What is General relaivity: Definition and 150 Discussions

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  1. Leureka

    I Does potential energy curve spacetime?

    Hi there, I looked around on the net but I didn't quite find the answer to my question. I preface that I don't have training in GR, even though I know about the basics (like what tensors are, geodesics, a bit about topology and differential geometry...). So I wasn't sure if to put this question...
  2. O

    I Is the Black Hole Information Paradox Truly Resolved?

    from what I understand it is believed that information is preserved but we are still working out how exactly, is this the case?
  3. Safinaz

    A A question from a paper on perturbation theory

    Where ##\delta \phi## is the first-order perturbation of a scalar field, ##\Phi## is the first-order perturbation of the space-time metric, and ##H## is the universe’s scale factor. It’s mentioned that this relation is given in reference: https://arxiv.org/pdf/1002.0600.pdf But I can't find...
  4. M

    I Physical meaning of zero time metric

    I am reading Wald's General Relativity and just did problem 2.8(b). The result I get is ##\omega^2(x'^2+y'^2)-1## as the coefficient for ##dt^2##, and I am wondering about the physical significance of when ##x'^2+y'^2=\frac{1}{\omega^2}##, what would this mean? Mads
  5. Nitacii

    Integrate source terms for test EM field in Kerr spacetime

    Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes. We need to find the integral where with $$ J_m =(\sqrt{2}(r−ia\cos⁡θ))^{−1} i(r^2+a^2)\sin⁡(θ)j, $$ $$ J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...
  6. Steve Rogers

    I Quasi-local mass as a measure of the gravitational energy?

    I'm self-studying the mathematical aspects of quasi-local mass, or quasi-local energy (e.g. Hawking energy), and a fundamental question has been lingering in my mind for a long time: why does quasi-local mass provide us with a measure of the gravitational energy? In general relativity...
  7. vinicius_linhares

    A Newmann-Penrose Spin coefficients for Schwarschild metric

    I need to use the N-P formalism to apply in my work so I'm trying first to apply in a simple case to understand better. So in this article ( https://arxiv.org/abs/1809.02764 ) which I'm using, they present a null tetrad for the Schwarszchild metric in pg.14 (with accordance with the...
  8. namelessuser

    I Quantum Mechanics vs Einstein: Light Btwn Black Holes, Double Slit Experiment

    Quantum mechanics vs Einsteins theory of relativity: How does light move between two black holes if we create a double slit experiment in front of the light? Do the light waves distribute themselves equally on the screen or does gravity distort light waves at the edges? So just imagine doing...
  9. sarriiss

    A Preserving Covariant Derivatives of Null Vectors Under Variation

    Having two null vectors with $$n^{a} l_{a}=-1, \\ g_{ab}=-(l_{a}n_{b}+n_{a}l_{b}),\\ n^{a}\nabla_{a}n^{b}=0$$ gives $$\nabla_{a}n_{b}=\kappa n_{a}n_{b},\\ \nabla_{a}n^{a}=0,\\ \nabla_{a}l_{b}=-\kappa n_{a}l_{b},\\ \nabla_{a}l^{a}=\kappa$$. How to show that under the variation of the null...
  10. E

    General relativity - Using Ricc and Weyl tensor to find the area

    I have the following question to solve:Use the metric:$$ds^2 = -dt^2 +dx^2 +2a^2(t)dxdy + dy^2 +dz^2$$ Test bodies are arranged in a circle on the metric at rest at ##t=0##. The circle define as $$x^2 +y^2 \leq R^2$$ The bodies start to move on geodesic when we have $$a(0)=0$$ a. we have to...
  11. E

    A Solving Geodesics with Metric $$ds^2$$

    I have the following question to solve:Use the metric: $$ds^2 = -dt^2 +dx^2 +2a^2(t)dxdy + dy^2 +dz^2$$ Test bodies are arranged in a circle on the metric at rest at $$t=0$$. The circle define as $$x^2 +y^2 \leq R^2$$ The bodies start to move on geodesic when we have $$a(0)=0$$ a. we have to...
  12. H

    I Dark Energy Strength in Great Voids of Galaxies

    Assuming dark energy is fairly, uniformly distributed through out the cosmos, how strong is it, or how much energy is associate with it, out in the deepest, emptiest voids in space? I'm specificlaly refering to the great voids in between the great walls of galaxy clusters. I'm making the...
  13. L

    B If gravity was a force wouldn't going back in time cause us to float?

    This might sound as a dumb and silly question but if you think about it, it makes sense. If we wrongly assume that gravity is a force just like any other, and given the fact that time is closely related to gravity and that gravitational time dilation is a thing, wouldn't reverse time travel...
  14. S

    I Explore Spacetimes, Metrics & Symmetries in Relativity Theory

    I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970) In the paper, the authors describe "spacetimes without symmetries". When I mentioned that, one of my friends said that no spacetime predicted or included in the theory of relativity...
  15. T

    Why was my post deleted on PF?

    I'm not aware of the mathcode here, so forgive me for not posting my work straight away. I simply need to ascertain what code first displays equations. $a$ a a
  16. L

    A Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor

    Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units? Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR? If so, What...
  17. P

    A Popular Pseudoscience Video on General Relativity: Analysis & Criticism

    Here is the video: [link deleted by moderators] His basic idea is to take the spacetime interval and add a 5th term for the 5th dimension he is describing so it looks like: $$\Delta S^2 = c^2\Delta t^2 + c^2\Delta w^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 $$ where w is the difference in time...
  18. N

    I Orbital Precession Calculation: Unit Explained

    Hi, I've just calculated the orbital precession for the earth using the sigma formula of general relativity. $$ \sigma=\frac{24 \pi^{3} R^{2}}{T^{2} c^{2}\left(1-e^{2}\right)}=\frac{24\pi^3×1.5×10^{11}}{3×10^7×3×10^8(1-0.0034^2)}=0.012 $$ What is the unit of the result? Degrees per century or...
  19. B

    I Observing a Collapsing Shell: Time Dilation Explained

    What does and observer inside of a collapsing shell observe? Lets say we have a shell of matter collapsing to a black hole. What would observers near the center see? How would the rest of the universe appear when, The shell is approaching the Schwarzschild radius? After the shell passes the...
  20. Safinaz

    A The scale of an extra dimension

    Any help to understand how the authors of this paper Fine Tuning Problem of the Cosmological Constant in a Generalized Randall-Sundrum Model calculted this size of the extra dimension Equ. (3.8) from the scale factor defined by Equ. (3.3) ? Specifically, this paragraph after Equ. (3.8) -...
  21. U

    A The force from the energy gradient

    From this post-gradient energy in classical field theory, one identifies the term ##E\equiv\frac{1}{2}\left(\partial_x\phi\right)^2## as the gradient energy which can be interpreted as elastic potential energy. Can one then say that $$F\equiv -\frac{\partial...
  22. Tertius

    I Co-Moving Coordinates & Lapse Function N(t) in ADM Decomposition

    In the ADM decomposition, like in the construction of the FRW metric, the coordinates are defined to be co-moving, so we know $$d\tau = dt$$ (i.e. the lapse function is normalized away) Starting from a five-dimensional embedded hyperboloid (as in carroll pg. 324) ## -u^2 + x^2 + y^2 + z^2 + w^2...
  23. Safinaz

    I The Units of the Cosmological Constant: eV^2

    In natural units, it’s known that the unit of the cosmological constant is ##eV^2##. I don‘t get why in this paper : https://arxiv.org/pdf/2201.09016.pdf page (1), it says the value of ##\Lambda \sim meV^4##, this means ##\Lambda \sim (10^6 ~ eV)^4 \sim 10^{24} eV^4 ##, shoud not the unit ##eV...
  24. Spockishere

    B Travel 7 Light Years at 50000km/s - How Long?

    let's say i would like to drop by one of my pals on a certain planet, 7ly away. I got to 42 years but it doesn't really sound correct.
  25. S

    Normal vector of an embedding surface

    I will only care about the ##t## and ##x## coordinates so that ##(t, z, x, x_i) \rightarrow (t,x)##. The normal vector is given by, ##n^\mu = g^{\mu\nu} \partial_\nu S ## How do I calculate ##n^\mu## in terms of ##U## given that the surface is written in terms of ##t## and ##x##? Also, after...
  26. M

    A Wald's Abstract Index Notation: Explaining T^{acde}_b

    In the second paragraph on page 25 of Wald's General Relativity he rewrites T^{acde}_b as g_{bf}g^{dh} g^{ej}T^{afc}_{hj} . Can anyone explain this? I am confused by the explantion given in the book. Especially puzzling is that the inverse of g seems to be applied twice, which I can't make sese...
  27. Lars Krogh-Stea

    B Energy Conservation w/ Charged Battery Time Travel

    Hi! I want to start with saying that I'm not an expert on these type of problems, but I will be gratefull for some calarifications. I've heard that there's nothing in psysics that says that time travel is impossible. I want to make a case with the time traveling battery. Could be any mass with...
  28. S

    A Does Spacetime Absorb Energy in General Relativity?

    Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...
  29. Tertius

    I Computing Volume in General Relativity: Use of Tensor & Friedmann Eqns

    When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...
  30. phyz2

    I Klein Gordon Invariance in General Relativity

    Hello! I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism. This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$ I don't see how ##g^{\mu\nu}\to...
  31. U

    Finding Event Horizon & Ergosphere: Derivations & Formulas

    Homework Statement:: See below. Relevant Equations:: See below. I am trying to calculate the event horizon and ergosphere of the Kerr metric. However, I could not seem to find a proper derivation or formula to calculate the event horizon and ergosphere. Could someone point me to the...
  32. S

    I Gravitational force equation derived from GR

    Hello everyone, I know that GR equations are complicated and beyond my scope. But does GR give a simple gravitational equation: Force (as we know it) as a function of distance? (without any complicated tensors). - If yes. What is the equation? Does it give us something similar to Newtons...
  33. S

    I Calculate Ricci Scalar & Cosm. Const of AdS-Schwarzschild Metric in d-Dimensions

    I know some basic GR and encountered the Schwarzschild metric as well as the Riemann tensor. It is known that for maximally symmetric spaces there is a corresponding Riemann tensor and thus Ricci scalar. Question. How do you calculate the Ricci scalar ##R## and cosmological constant ##\Lambda##...
  34. U

    How to prove ##V_{ai;j}=V_{aj;i}## in curved space using the given equation?

    Question ##1##. Consider the following identity \begin{equation} \epsilon^{ij}_{\phantom{ij}k}\epsilon_{i}^{\phantom{i}lm}=h^{jl}h^{m}_{\phantom{m}k}-h^{jm}h^{l}_{\phantom{l}k} \end{equation} which we know holds in flat space. Does this identity still hold in curved space? and if so, how...
  35. H

    A Time Dilation in Reissner-Nordström Metric: Even or Odd?

    In the Reissner–Nordström metric, the charge ##Q## of the central body enters only as its square ##Q^2##. The same is true for the Kerr-Schild form. This would seem to imply that all effects are even functions of ##Q##. For example, the gravitational time dilation is often written as $$\gamma =...
  36. U

    Help with variation of the 3-dimensional ##\sigma##-model action

    Consider the following action $$S=\int\mathrm{d}^3x\sqrt{h}\left[R^{(3)}-\frac{1}{4}\mathrm{Tr}\left(\chi^{-1}\chi_{,i}\chi^{-1}\chi^{,i}\right)\right]$$ where ##h## is the determinant of the 3-dimensional metric tensor ##h_{ij}## and ##R## is the Ricci scalar. I want to get the equations of...
  37. only1god

    I What if Einstein equivalence principle is proven wrong one day?

    What would be the consequences of such thing? How it will affect physics theories and the world?
  38. U

    Help with a calculation about gravitational waves

    An exact gravitational plane wave solution to Einstein's field equation has the line metric $$\mathrm{d}s^2=-2\mathrm{d}u\mathrm{d}v+a^2(u)\mathrm{d}^2x+b^2(u)\mathrm{d}^2y.$$ I have calculated the non-vanishing Christoffel symbols and Ricci curvature components and used the vacuum Einstein...
  39. R

    Relativity I want to learn special relativity. More details below

    I want to learn special relativity.I have read a tiny bit of 2nd edition of Spacetime Physics: Introduction to Special Relativity and am liking it. Is it a good book? I also want problems to solve. I tried Special Relativity: For the Enthusiastic Beginner but found it to difficult. Does anyone...
  40. Safinaz

    A How Randall-Sundrum model has solved the hierarchy problem?

    I'm trying to understand how the RS model solved the hierarchy problem from this mass relation $$ M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$ Equ. 16 in their paper: https://arxiv.org/abs/hep-ph/9905221 With k as large as the Planck scale, the exponential will be so small and...
  41. Safinaz

    A Deriving an action from a metric

    Hello! The paper I study is related to string theory and modified gravity theories topics. As they say in page 5 “The four-dimensional effective theory now follows by substituting Eq. (13) into the original action, Eq. (4)” I wonder how did they drive a 4- dimensional effective metric...
  42. U

    Help with Kaluza Klein Christoffel symbols

    If I want to calculate ##\tilde{\Gamma}^\lambda_{\mu 5}##, I will write \begin{align} \tilde{\Gamma}^\lambda_{\mu 5} & = \frac{1}{2} \tilde{g}^{\lambda X} \left(\partial_\mu \tilde{g}_{5 X} + \partial_5 \tilde{g}_{\mu X} - \partial_X \tilde{g}_{\mu 5}\right) \\ & =\frac{1}{2}...
  43. S

    Relativity Math of GR Exercises from Spacetime & Geometry by Sean Carroll

    I have been reading the book Spacetime and Geometry by Sean Carroll, especially Ch. 2 Manifolds and Ch. 3 Curvature. I'm just wondering are there any lecture notes or books with lots of practice problems (with solutions or at least answers the better) that is suitable for physicist? To give an...
  44. N

    I Position Vector in Curved Space Time: Explained

    It is said that: It is not possible to write a position vector in a curved space time. What is the reason? How can one describe a general vector in a curved space time? Can you please suggest a good textbook or an article which explains this aspect?
  45. U

    Help in understanding the derivation of Einstein equations

    There are two parts to my question. The first is concerns the variation of the Reimann tensor. I am trying to show $$\delta...
  46. S

    I If gravity is not a force, what is holding us down?

    OK. Gravity is not a force it is a contraction or curvature of space. I was free-falling and now I hit the ground. Why don't I float through the universe, or go upward instead of still trying to go downward. Because I hit the ground, and now there is no force(like gravity) and my free-falling...
  47. C

    Proving ##C## is constant in 4-dim ##R_{\mu\nu}=Cg_{\mu\nu}##

    This question wasn't particularly hard, so I assume metric compatibility and input Ricci tensor to the left side of Einstein's equation. $$R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=Cg_{\mu\nu}-\frac{1}{2} (4C)g_{\mu\nu}=-Cg_{\mu\nu}$$ Then apply covariant derivative on both side...
  48. U

    I Why is Scalar Massless Wave Equation Conformally Invariant?

    It can be shown mathematically that the scalar massless wave equation is conformally invariant. However, doing so is rather tedious and muted in terms of physical understanding. As such, is there a physically intuitive explanation as to why the scalar massless wave equation is conformally invariant?
  49. Ebi Rogha

    B Exploring Energy-Mass Equivalence: Converting Energy to Matter in Everyday Life?

    a) Can we convert energy to mass (matter) in every day life? b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?
  50. snypehype46

    I Computing Ricci Tensor Coefficients w/ Tetrad Formalism

    I'm reading "Differentiable manifolds: A Theoretical Physics Approach" by Castillo and on page 170 of the book a calculation of the Ricci tensor coefficients for a metric is illustrated. In the book the starting point for this method is the equation given by: $$d\theta^i = \Gamma^i_{[jk]}...