about GR as much as possible, and improve myself to become...

We recently touched base with gravity in regards to general relativity and I'm a bit perplexed. So apparently (and correct me if I'm wrong) gravity is created when the mass of the universe warps, or bends, space-time. I've read all those analogies about a trampoline curving due to an object of...

Are there any interpretation to general relativity that described gravity as field (which do not have to be vectorfield, but may have 10 components) and physical-space as classical euclidean space? Can it be mathematically proven that such interpretation can not exist? I am not talking about...

G-Waves is a buzzword recently :) At the beginning I thought G-waves as the propagation of the changes of the curvature caused by a mass when the status of the mass (e.g. value or location) changes...But moment ago, I was told that G-waves are different from the waves that transmitting the...

Homework Statement A distant observer is at rest relative to a spherical mass and at a distance where the effects of gravity are negligible. The distant observer sends a photon radially towards the mass. At the distant observer, the photon's frequency is f. What is the momentum relative to...

Hello, since gμν gμν = 4 where g = diag[1,-1,-1,-1], see: https://www.physicsforums.com/threads/questions-about-tensors-in-gr.39158/ Is the following equation correct? xμ xμ = gμνxν gμνxν = gμν gμνxν xν= 4 xμ xμ If not, where is the problem? Cheers, Adam

I'm reading Zee's Gravity book, can anyone help me understand the explanation on this part, I understand everything except the last part, he said to use (I.4.14) so that I could solve for the quantity shown in the image, what does he mean by that and how?

I've been looking over the idea of the multiverse recently. I am trying to grasp exactly why so many physicists believe in the idea when it seems more philosophical than scientific. Are there any good indicators pointing towards the theory from QM or GR? The gripe that I also see with it...

Are spacetime and the gravitational quantum field (still hypothetical) separate entities? Would the gravitational field be more fundamental, one of the various entities from which spacetime as a whole is composed? Gravitons, which are believed to transmit the force of gravity, would surely be...

Many popular accounts claim that gravity waves move at the speed of light. Now, I know 2 things: Special relativity says their speed cannot be greater than the speed of light in a vacuum. Gravity is a different fundamental force than the electromagnetic force. The same goes for their fields...

I'm reading A. Zee's GR book and I'm in the section in which he is showing how to transform coordinates to be locally flat in a neighborhood of a point. He said that we can always choose our neighborhood to be locally flat for any space of any dimension D. "Look at how the metric transforms...

Homework Statement Find the locally flat coordinates on the Poincaré half plane. Problem I.6.4 by A. Zee Homework Equations [/B] Poincaré Metric: ##ds^2 = \frac{dx^2 + dy^2}{y^2}## The Attempt at a Solution First, I'm having problems with the explanation in Zee's book. He said that we can...