General relativity Definition and 999 Threads

Why the Shapiro time delay is calculated with respect to the difference in coordinates and not with respect to the physical distance? I follow the discussion of Clifford (Theory and Experiment in Gravitational Physics) which uses isotropic coordinates and PPN approximation. To make more clear my...

I'm reading the Wiki article below to say the invariant mass of photons in an expanding volume of space will decrease. I thought invariant mass of a photon was always zero and the energy of photon changed due to the expansion of space. So where did I go wrong? Quote from Wiki General...

In the Einstein Field Equations: Rμν - 1/2gμνR + Λgμν = 8πG/c^4 × Tμν, which tensor will describe the coordinates for the curvature of spacetime? The equations above describe the curvature of spacetime as it relates to mass and energy, but if I were to want to graph the curvature of spacetime...

Talking about relativity, time dilation and clock synchronization. What time of reference does PF Forum use? If you see a thread being answered at: "Today 10:00 am" Is it 10:00 am on PF server or 10:00 am on your computer?

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...

Homework Statement Let g_{\mu\nu} be a static metric, \partial_t g_{\mu\nu}=0 where t is coordinate time. Show that the metric induced on a spacelike hypersurface t=\textrm{const} is given by \gamma_{ij} = g_{ij} - \frac{g_{ti} g_{tj}}{g_{tt}} . Homework Equations Let y^i be the coordinates...

Homework Statement Energy density of radiation ##\rho_r = 8 \times 10^{-14} J m^{-3}## and energy density of matter ##\rho_m = 2.63 \times 10^{-10} J m^{-3}##. Baryon density parameter is ##\Omega_b = 0.04##. Temperature of CMB today is ##2.73 K##. Ionization energy of Hydrogen is ##13.6 eV##...

Homework Statement I am given this metric: ##ds^2 = - c^2dt^2 + a(t)^2 \left( dx^2 + dy^2 + dz^2 \right)##. The non-vanishing christoffel symbols are ##\Gamma^t_{xx} = \Gamma^t_{yy} = \Gamma^t_{zz} = \frac{a a'}{c^2}## and ##\Gamma^x_{xt} = \Gamma^x_{tx} = \Gamma^y_{yt} = \Gamma^y_{ty} =...

"In quantum gravity, the problem of time is a conceptual conflict between general relativity and quantum mechanics. Roughly speaking, the problem of time is that there is none in general relativity. This is because in general relativity, the Hamiltonian is a constraint that must vanish. However...

http://arxiv.org/abs/1503.08640 New first order Lagrangian for General Relativity Yannick Herfray, Kirill Krasnov (Submitted on 30 Mar 2015) We describe a new BF-type first-order in derivatives Lagrangian for General Relativity. The Lagrangian depends on a connection field as well as a...

Homework Statement A sub-atomic particle is near the event horizon of a black hole. Due to the nearby gravitational field, the Ricci Curvature Tensor is changing rapidly. The particle then performs quantum tunneling. Homework Equations Which version of spacetime does the tunneling particle...

I found the picture but I painted very wrong .

I read somewhere that speed can be higher then c in General Relativity.Can you show me a website

I read about relativity and some people claim to be incomplete so what is the incompleteness.

Space does not exist, so time can http://arxiv.org/abs/0909.1861 Can someone explain to me, what this article means by "space does not exist"?

Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?

Hi, my question is the title, if Ricci tensor equals zero implies flat space? Thanks for your help

Now, I am reading Carroll's http://arxiv.org/abs/gr-qc/9712019. On a page 88 he defines basic vectors, which are orthonormal (3.114) and basic vectors given by gradients of coordinate functions. Are these later basis vectors not obviously orthonormal?

Hello, I have a conceptual problem. How can both General Relativity and a theory of Quantum Gravity simultaneously exist? GR describes gravity as the curvature of spacetime, while QG is most likely a gauge theory. Furthermore, if gravity is indeed describedby particle interactions-what does...

I am studying general relativity from Hobson and came across the term 'lifetime' of a closed (k>0) universe, ##t_{lifetime}##. I suppose at late times the curvature dominates and universe starts contracting? Are they simply referring to ##\int_0^{\infty} dt##? If so, would the bottom expression...

Homework Statement (a)Sketch how the contributions change with time (b)For no cosmological constant, how long will this universe exist? (c)How far would a photon travel in this metric? (d)Find particular density ##\rho_E## and scale factor (e)How would this universe evolve?[/B] Homework...

I'm utterly confused by co-moving distance, transverse comoving distance and proper distance. Is comoving distance = proper distance? Then what is transverse comoving distance? Here's what I know so far: The FRW metric can either be expressed as ds^2 = c^2dt^2 - a^2(t) \left[ \frac{dr^2}{1-kr^2}...

Hi, I have been studying general relativity using Hobson's lately, particularly about the FRW universe. I know that for a matter universe with curvature, H^2 = \left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2} Another expression I came across is also 1 = \Omega_m +...

Homework Statement (a) Find the christoffel symbols (Done). (b) Show that ##\phi## is a solution and find the relation between A and B.[/B] Homework EquationsThe Attempt at a Solution Part(b) \nabla_\mu \nabla^\mu \phi = 0 I suppose for a scalar field, this is simply the normal derivative...

I was reading through hobson and my notes where the covariant acts on contravariant and covariant tensors as \nabla_\alpha V^\mu = \partial_\alpha V^\mu + \Gamma^\mu_{\alpha \gamma} V^\gamma \nabla_\alpha V_\mu = \partial_\alpha V_\mu - \Gamma^\gamma_{\alpha \mu} V_\gamma Why is there a minus...

Homework Statement (a)Find how ##\rho## varies with ##a##. (b) Show that ##p = \frac{2}{\lambda^2}##. Find ##B## and ##t_0##. (c) Find ##w## and ##q_0##. What values of ##\lambda## makes the particle horizon infinite? Find the event horizon and age of universe. (d) Find luminosity distance...

Homework Statement A 26 year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away. The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth. The biologist’s son is 3 year-old when she left. Assume...

Homework Statement [/B] (a) Find the value of A and ##\Omega(\eta)## and plot them. (b) Find ##a_{max}##, lifetime of universe and deceleration parameter ##q_0##. Homework Equations Unsolved problems: Finding lifetime of universe. The Attempt at a Solution Part(a)[/B] FRW equation is...

Homework Statement (a) Find the FRW metric, equations and density parameter. Express the density parameter in terms of a and H. (b) Express density parameter as a function of a where density dominates and find values of w. (c) If curvature is negligible, what values must w be to prevent a...

I'm reading An Intro to GR, Hughston and Tod, it says that in GR the idea is that the geometry of st varies from point to point, represented by allowing the metric to vary over space-time. It uses a (+,-,-,-) signature and so ##proper time=ds^{2}##. It then makes the comment that proper time...

HI - we know that the orbit of mercury precesses (I hope I am using the right terminology here). Which basically means that the orbit seems to undergo some sort of rotation in the ecliptic plane. Does this also mean that the period of Mercury's orbit as seen from the Earth is not uniform but...

Homework Statement [/B] (a) Find the christoffel symbols (b) Find the einstein equations (c) Find A and B (d) Comment on this metric Homework Equations \Gamma_{\alpha\beta}^\mu \frac{1}{2} g^{\mu v} \left( \partial_\alpha g_{\beta v} + \partial_\beta g_{\alpha v} - \partial_\mu g_{\alpha...

Homework Statement (a) Find ##\dot \phi##. (b) Find the geodesic equation in ##r##. (c) Find functions g,f,h. (d) Comment on the significance of the results. Homework Equations The metric components are: ##g_{00} = -c^2## ##g_{11} = \frac{r^2 + \alpha^2 cos^2 \theta}{r^2 +\alpha^2}##...

Taken from Hobson's book: How did they get this form? \dot u^{\mu} = - \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u^{\mu} g_{\mu \beta} \delta_\mu ^\beta = - g_{\mu \beta} \delta_\mu ^\beta \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u_{\mu} = - \frac{1}{2} g_{\mu \beta} \delta_\mu ^\beta...

Is anyone familiar with Atlas 2 for mathematica to calculate the Riemann Tensor, Ricci Tensor, and scalar I have a metric that I need to calculate these things for. Can anyone help? I'm not too up on Mathematica either.

I have been looking online for books on introductory level quantum mechanics and General relativity that provide a mathematical introduction to these theories. Most of the books I have read until now provide a laymans introduction to these things. Since I'm only pursuing this as a hobby and...

Taken from Hobson's book: How is this done? Starting from: R_{abcd} = -R_{bacd} Apply ##g^{aa}## followed by ##g^{ab}## g^{aa}g^{aa} R_{abcd} = -g^{ab}g^{aa}R_{bacd} g^{ab}R^a_{bcd} = -g^{ab}g^{aa}R_{bacd} R^{aa}_{cd} = - g^{ab}g^{aa} R_{bacd} Applying ##g_{aa}## to both sides...

In a previous thread, reference was made to an entertaining "defense" of relativity by Einstein, which can be found here: https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity One of the arguments Einstein makes in this dialog is that the twin paradox can be...

Assume we have a free-falling particle in gravity in a static metric. Its worldline is described by: g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} where ##|h_{\mu \nu} << 1|##. Taken from Hobson's book: Why did they let ##g^{k\mu} = \eta^{k\mu}##?

Hi guys! I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please? Relevant equations: ∫u dv = uv - ∫v du

Guys , i have just completed my high school (4 days back) and know just the basic maths and physics (only what was taught in school).I have a great interest in physics and want to become a researcher.I am free for 3-4 months (after which i will join a college for majors in physics) and in that...

Are the general principles of string theory “the properties of fundamental particles are due to their unique vibrational pattern of strings in 10 or 11 or 26 dimensions” incompatible with both general and special relativity? due to an observer would be able to detect changes in properties of...

I stumbled upon this video: which seems to claim that past present and future exist at the same time due to the fact that observes in different frames would not agree on the order of events. The video claims that there are frames in which Mozart is alive. I don't think that this is correct...

Hello everyone, I'm studying some applications of AdS/CFT and I came across an expression of the Maxwell field written in the following way: $$ A=A_t(r)dt+B(r)xdy. $$ How does this notation work? Is it simply a way of writing the four-vector? If so, why do we use this notation? Thanks a lot!

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...

http://en.wikipedia.org/wiki/Kaluza–Klein_theory ##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche) http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments) Also, a lot (if not all...

Homework Statement (a) Show that the equations satisfy FRW equations. (b) Show the metric when ##\eta## is taken as time Homework EquationsThe Attempt at a Solution [/B] The FRW equation is: 3 \left( \frac{\dot a}{a} \right)^2 = 8\pi G \rho Using ##\frac{da}{dt} = \frac{da}{d\eta}...

What do they mean by 'Contract ##\mu## with ##\alpha##'? I thought only top-bottom indices that are the same can contract? For example ##A_\mu g^{\mu v} = A^v##.

I have been reading section 3.1 of Wald's GR book in which he introduces the notion of a covariant derivative. As I understand, this is introduced as the (partial) derivative operators \partial_{a} are dependent on the coordinate system one chooses and thus not naturally associated with the...

What do they mean by contracting ##\mu## with ##\alpha## ?