General relativity Definition and 999 Threads

"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

Fellow Nerds, I'm looking for a quantitative relationship between the gravitational strength of a point on a field and the speed of expansion of space at that point. Given a cosmological constant and a metric, is it possible to pinpoint a certain point of space and ask how quickly that space is...

I am reading the proof of the Riemannian Penrose Inequality (http://en.wikipedia.org/wiki/Riemannian_Penrose_inequality) by Huisken and Ilmamen in "The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality" and I was wondering why they restrict their proof to the dimension ##n=3##...

The Schwarzschild spacetime is defined by the following line element \begin{equation*} ds^2 = - \left( 1 - \frac{2m}{r} \right)dt^2 + \frac{1}{1-\frac{2m}{r}}dr^2 + r^2 d\theta^2 + r^2\sin \theta^2 d\phi^2. \end{equation*} We can use the isotropic coordinates, obtained from the Schwarzschild...

How are the effects of antimatter on gravity different than regular matter?

Hello, I'm Harry. I'm new here, hope not breaking any posting rules in any ways :) I have a question and would like to ask for some suggestions and information. The question is about general relativity or gravity and structure of the Universe in general; I know there are definitely quite a...

I've been leafing through a recently bought copy of James B Hartle's Introduction to Einstein's General Relativity and I notice that some of the questions have one or more letters assigned to them, such as A, B, C, S, P. It seems that my Pearson New International Edition does not contain the key...

Randall Munroe, creator of the webcomic XKCD, wrote a piece for the New Yorker, in which he explains special and general relativity using only the thousand most common words in the English language. Here's an excerpt. Read the full piece at...

What is a good book on GR? I have a good amount of experience with SR, and have spent a good deal of time researching GR, from Wikipedia, to PDF's, and youtube videos. I am moderately comfortable with Tensors, but a book that covers them in depth would be nice, not necessary, however. (I can...

Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!

Homework Statement [/B] Consider ##\mathbb{R}^3## in standard Cartesian co-ordinates, and the surface ##S^2## embedded within it defined by ##(x^2+y^2+z^2)|_{S^2}=1##. A particular set of co-ords on ##S^2## are defined by ##\zeta = \frac{x}{z-1}##, ##\eta = \frac{y}{z-1}##. Express...

Hello Everyone, Back when Einstein was formulating General Relativity his equations just could not predict a static universe. I have read that they actually predicted an expanding Universe. Later Friedmann derived an equation from GR that would explain how an Expanding Universe would evolve...

OK, so my basic understanding is that GR is all about geometry of space-time. It's all geometry, no other mechanism. This explains why objects change direction due to gravity. But why does the speed increase? How does pure geometry cause a change in speed? Also, where does this kinetic...

Homework Statement The aim is to find a solution for the scale factor in a Robertson Walker Metric with a scalar field and a Lagrange multiplier. Homework Equations I have this action S=-\frac{1}{2}\int...

If gravity is not a force, rather the curvature of space time influenced by a body's mass, then why do we perceive an acceleration due to gravity, as though there was a force? In my mind, it would make sense for the bend in space to only cause a massive object to change direction. I suppose if...

1. A spacecraft going at .99c is heading straight towards a star that's at a distance of 60,000 light years. Another ship 25,000 light years below the first one also is heading towards the star also at .99c. What what is the related rate between the time dilation of the first spacecraft to...

I have some questions related to this video: In the Einstein view of gravity, time is warped. Is this warped time same as the gravitational time dilation? In other words, is the curved time axis due to different clock speeds at different height in a gravitational field? Further, can the tidal...

Suppose we are in a Minkowskian space, away from all the source of gravity, and observe an accelerated frame from this frame. Acoording to Equivalence principle, we can consider the accelerated frame to be at rest and assume we have gravity in the accelerated frame. Thus, observer in the...

Homework Statement Compute $$T_{\mu\nu} T^{\mu\nu} - \frac{T^2}{4}$$ For a massless scalar field and then specify the computation to a spherically symmetric static metric $$ds^2=-f(r)dt^2 + f^{-1}(r)dr^2 + r^2 d\Omega^2$$Homework Equations $$4R_{\mu\nu} R^{\mu\nu} - R^2 = 16\pi^2 \left(...

According to equivalence principle, gravity can be treated like acceleration "locally". Based on this principle we can treat a non-inertial frame at rest and explain the fictitious forces (of Newton's Laws) as gravity. From this we can prove that time elapses at different rates at different...

Hello everyone! As an admirer of string theory, I have strong interest in the theories that purport to unify general relativity with quantum mechanics. In the case of string theory, the goal is to find a form of describe the force of gravity according to the principles of quantum mechanics, ie...

According to general relativity, time is a dimension, one of four dimensions that form 4D spacetime - a structure which is mathematically symmetrical and homogeneous. Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies...

Homework Statement I'm reading Zee's book Einstein Gravity, I'm in the section where he said that given an array of two numbers p=(ap1, bp2), it is not a vector unless a=b. He just stated it without really showing how it must be like that. I know that a vector should satisfy a transformation...

The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...

Hello, I'm not an Academic, I love physics as a casual hobby. So I have few questions that stuck in my mind. Here is the first one: By Einsteins General Relativity everything including us stuck to Earth by gravity. Earths mass bends the Spacetime. The gravity means: deformed space is pushing us...

So, it always (at least in the books that I have read or scanned) that the Einstein-Hilbert action $$S=\int{\sqrt{g}d^4xR}$$ is directly posed without an explanation of its origin. My question is how did it occur to Hilbert or Einstein to write down this specific form of action?

I'm about to start my senior year at university pursuing a double major in physics and electrical engineering. I decided recently that I wanted to go to graduate school for physics so I started thinking about the area I would like to specialize in. My current university does most of its research...

What impact has Eduard Prugovecki's work in QGR have on nowadays research?

Equivalence principle says that gravitational forces are equivalent physically to inertial forces. Can someone explain what is meant by that and how was it concluded?

It took einstein 4 years to complete his general theory of relativity but the fundamental idea behind this work is that he believed that space is curved , how he is sure about this idea from the beginning ?