Gr Definition and 937 Threads

I am currently taking graduate course in GR following Carroll and Wald and we just started covering causal structure. In all my years studying physics this has been the first time something made me stop and go "I would love to spend a decade on this". To me it's a perfect blend of well posed...

Hello, Is the covariant conservation of the matter energy momentum tensor Tμν ; μ = 0 also valid in a theory of gravity having an action for the gravitational field different from the Einstein Hilbert action ? I'm asking because in GR the einstein field equations require Tμν= Gμν where Gμν;μ=0...

When a collider such as the lhc accelerates two protons side by side, would thy seem to gain mass and then distort st? And if so, would the lab frame see them attract each other? How would the attraction be explained from the perspective of each particle, if they don't see the other particle...

I was thinking about a gendanken experiment that I don't know how to solve: Imagine we tie one extrem of a rope in the Earth and the other one in the Sun, with some tension, and connected to a dynamometer (obviously in ideal conditions: no heat, no rotation etc.). My question is: when will the...

1) I read different texts on Contravariant , Covariant vectors. 2) Contravariant - they say is like vector . Covariant is like gradient From what I see they have those vector spaces because it eventually helps get scalar out of it if we multiply contravariant by covariant Also Contravariant...

Hello Forum, I have read Einstein famous thought experiments about the elevator. 1) Being inside an elevator accelerating upward in absence of a gravitational field is equivalent to being inside the same elevator at rest inside a homogeneous gravitational field. 2) An elevator in free fall...

LIGO announced the detection of gravitational wave event GW150914, which coincided with the numerical waveform predicted by GR. The PRL paper says "Using fitting formulas calibrated to numerical relativity simulations, we verified that the remnant mass and spin deduced from the early stage of...

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...

Under SR, we can talk about inertial frames that apply globally. However apparently, under GR, this concept only applies locally, because it breaks down on larger scales. Can anyone provide an explanation as to why this is? Is this due to the fact that space-time is warped in GR?

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...

I have started reading about the Lagrangian in General Relativity, in relation to the Einstein-Hilbert action, and there is something that does not make sense to me. The Lagrangian is split into two pieces, one derived from the Ricci curvature and the other labeled L_matter, so far so good...

string theory is a scalar-tensor theory of gravity, with higher order corrections. in light of the result discovery of gravitational waves of 2 black holes merging, matching GR in the strong field regime, how much deviation should strong theory differ from GR in the strong field regime and can...

I am just trying to understand if gravitational radiation does work when passing through an object? And how much mass or energy typically is lost from the merging of 2 Black Holes?

Homework Statement The question as follows: Calculate the energy that is required to accelerate a particle of rest mass ##m\ne 0## from speed ##v## to speed ##v+\delta v## (##\delta v \ll v##). Show that it would take an infinite amount of energy to accelerate the particle to the speed of...

I've been studying Cosmology, albeit at a very laymen's level. I find it interesting, if not a little confusing, that galaxies are allowed under GR to recede from each other at speeds greater than c. One of the explanations given (from Leonard Susskind's video lectures on cosmology) was...

Hi, I just saw a video about the twin paradox, explained by using GR. I was wondering whether I understood the video correctly. The video states that when the rocket twin is first accelerating away from earth, his clock and his Earth twin's clock are different, but, roughly the same because of...

Is the metric tensor a tensor of rank two simply because the line element (or equivalent Pythagorean relation between differential distances) is "quadratic" in nature? This would be in opposition to say, the stress tensor being a tensor of rank two because it has to deal with "shear" forces. I...

My daughter's high school physics class is using Giancoli (6th ed.) as their text. I'd previously looked at the treatment of SR, and it seemed OK, although old-fashioned. But this morning I started flipping through ch. 33, "Astrophysics and Cosmology," and I was pretty shocked. It reads like a...

The motivation for this post comes from a discussion on another thread https://www.physicsforums.com/threads/questions-regarding-mass-volume-x-density.851172/ It seems worthwhile to me to try a simplification in this post to hopefully avoid the complications raised in the cited thread. Assume...

What is the physical interpretation of Cartesian coordinates in GR? Say, e.g., a system centered at the center of a spherical mass. What are x,y, and z physically, i.e., how are they measured?

Hey guys, just curious of your opinions on this matter. Which graduate schools are the best to earn a Ph.D. in physics theory from and research in concerning the theoretical sub-fields Quantum Field Theory, General Relativity, and Elementary Particle Physics (maybe String Theory)? Which has...

I am new to this forum and relatively new to learning physics itself. I have a very basic question. What is the motivation for looking for a unified theory of quantum gravity? Other than the aesthetics of having a unified understanding of reality, do we have any physical or mathematical reason...

Hello, I’d have a question regarding two apparently different formulas for the time reduction factors for observers in orbit around a rotating black hole, as reported in this nice thread: Equation for time dilation of body in orbit around Kerr black hole? The first one is: $$A=\sqrt{g_{tt} +...

The question is as follows: Prove that any timelike vector for which ##U^0>0## and ##\vec{U}\cdot \vec{U} = -1## is the 4-velocity of some world line. I need to show that there exists a 4-vector ##\vec{x}##, s.t ##\frac{d\vec{x}}{d\tau} = \vec{U}##, where ##\vec{x}## is a world line of some...

I have a generic question on solution procedure. Suppose I consider a system of several point-like bodies interacting only via gravitation. I formulate PDE+ODE system, containing EFE and geodesic motion of the bodies. Since EFE do not define metric uniquely, I need to impose a particular...

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...

Background: I'm just a guy who took some (very old fashioned) undergrad GR course some years ago. I'm only know about the basic stuff and nothing of the more advanced stuff. Question: Is there an statistical mechanics for GR that resembles the one in classical mechanics?, I mean with...

For three years now i have been attempting to find some fundamental properties of gravity from which the three relativistic variables of GR, time dilation and the radial and tangent length contractions, could be determined without incorporating the EFE's. There is no rule or reason that i know...

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...

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...

[Moderator's note: spun off from previous thread on a different topic.] how general relativity explains the variation in value of g at equator and poles? why the twist in spacetime is more at poles than equator and not viceversa

Recently I've had some discussions about time in GR. I've always read in different places that people usually want a spacetime to have a hypersurface-orthogonal timelike Killing vector field so that they can assign a time dimension to that spacetime. But Why is this needed? I can understand it...

Hello everyone I need a good book dealing with the mathematical foundations of GR. I am looking for a rigorous one but i don't need a book on Differential Geometry. Just the stuff i need for GR. Thanks for the replies!

I know there are solutions with CTC, I know about: 1. Goedel Universe 2. Case with moving infinite sticks 3. Ring singularity inside the rotating BH However, in all 3 cases above CTC is "eternal" - the universe "always" contains CTC, and case 3 is a part of the "eternal" BH, We know...

I was told that the bulk density of SP Gr of ASTM C128 for fine aggregrate is (dry weight of aggragrate)/ ( weight of pycnometer filled with water + saturated surface dry of sample - weight of pycnometer filled with water and aggragrate )...What does the ( weight of pycnometer filled with water...

the news media has published the fact that there has thus far been no detection of gravitational waves as predicted by GR. eg Parkes Pulsar Timing Array found nothing after 11 years. If there are no gravitational waves, then GR is wrong. a common argument for gravitons is that there are...

When 2 bodies are locked over relatively large distances (like locked Earth and Venus), do they lock, naively speaking, to the position where another's body is seen (delay distance/c is taken into account) or to the position where other body is actually at the moment (because of Relativity of...

Schutz states in his book in the black hole section that: At r<2GM, r is a timelike coordnate, while t has become spacelike: even more evidence for the funniness of t and r! Since the infalling particle must follow a timelike world line, it must constantly change r, and of course this means...

Wikipedia says: Traditional big bang cosmology predicts a gravitational singularity before this time, but this theory relies on general relativity and is expected to break down due to quantum effects. https://en.wikipedia.org/wiki/Chronology_of_the_universe Although I found other pages, I have...

Hi all! Been a while since I was on PF and I greatly regret it. Forgot how great the community was. Anyways on to my point. I'm going into my second ywar of post secondary and planning to major in physics, and have the eventual goal of understanding both General relativity, and Quantum...

Hi. I am self-studying GR and have many questions. Here are a few. If anyone can help me with any of them I would be grateful. 1 - What is the difference between Tu v and Tvu ? 2 - I have read that the order of indices matters in tensors but when transforming tensors from one coordinate...

Hi guys, I don´t understand too much the Newtonian limit of General Relativity. My question is: In this limit ga b (x) = ηa b (x) + ha b (x) where O(h2→0). Then, according to GR, it's straightforward to demonstrate that the Einstein equation Gt t = k*Tt t in that limit leads to Poisson equation...

So, I am following the PI lecture series by Neil Turok. He starts with the following description of harmonic gauge condition $$g^{\mu \nu}\Gamma^{\lambda}_{\mu \nu}=0$$ He then claims that for linearized gravity (weak field) i.e. $$g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} $$ with $$ |h_{\mu...

Hello. I am not familiar with differential geometry and curvature tensors, yet I am having a great deal of questions to ask. First when we lay a set of coordinates for an n-dimensional plane, let's say 2 coordinates for a surface embedded in a 4D space the vectors we begin with to describe our...

From what I have read, it sounds like GR predicts that under certain conditions, space itself will expand. If this is incorrect, please just let me know and ignore the below. While I don’t know the math involved in GR, I can understand explanations of how gravity distorts space-time, to alter...

I Have been reading hartle's book on Gr which states that basis four vectors point in x,y,z,t coordinate axes. So are they similar to the coordinate axis of Cartesian plane.

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...