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.
Hi,
It is usually claimed that a person in an accelerating elevator with an acceleration equals to the gravity of the earth; this person cannot make any experiment that makes him know whether he is in the elevator or on the surface of earth.
However, if this person project two light beams...
I am collecting ways to visualize the curvature of spacetime -- and movement of objects affected by gravity -- as per Einstein's GR. Alternatives to the bowling ball / trampoline image so often used in the popular press. Images that show the similarities / differences between Newton & Einstein...
Background: I'm about to graduate with a mathematics degree(in the US), hence I have exposure to multivariable calculus, real analysis, abstract algebra, complex variables etc (no differential geometry however). I have also taken a class on QM(using Griffiths) and I saw some SR during a Modern...
In my physics education, I shied away from heavily theoretical stuff like General Relativity. I took the required sequence in Quantum Mechanics but having never used it on the job, much of that knowledge has faded too. I started a course in Quantum Field Theory but dropped it. I had friends...
Is there a sensible way of defining a displacement vector in a general manifold? That is, the displacement vector being the difference between position vector at two different points... the problem is that these two different points have, in general, different tangent vector spaces. Never the...
Hi, I'm wondering if it is possible to measure radii of stars using general relativity, given its explanation of gravity as curvature of space.
Thank you
I am still learning general relativity (GR). I know we can find the path of a test particle by solving geodesic equations. I am wondering if it is possible to derive/convert metric tensor to gravity, under weak approximation, and vice versa.
Thanks!
This is an inquiry about some of the details of the bending of the trajectory if a photon by curved space-time (S-T) from the perspective of general relativity (GR).
The environment in this scenario contains a black hole at its center, a photon passing by the black hole a km above the event...
If someone wanted to pursue a career in gravitational wave physics, and work at places like LIGO, studying astrophysical objects such as black holes and neutron stars, etc.
What are some key courses/skills that person should take/learn as an undergraduate, and graduate student?
I have little exposure to mathematics beyond high school algebra and physics, but I have become increasingly interested in physics, particularly its most towering achievements of modern times : Quantum Physics, as well as A. Einstein’s Special and General Relativity, the latter of a...
After I read Martin_K's post of 4:14 Oct. 30 on the frozen image of an object just before it fell through a black hole's event horizon, the next few minutes I was jumped by a handful of related ideas.
First, the frozen image scenario is illustrative because when photons are frozen in place...
Hi, the trace of the extrinsic tensor K(Myu,Nu) in Alcubierre metric, relative to the foliation normal vector is non zero on the front x=rs+R and rear x=rs-R "walls". This is the normal volume component Tr =k(1,1)+k(2,2)+k(3,3) and should affect the Ricci tensor in Lorentzian/Minkowsky 4D. How...
What is currently the common opinion on Chronology Protection manifested by Hawking almost 30 years ago?
There does not seem to be any fully accepted no-go result for Thornian time machines. Energy conditions can be violated in QFT, semi-classical results suffer from counter-examples, Novikov's...
Is the increase in mass/density of an object in motion purely relativistic?
What I mean is if you were in a spaceship approaching the speed of light would you be able to measure a change in your mass/density or would the change only be observable to someone at rest. I'm aware of the Lorentz...
Hi.
I want to learn - amateurishly - Quantum Mechanics, and General Relativity, but my experience with Physics is very small.
I want to ask, what should I learn - what books should I read - before I start to learn those theories?
Sorry for my english.
Hello,
I was wondering if somebody could help me by suggesting a concrete topic in GR for my master's dissertation. My background is from Mathematics, but I have followed first year masters program courses in Theoretical Physics, including one on General Relativity based on Schutz's book...
As far as I know, a object will experience time slower when its speed is close to the speed of light.
But photons themselves moves at the speed of light, does that mean that they experience no time?
I will be proceeding onto my masters degree in theoretical physics in about two months time. My goal is to learn as much as I can about quantum and statistical physics, as this is the field in which I would like to do my PhD.
In my second semester, I have the chance to either study the...
Hi, I have the following problem:
Given the 5-D generalization of the Schwarszschild solution with line element:
ds^2=-\Bigg(1-\frac{r^2_+}{r^2}\Bigg)dt^2+\Bigg(1-\frac{r^2_+}{r^2}\Bigg)^{-1}dr^2+r^2[d\chi^2+\sin^2(\chi)(d\theta^2+\sin^2(\theta)d\phi^2)]
where ##r_+## is a positive constant...
Hi, I'm the given the following line element:
ds^2=\Big(1-\frac{2m}{r}\large)d\tau ^2+\Big(1-\frac{2m}{r}\large)^{-1}dr^2+r^2(d\theta ^2+\sin ^2 (\theta)d\phi ^2)
And I'm asked to calculate the null geodesics.
I know that in order to do that I have to solve the Euler-Lagrange equations. For...
I am making this thread to discuss interesting open questions in Gravity and Cosmology with people working in these or even relevant area.
Anyone who is working in these (and relevant) areas, please identify yourself here and we will begin and hopefully people will catch on and contribute.
I am doing a problem from Schutz, Introduction to general relativity.The question asks you to find a coordinate transformation to a local inertial frame from a weak field Newtonian metric tensor ##(ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2))##. I looked at the solution from a manual and it...
I have a question. I know that events don't happen simultaneously but rather they are ordered chronologically by time, but why? What is time and how does it stretch events and why does it have the rhythm/flow that it currently has?
Homework Statement
This is Problem 2 from Chapter 1, Section V of A. Zee's Einstein Gravity in a Nutshell. Zee asks us to imagine a colony of "eskimo mites" that live at the north pole. The geometers of the colony have measured the following metric of their world to second order (with the...
Homework Statement
Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and...
If dark matter is a supersolid that fills 'empty' space and is displaced by visible matter, then is this the same notion as the spacetime fabric having mass and being curved by visible matter?
I've been reading up on Killing vectors, and have got on to the topics of homogeneous, isotropic and maximally symmetric space-times. I've read that for an isotropic spacetime, one can construct a set of Killing vector fields ##K^{(i)}##, such that, at some point ##p\in M## (where ##M## is the...
So the other day I saw a YouTube video on how gravity works according to general relativity.
From what I understand, objects bend space_time with their mass and create a shape which is close to a cone. Since objects only move forward in time through a straight line, the bent space_time makes...
Hello everyone,
I'll go straight to the question. The gravitational time dilation is equal to tearth = tspace*sqrt(1 - rs/r), with rs = 2GM/c2.
However, the formula for speed of light in gravitational field is equal to v = c(1 - rs/r).
My intuition tells me that these two formulas must be the...
Most often, general relativity is formulated in terms of Einstein's field equations:
whose terms are familiar to readers in this forum.
But, I understand (and feel free to correct me or qualify my statement if I am incorrect) that it is also possible to describe general relativity with an...
Homework Statement
Consider the Godel Metric in spherical coordinates as on page 6 here;
ds^2=4a^2\left[-dt^2+dr^2+dz^2-(\sinh^{4}(r)-\sinh^{2}(r))d\phi^2+2\sqrt{2}\sinh^{2}(r)dt d\phi)\right]
This is a solution to Einstein's Equations if we have ##a=\frac{1}{2\sqrt{2\pi\rho}}## and ##\Lambda...
Reading Chandrasekhar's The mathematical theory of black holes, I reached the point in which the Newman-Penrose GR formalism is explained. Actually I'm able to grasp and understand the usage of null tetrads in GR, but The null tetrads used in this formalism, are very special, since are made by...
Hello everyone,
I'm sure a lot of you know that the Christoffel symbols are not tensors by themselves but, their variation is a tensor.
I want to revive a post that was made in 2016 about this: The Variation of Christoffel Symbol and ask again "How is that you can calculate ∇ρδgμν if δ{gμν} is...
I see this has been already discussed but the old threads are closed.
EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited
"In this example, Einstein presents a paradox in QM suggesting that QM is inconsistent, while Bohr attempts to save consistency of QM by combining QM with the...
Hi All. On Tuesday I have to present my research proposal for my undergrad research. I intend to model our solar system using general relativity and compare and contrast my results with observations. Attached is my paper that I had to submit to my adviser. He suggested that I talk about some...
Homework Statement
Calculate the volume of a sphere of radius ##r## in the Schwarzschild metric.
Homework Equations
I know that
\begin{align}
dV&=\sqrt{g_\text{11}g_\text{22}g_\text{33}}dx^1dx^2dx^3 \nonumber \\
&= \sqrt{(1-r_s/r)^{-1}(r^2)(r^2\sin^2\theta)} \nonumber
\end{align}
in the...
I've been reading Straumann's book "General Relativity & Relativistic Astrophysics". In it, he claims that the twice contracted Bianchi identity: $$\nabla_{\mu}G^{\mu\nu}=0$$ (where ##G^{\mu\nu}=R^{\mu\nu}-\frac{1}{2}g^{\mu\nu}R##) is a consequence of the diffeomorphism (diff) invariance of the...
Homework Statement
Question attached:
Homework Equations
see below
The Attempt at a Solution
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my main question really is
1) what is meant by 'abstract tensors' as I have this for my definition:
to part a)
##V^u\nabla_uV^a=0##
but you do say that ##V^u=/dot{x^u}## ; x^u is a...
What is the deviation in the expansion of the universe exactly quantified, when I would assume general relativity and project it backwards?
As a statistician I am asking for data, for either the backwards projected general relativity case and either the real expansion case, as it is...
I am posting this paradox as a brain teaser
If we drilled a tunnel through the earth, to the other side, and measured gravity in the tunnel, gravity would be zero in the center of mass. This is Newtonian gravity and is connected to the vector addition of the gravitational force; cancels in...
So, I've been studying some tensor calculus for general theory of relativity, and I was reading d'Inverno's book, so out of all exercises in this area(which I all solved), this 6.30. exercise is causing quite some problems, so far. Moreover, I couldn't find anything relevant on the internet that...
According to various sources, the Moon is separating from Earth 4 cm every year. I’ve searched for the explanation and I’ve found the following:
The friction the seas and oceans from the Earth make with it’s soil causes the Earth’s rotation to slow down. This causes the Moon to speed up...
Let us assume a "toy-metric" of the form
$$ g=-c^2 \mathrm{d}t^2+\mathrm{d}x^2+\mathrm{d}y^2+\mathrm{d}z^2-\frac{4GJ}{c^3 r^3} (c \mathrm{d}t) \left( \frac{x\mathrm{d}y-y\mathrm{d}x}{r} \right)$$
where ##J## is the angular-momentum vector of the source.
Consider the curve
$$ \gamma(\tau)=(x^\mu...
According to General Relativity, everything must be causal, something from the future cannot effect the past, and spacetime geometry is this way. By this logic, does this mean that if we were to ever time travel, via any means, arriving in the past is a violation of causality, as you are...
I am a working professional trying to get back to some physics that I used to enjoy a couple of decades ago. I still do remember the basic calculus (integrals, partial derivatives, basic ODE) and am interested in studying General Relativity. I have a decent understanding and memory of Special...