General relaivity Definition and 162 Threads

Homework Statement: The order of indices of the Christoffel symbol of the 1st kind seems to vary from source to source. Is there a preference, and if so why? Relevant Equations: Christoffel symbol of the 1st kind. The 1st definition of the Christoffel symbol of the 1st kind I came across was...

more specifically what does high energies mean in this context, does it actually mean a high amount of energy? I can intuitively understand why it breaks down at small scales where quantum effects take place. for example it is said that high speed collisions produce a lot of energy and general...

According to general relativity, mass and energy cause the curvature of spacetime. To have perfectly flat spacetime, there must be a completely empty vacuum state with no mass or energy. Does this mean that perfectly flat spacetime cannot exist if mass and energy are present? Let's assume that...

There is good enough experimental evidence for the existence of a Photon Sphere. Is there clear unequivocal experimental evidence for the existence of an Event Horizon ?

I have read that we can define covariant derivative for spinors using the spin connection. But I can't see its proof in any textbook. Can anyone point to a reference where it is proved that such a definition indeed transforms covariantly ?

I was reading this paper that puts forward the argument that Gravitational energy in GR is unnecessary and doesn't exist and that got me wondering if this is a fringe theory or what exactly is the mainstream view regarding gravitational energy in GR? Also does GR predict or need the existence...

from Sean Carroll's blog " “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields”. This is an explanation that I have seen mentioned somewhat frequently, my question is in the case of phantom dark energy...

I came across this statement "The covariant energy-momentum conservation lawis ∇𝜇𝑇𝜇𝜈=0. Be careful though: "convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved. To get actual conserved quantities you need a symmetry. In particular...

According to this Sean Carroll article, “https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ “ And other threads in here, depending on your definition of energy, dark energy does not violate conservation of energy, my questions is if this is true regardless of the type...

When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured r and φ in fuction of time attributing to these coordinates an Euclidean meaning, that is, assuming...

Varying ##\partial_\lambda\phi\,\partial^\lambda\phi## wrt the metric tensor ##g_{\mu\nu}## in two different ways gives me different results. Obviously I'm doing something wrong. Where am I going wrong? Method 1: \begin{equation} (\delta g_{\mu\nu})\,\partial^\mu\phi\,\partial^\nu\phi...

The existence of dark matter was initially proposed to address discrepancies between observed galaxy rotation curves and the expected behavior dictated by our current understanding of gravity. Typically, it's argued that stars at the edges of galaxies rotate faster than expected, leading to...

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...

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

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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) -...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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##...

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...

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 =...

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...

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

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...