General relativity Definition and 999 Threads

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...

It had previously been verified within our own galaxy. http://uopnews.port.ac.uk/2018/06/22/einstein-proved-right-in-another-galaxy/

Greg Bernhardt submitted a new PF Insights post How to Better Define Information in Physics Continue reading the Original PF Insights Post.

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...

Greg Bernhardt submitted a new PF Insights post Solving Einstein's Field Equations in Maxima Continue reading the Original PF Insights Post.

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 [/B] 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...

This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.

I have been trying to understand the implications of a thought experiment and am interested to know either where it's going off course or what those implications might be. Through some reading of earlier threads on this forum I have verified my starting hunch that photons bend spacetime despite...

I know this is a naive question that has almost certainly been brought up numerous times before, but my search abilities seem not to be sufficient for finding a good answer, so if anyone just refers me, that would be fine. The question: Special relativity concerns comparisons between pairs of...

I am reading Polchinski's review on AdS/CFT https://arxiv.org/abs/1010.6134. I have a very simple question, and please help me out. Thanks in advanced. The question abou formula (3.19) The scalar effective bulk action is given by $$ S_0=\frac{\eta}{2}\epsilon^{1-D}\int d^Dx \phi_{\rm cl}...

So recently I saw a video with Richard Gott explaining a self-creating universe. There's three quick questions I'm confused about that I did not understand very well from the video: 1. How does a closed time-like curve allow the universe to self-create? Wouldn't the universe just go around the...

The discussion here https://www.physicsforums.com/threads/general-relativity-the-sun-revolves-around-the-earth.245334/ concludes that in general relativity there are no privileged reference frames so that, for example, it would be valid to use the Earth as a reference frame and say that...

Could we hypothetically use it to create a region of space with the magnitude of the stress component of stress energy tensor greater than magnitude of mass denisty component?

From Verifying the Theory of Relativity by Chandrasekhar Sir J.J. Thomson, as President of the Royal Society at that time, concluded the meeting with the statement', I have to confess that no one has yet succeeded in stating in clear language what the theory of Einstein's really is'. And...

I need to simulate the Friedman equations under different conditions of flat space. Can someone please tell me a good package in MATLAB, Mathematica or stand alone. I am most well versed in MATLAB but have coded in Mathematica before.

What is the best book to learn general relativity for undergraduate and graduate students ? And why?

Hi everybody, and thanks in advance. My doubt is: why should the mass go in the singularity? I'm thinking about this situation: imagine a sphere with radius R<2M; then that sphere generates a BH. Schwarzschild tensor metric is valid only in the exterior region of the mass and for this reason i...

I've always read that these two theories are incompatible, and how General Relativity works for large scales while Quantum Theory represent reality in extra-small cases. So my question is where is the limit where General relativity ceases to exist and Quantum Theory gives a better portrait of...

I saw a video of a talk by Susskind discussing his ER = EPR idea. This post isn't actually about that talk, except that it got me thinking about wormholes. Without exotic means, I understand that it is basically impossible to have a traversible wormhole connecting two distant points in space...

Hey all, I'm trying to come up with a senior thesis project in the realm of GR. It doesn't have to be new, just new to me. I'm having trouble coming up with ideas (or knowing whether or not they would be good for this). One idea that I just came up with: Numerically solve EFE for the solar...

Hi all, I understand the mathematics behind special relativity pretty well, but I only have a bare conceptual understanding of general relativity. My understanding is that energy, momentum and stress (as described in the energy-stress tensor) are what contribute to space-time curvature and...

I have a major in mathematical physics and mathematics and currently I'm on a graduate course in Physics working on a master's thesis. When I started the graduate course I was going to work on General Relativity and Quantum Field Theory on Curved Spacetimes (QFTCS). It turns out that by several...

So General Relativity explains the force of gravity as mass/energy induced curvature of spacetime. This correctly predicts gravitational time distortion, nonlinear geodesics and gravitational lensing, the anomalous precession of planetary orbits, the schwarzchild metric, and so on. Could the...

Homework Statement Consider the metric ds2=(u2-v2)(du2 -dv2). I have to find a coordinate system (t,x), such that ds2=dt2-dx2. The same for the metric: ds2=dv2-v2du2. Homework Equations General coordinate transformation, ds2=gabdxadxb The Attempt at a Solution I started with a general...

I have the following question considering frame dragging: A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is...