Gr Definition and 952 Threads

Index notation in GR is really confusing ! I'm confused about many things but one thing is the order of index placement , ie. is Λa b the same as Λba ? And if not what is the difference ? Thanks If anyone knows of any books or lecture notes that explain index gymnastics step by step...

Pretty straightforward title. Looking for recommendations. I've read Kip Thorne's Black Holes and Time Warps, Einstein's Relativity, The Special and General Theory, and a few other titles, just looking for recommendations on where to go next. I've only covered Integral calculus and linear...

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same. I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of...

I will order books about GR.Here what I think https://www.amazon.com/dp/1589880447/?tag=pfamazon01-20 https://www.amazon.com/dp/0070379858/?tag=pfamazon01-20 https://www.amazon.com/dp/0471925675/?tag=pfamazon01-20 I will order these. Here the extra books which I need recommend.Is these are...

Hello! I am a master student, and I am about to start working on my master thesis, which, in my counrty, is a substantial work of 6 months which usually involves original research. I will be supervised by two professors of Statistical Mechanics, who have many research interest. In these days...

Suppose I have a toroidal tube, in which I lock a lucky/unlucky mouse. Then I start spinning the torus [of radius ##r##] around its center with some velocity ##\beta##. Then the centrifugal acceleration felt by the mouse due to rotation is given by some special relativistic maths: a=...

Hi, GR explains the perihelion precession of Mercury, the deflection of light and the gravitational redshift pretty accurately. However, predictions for larger scales seem to be quite wrong, and physicists introduce stuff like the cosmological constant, dark matter and energy. Why are they...

Hi! So I have noticed that phenomena, like gravitational lensing, are proven to exist, and GR is the only logical reasoning for them? If those parts of it have been proven, how could GR be possibly wrong? And if it was correct, wouldn't there have to be a way to make it work on a quantum...

Am I correct in thinking that the force of gravity between 2 test objects at rest on a planet's surface is less than it would be for the same objects at rest in deep space? I understand that this occurs because in GR gravitational potential has a mass value which is lost on the surface, while...

I have question, is GR compatible with SO(3)?

Hi guys. How do astrophysicists measure the redshift of electromagnetic waves from galaxies due to gravity without the use of General Relativity? If I can be more specific, how do astrophysicists know that the gravitational redshift of light emitted from some part of a galaxy or galaxy cluster...

So, I feel like I have a pretty good grasp of Special Relativity, but GR is a whole different beast. I am really stuck on where the acceleration comes from for Gravity. For instance, it's easy for me to understand how an orbit can form from bent space (an analogy for the way I think of it is a...

I have a problem in understanding krushkal extension of Schwarzschild metric. So i solved the Einstein equation for the vacuum part of a spherically symmetric matter distribution and solved it in the inside region too. they are fine and compatible at schwarzchild radius. But the problem i am...

Rovelli & Vidotto's Planck Stars describes a possible quantum black hole - white hole transition through a quantum bounce somewhat analogous to the LQC bounce. In another thread, @marcus pointed out to me that this was not necessarilly considered the most likely scenario for a QG black hole. Is...

I am trying to get my head around curvature, geodesics and acceleration in GR. I've put together the following paragraph that attempts to describe qualitatively how I think these things play together. In Newtonian mechanics, a freely falling object accelerating towards the Earth implies a force...

Is it possible to read and understand General and Special relativity on your own (by studying from the right textbooks),without a degree in physics? I know the basic stuff in calculus ,algebra ,geometry and Newtonian physics etc ...how will i know whether i am upto it?

I have seen written out in various places (including this forum) the effective potential function that comes from the solutions to the Schwarszschild Geodesic. But I haven't been able to find the effective potential functions for other solutions to Einstein's field equations. Are there...

If Einstein proved that light (a massless object) can be bent because of space-time. Then what happens to Newton's gravitation equation F = Gmm/r^2. Obviously this cannot apply to light, so technically this should fall completely, having both Newton's and Einsteins discovery working at the same...

IIUC, there are two different interpretations of GR - either as curvature of space time (as in Misner Thorne Wheeler) or as a (spin-2)field that influences all matter (as in the books by Weinberg or in the Feynman Lectures on Gravitation) and that leads to the underlying Minkowski metric being...

Are there software like games or simulations where General Relativity is used or are most based on Newtonian spacetime? I wonder what would be the results or difference if GR based on diffeomorphism invariance is used on the moving subjects and objects in the games versus that of basing them on...

From the things I've studied till now, the thought came into my mind that all of the known solutions of Einstein's Field Equations are Lorentzian. Is it correct? And if it is correct, is there something in EFEs that implies all solutions to it should be Lorentzian? And the last question, do more...

If you view free fall as an inertial frame and therefore items at "rest" on the Earth's surface are accelerating away from the centre of mass I do not understand how energy is conserved. Taking this view, relative to the free fall frame the items will be gaining velocity which implies that the...

In SR, we may choose any inertial observer and his reference frame at which he is at rest, and other observers are movin wrt to him. All the moving observers 'slice' spacetime in a different way than the observer at rest, at different angles relative to his simultaneity surfaces. This is all...

On youtube, I came across to one of many videos trying to explain General Relativity. One of the comments was interesting to me: "I understand how gravity causes an object with velocity to go in curves or to orbit, due to the curvature of space-time: the object thinks that it's traveling in a...

Hi guys, in GR a free-falling observer will measure the local speed of light as c, like in SR. My question is will an accelerated (non-inertial) observer locally measure a greater speed than c, or will he also measure the local speed of light as c. For instance, if there is an object that is...

Hi all, I'm fairly new to GR, and I'm also somewhat new to tensors as well. I'm looking for some detailed explanation of a tensor, as I want to begin studying GR mathematically. I watched a video that was posted on PF not too long ago that was pretty good. I'm having trouble remembering who it...

Say we have an elevator moving through deep space at a constant velocity. We have a light emitter at the "top" of the elevator pointing towards a detector at the bottom of the elevator. We shine the light and notice that the frequency at which the light was emitted at the top is the same as...

I'm stuck on deriving the follow. Context: FRW Metric, dust dominated universe, use of conservation of energy-momentum tensor. I'll now state all the equations I can see are relevant. (But just in case the source is http://arxiv.org/pdf/gr-qc/9712019.pdf and it's eq 8.43). ## \frac{d}{dt}(\rho...

In the book General Relativity by Norbert Straumann, He derives the Kerr's solution in the chapter about black holes and then modifies it to get the Kerr-Newman solution. Then he calculates the g-factor of a rotating charged black hole using the Kerr-Newman solution(and gets the amazing result...

I am having trouble connecting some of the differential geometry in gr to what is actually measurable in the real world. As far as i understand we can measure physical quantities in terms of coordinates x^\mu on the tangent space of a 4-dim Pseudo-Riemannian manifold M. So let's say we are...

Mod note: OP warned about not using the homework template. I have read that 'a(t) determines the value of the constant spatial curvature'.. Where a(t) is the scale factor, and we must have constant spatial curvature - this can be deduced from the isotropic at every point assumption. I'm trying...

It is often stated that when one tries to find a stress-energy tensor of gravitational field in GR, the resulting quantity is zero because we can always make the metric zero at a point by a coordinate transformation. So there is no local measure of energy-momentum for gravitational fields. But I...

Hi everyone! I really like physics from what I've seen so far, and I'd love to try some on my own to see if it's something I'm interested in possibly pursuing. I am planning on going into computer science, but this is something that I feel I should try. Are there any books that would be good...

How will we define gravity in terms of General Relativity.? Technical and scientifically approved definition are appreciated

I am trying to reconcile the definition of contravariant and covariant components of a vector between Special Relativity and General Relativity. In GR I understand the difference is defined by the way that the vector components transform under a change in coordinate systems. In SR it seems...

There are various different ways to try to add up the effective total mass of a configuration of masses in GR in such a way that it comes out to be equal to the total of the source mass as measured locally minus the gravitational binding energy. One of these is for example the Komar mass, which...

In an attempt to solve the mystery of dark energy, I came across problems concerned with the General Relativity. In it, I observed that many of the problems were related with the tensor calculus. I want to know that what importance does tensor calculus hold in GR? Are there any other fields of...

Hi all, I am extremely interested in GR, but somehow feel that the books I read are not really enough. Frankly, I find many question on this site and elsewhere completely bewildering, which makes me think that I don't have a solid foundation, especially in classical mechanics and various...

Hello, so I will be starting Calculus 3 (vector and multivariable calc) and physics 1 (intro calculus based mechanics) this next semester. I am interested in using this next semester to go further into both of those topics and I am curious how I would start? I am interested in studying Calc 3...

Consider an homogeneous spherical universe, with mass density \mathcal{\rho}_M . Then the total energy of some test-mass m at radius R(t) from the center is given by: E_{tot} = E_{kin} + E_{pot} = \frac{1}{2} m \dot{R}^2(t) - \frac{4 \pi}{3} Gm \mathcal{\rho}_M R^2(t) Or that: \Big(...

Start with an existing black hole and an event horizon radius R at time T. Say the black hole is being "fed" an infinite series of golf balls, one after the other, which are all stamped numerically such that the current golf ball external to the event horizon is 1.0 * 10^32. See linked img...

What is the relationship between the differentiable manifold that is space-time and the physical space around us? How does one relate the three seemingly Cartesian coordinates around us, those which we can measure out with a ruler, to the coordinates of the Lorentzian manifold? If i say, measure...

In introductory texts about GR, it is sometimes stated that one of the things that guided Einstein to GR, was the effects of accelerated motion ( don't know whether proper or coordinate acceleration) , things like Ehrenfest paradox. But after that, they completely forget about acceleration and...

Homework Statement Consider the Schwarschield Metric in four dimensional spacetime (M is a constant): ds2 = -(1-(2M/r))dt2 + dr2/(1-(2M/r)) + r2(dθ2 + sin2(θ)dø2) a.) Write down the non zero components of the metric tensor, and find the inverse metric tensor. b.) find all the...

Hello, I am reading a book about General relativity, i understand that energy of the EM tensor go in the stress- energy tensor of GR equations. SO, EM field curve space. But i don't understand if space curvature impact EM field ? Is variation of space curvature can create EM field ? Clément

Dear all, Some of you might know that I am self studying General relativity starting with learning about tensor analysis. I am using D'Inverno's book on GR and currently doing tensor analysis. Do you think that I should also study the "level two material" as stated by D'Inverno as a first...

Hi guys! I am looking for good lectures or books on special relativity and/or general relativity. Thanks in advance for any feedback.

The field equations of general relativity are non-linear. There are exact analytic solutions to the equations for special symmetrical cases, e.g. Schwarzschild's solution for a black hole. But in general, wouldn't there be other chaotic solutions as well? A chaotic system is analytically...

I have read some basics knowledge about General Relativity and I see that it deal perfectly with gravity. But what about accelerated frames? Is there something similar to Lorentz Transformation for accelerated frame in General Relativity? (so that i can solve, maybe, the general twin paradox)...

When we talk about space-time curvature or the curvature of space, how many different "types" of curvature are there according to GR? For example, the rounded surface of a cylinder is curved in only 1 dimension, while the other is flat. For a sphere, both dimensions of the surface are curved...