What is General relativity: Definition and 999 Discussions
General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay and singularities/black holes. The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. Unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity; and how gravity can be unified with the three non-gravitational forces—strong, weak, and electromagnetic forces.
Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
Widely acknowledged as a theory of extraordinary beauty, general relativity has often been described as the most beautiful of all existing physical theories.
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...
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...
"The presence of this field, now believed to be confirmed, explains why some fundamental particles have mass when based on the symmetries controlling their interactions they should be massless." (wiki)
It would seem, to myself, a novice, that the Higgs field and its corresponding particle, if...
how two objects hit the ground at same time regardless of their weight of masses.
what is the reason of Acceleration is always constant via gravitational force for both of them. F=mg
F1/m1=F2/m2
I am trying to derive the geodesic equation using variational principle.
My Lagrangian is $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$
Using the Euler-Lagrange equation, I have got this.
$$ \frac{d^2 x^u}{dt^2} + \Gamma^u_{mk} \frac{dx^m}{dt} \frac{dx^k}{dt} =...
Homework Statement
Given the line element ##ds^2## in some space, find the transformation relating the coordinates ##x,y ## and ##\bar x, \bar y##.
Homework Equations
##ds^2 = (1 - \frac{y^2}{3}) dx^2 + (1 - \frac{x^2}{3}) dy^2 + \frac{2}{3}xy dxdy##
##ds^2 = (1 + (a\bar x + c\bar y)^2) d\bar...
Hello all,
This is most likely a question for those who have experience/knowledge of theoretical/mathematical physics at the graduate level and can provide recommendations following my criteria.
Here is some background about me:
I am a senior majoring in math and physics at a small...
What is the underlying feature of general relativity that, unlike Newtonian mechanics, results in the correct calculation of orbits i.e. including precession (e.g. Mercury). I not asking for the mathematics (i.e. the additional term in the equation) but rather what underlying "physical"...
Homework Statement
This is a problem from A. Zee's book EInstein Gravity in a Nutshell, problem I.5.5
Consider the metric ##ds^2 = dr^2 + (rh(r))^2dθ^2## with θ and θ + 2π identified. For h(r) = 1, this is flat space. Let h(0) = 1. Show that the curvature at the origin is positive or negative...
Homework Statement
The familiar Mercator map of the world is obtained by transforming spherical coordinates θ , ϕ to coordinates x , y given by
##x = \frac{W}{2π} φ,
y = -\frac{W}{2π} log (tan (\frac{Θ}{2}))##
Show that ##ds^2 = Ω^2(x,y) (dx^2 + dy^2)## and find ##Ω##
Homework Equations...
Expanding universe or contracting matter?
this may look very weird question, but what if instead of that the universe is expanding, all matter is contracting as a function of its (proper) time?
Δs' = Δs_0 /F(t)
The contraction of matter would effect on the length unit what we use.
I am...
I'm reading the book by Zee, I came across a paragraph saying that the world is not flat.
"Given an airline table of distances, you can deduce that the world is curved without ever going outside. If I tell you the three distances between Paris, Berlin, and Barcelona, you can draw a triangle on...
Mentor note: this discussion was split out of a different thread.
The speed of light in a vacuum is constant, but what I would like some information regarding is Black Holes. Does a Black Hole increase the speed of a light photon as it is being pulled into the Event Horizon?
Lorentz contraction problem:
By Bertrand Boucquillon
Components of the problem:
- Bob (observer)
- 2 identical rods that both measure 1 meter. Let's call them rod X and rod Y
- Point A
- Point B
Scenario (step by step):
1) Bob is at point A, and is at rest with both rods in his hands
2) Bob...
In special relativity, we can prove that the metric is -+++ for all observers and that is by making use out of lorentz invariance. Some on this forum say that it comes as a result of constancy of light and others say that Minkowski predated einstein in making that metric, which was confusing...
Homework Statement
I'm reading the book Relativity, Gravitation, Cosmology by Ta-Pei Cheng. I'm in the part where he derived the gravitational time dilation formula for static gravitational field,
τ1=[1+(Φ1-Φ2)/c2]τ2.
This implies that clocks at a higher gravitational potential will run...
A short film celebrating the centennial of Einstein's theory of General Relativity. EOIN DUFFY Animation (http://eoinduffy.me/) DAVID TENNANT Narrator WESLEY...
Does the stress-energy tensor depend on direction of the relative velocity of two celestial bodies? Assume vy is directed parallel to the gravitational field of the planet, vx and vz are perpendicular to the field, and that the speed would be the same whichever direction it is in. Does it matter...
So I saw that claims are being made that LIGO may have detected gravitational waves. http://www.nature.com/news/has-giant-ligo-experiment-seen-gravitational-waves-1.18449
My question is, if the universe were in fact multidimensional as string theory predicts, would gravitational waves propagate...
Hi, I'm new here and I'm trying to learn GR. I wanted to know the math books that I need to tackle GR properly, so far the books that I came across are:
Tensor Analysis on Manifolds by Bishop and Goldberg
Tensors, Differential Forms, and Variational Principles by Lovelock and Rund
I have a good...
I was reading through some main stream scientific literature, and I came across Sean Caroll's "Energy Is Not Conserved" post. Essentially, he contends that through general relativity energy is not conserved, at least not in conventional manner of thinking about energy.
Anyways, some portions of...
Homework Statement
A thin spherical shell of radius ## R ## rotates with angular velocity ## \Omega ##. Its total mass ## M ## is uniformly distributed. Find metric inside and outside the shell, assuming its small departure from the flat space-time. Find the angular velocity ## \omega ##...
In Newmann-Penrose formalism, a Null rotation with ##l## fixed is
$$l^a−>l^a\\
n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\
m^a−>m^a+cl^a\\
\bar{m}^a−>\bar{m}^a+\bar{c}l^a$$
Using this transformation, how to prove?
$$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$
Ref: 2-Spinors by P.O'Donell, p.no, 65