General Definition and 1000 Threads

I am having a class of general relativity. It seems that the professor will follow an approach which consist of achieve the action, and variate it to get the equations of motion (indeed, that's how we already got the geodesic equation, the dynamics of a particle in electromagnetism, the equation...

Why in general relativity do we need the physics of perfect fluids?

Spacetime is a differential manifold and at each point is attached a Minkowski spacetime. There the laws of physics are the usual ones without gravity. Gravity is the curvature of spacetime. To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is...

Hello, this is my first thread. Robert Wald, in General Relativity, equation (4.2.8) says : E = – pa va where E is the energy of a particle, pa the energy-momentum 4-vector and va the 4-velocity of the particle. How can I see this is compatible with the common energy-momentum-relation E2 – p2 =...

In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...

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...

\[ y'=-y+e^{(-2)t} \]

What mathematical topics do I need to know to start studying general relativity? From which textbooks can I learn them? I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and...

Hi, In general relativity, gravitation is not anymore a Force but a deformation of space time. I would like to know what's becomes the 3 law of Newton for gravity that action equal reaction ? When a apple fall on the earth, does "the force" is exactly the same as the one applied on Earth ...

The general formula for the nth term of the Fibonacci sequence where an=an-1+an-2 can determined by matrix diagonalizations Is there a way to determine the formula of any recursive sequence say an=a1+a2+...an-1

Following are not strictly physics questions. But cool questions to discuss. We need to add dark energy to our cosmological model if we strictly follow GR. This lead to some beliefs that GR is an effective theory. (1)Do you believe that GR is the fundamental theory? If GR is an effective...

The general eqn of parabola is ##(x-h)^2=-4a(y-k)##. This is the parabola whose vertex doesn't lie on origin and axis is parallel to y axis. It opens downwards. Vertex is (h,k). What will be the focus of this parabola and what is ##a## in general form? In the diagram a<0 which is...

I'd like a good set of notes or a textbook recommendation on how to approach vector differential equations. I'm looking for something that isn't specific to one type of application like E&M, fluid dynamics, etc., but draws heavily from those and other fields for examples. I'd strongly prefer a...

Hi everybody. I recently started to learn GR from a very begginer level. I would like to share with you some lines of discussion, to understand your approach to some specific topics which for me are key to better understand the whole story. If a put an accelerometer on the floor it reads 9.8...

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...

In both Wald and Carroll, a type (k,l) tensor has k dual vectors and l vectors, yet a (1,0) tensor is a vector and a (0,1) tensor is a dual vector. I must be missing something simple. Please explain.

P=mv *momentum equals mass X velocity. Light particles or "photons" are said to be "massless". And yet they have momentum. How is that possible? (p.s. I used to know the answer)

I recently noticed that "General Relativity: The Essentials" by Carlo Rovelli has been published. Based on the description, table of contents, and the Amazon reviews, it seems to me that it might be a spiritual successor to Dirac's "General Theory of Relativity." Is that an accurate assessment...

Hi all, What I notice is that there's a significant difference in style between the GR texts and the other textbooks. In particular, GR texts very much try hard to read like a math textbooks, emphasizing theorems and abstract definitions, which I'm not sure are practically useful (though...

I want to learn General Relativity so I am looking for a good beginners book with low amounts of math and clear explanations. Any suggestions?

hello it is well known that gravitationl force is actually a fictitious force generally speaking,are fictitious forces still necessary in general relativity ? the fictitious forces which we experience on a bus or on a car can also be understood as due to the spacetime distortion ?

I found an interesting list of "must-read" papers in the field of general relativity compiled by Emanuele Berti: https://pages.jh.edu/eberti2/posts/must-read-paper-list/ Are there any notable exceptions, or other "classic" papers that - in your view - every relativist ought to have read?

Which is the mathematical procedure to obtain ##\delta r = \frac{GM}{3c^2}## from ##\nabla^2 V = R_{00} = 4\pi G\rho## where ##\nabla^2 V## is volume contraction of a spherical mass of density ##\rho## and ##R_{00}## is the 00 component of Ricci tensor ##R_{ij}##?

Hello everyone - The gravitational force near the edge of the galaxy at point A (see attached image) can be calculated by assuming that all the galactic mass is located in the center of the galaxy. - In order to calculate the gravitational force in the middle of the galaxy (point B) we take...

Summary:: Where can I take a general physics course 101 at online? Looking for a general physics course that starts with algebra that I can do online.

We know $$ K(x,t) = \frac{1}{\sqrt{4\pi t}}\exp(-\frac{x^2}{4t}) $$ is a solution to the heat equation: $$ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} $$ I would like to ask how to prove: $$ u(x,t) = \int_{-\infty}^{\infty} K(x-y,t)f(y)dy $$ is also the solution to...

[a] Find the general solution of $y^\prime + 3y=t+e^{-2x}\quad \dfrac{dy}{dx}+f(x)y=g(x)$ \$\begin{array}{lll} \textsf{Similarly} & \dfrac{dy}{dx}+Py=Q\\ \textsf{hence} & \mu(x)=\exp\left(\int f(x)\,dx\right)\\ \textsf{then} & \mu^\prime(x)=\exp\left(\int...

Find the general solution of $y'−2y=t^{2}e^{2t}$ and use it to determine how solutions behave as $t \to \infty$ ok presume the first thing to do is to find $u{x}$ $\exp{\displaystyle\int{2} y}=e^{-2} or \dfrac{1}{e^2}$

Assumptions 1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way. 2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...

What exactly is the difference in the way an general physics book (Halliday and Resnick, Young and Freedman) covers topics like mechanics, EM, and thermodynamics, compared to respective books like Kleppner and Kolenkow, Griffiths, and Schroeder, other than the amount of material covered for each...

I could solve a similar (rather, a specific case of the above) where the current entered through a corner and left from the corner opposite to it along the body diagonal of the cube. For this specific case, I was able to easily exploit symmetry to deduce the answer (0). However, I cannot think...

Let's say a small object orbits around massive object at some distance in perfectly circular orbit. In Newtonian physics the force acted upon orbiting body is: Force = m1 * orbital_speed^2 / distance = G * (m1*m2) / r^2 for an object of 1kg orbiting a body of 2*30^kg at the distance of 1.521 *...

We study metrics, in them, we take time as a coordinate. I mean to say that if time is a coordinate then in normal mathematical language, we can have negative coordinate values as well. This confuses me a lot as I want to see and understand the concept from the true physicist's perspective...

In Sydney Coleman Lectures on Quantum field Theory (p48), he finds : $$D\mathcal{L} = e^{\mu} \partial _{\mu} \mathcal{L}$$ My calulation, with ##\phi## my field and the variation of the field under space time tranlation ##D\phi = e^{\mu} \frac{\partial \phi}{\partial x^{\mu}}## ...

It's the second question. Limiting equilibrium by a force of 5N means even friction is acting in the same direction. I don't understand how to calculate. Pls help

Iam not able to get the ans for q(a) which is 6.5 m/s I don't understand how to calculate (b)

Hello everyone! I have two questions which had bothered me for quite some time. I am sorry if they are rather trivial. The first is about the general solution of the hydrogen atom schrödinger-equation: We learned in our quantum mechanics class that the general solution of every quantum system...

Hey, I have some trouble deciding between 4 courses at the University of Sheffield (I am applying late, but there are still vacancies on all of these courses and as far as I know I can get a place at anyone of them). All of these courses are Foundation Year (FY) courses (they include an...

I calculated (a) I don't know how to calculate (b)

A woman on a sledge moves in a straight line across horizontal ice. Her initial velocity is 2 m/s. Throughout the journey her acceleration is given by a= -0.01t m/s^2, where t is the time from the start in seconds. Find the distance that she travels before coming to rest. Iam getting the ans...

A goods train starts from rest at point A and moves along a straight track. The train moves with acceleration a m/s^2 at time t s, given by a=0.1t^2(6-t) for 0<t<6. It then moves at constant velocity for 6<t<156 before decelerating uniformly to stop at point B at t=165. Calculate the distance...

Does $$\partial^\beta(g_{\alpha\beta}A_\mu A^\mu)$$ mean the same as $$\frac {\partial (g_{\alpha\beta}A_\mu A^\mu)}{\partial A^\beta} ?$$ If not could someone explain the differences?

A particle starts at the origin and moves along the X- axis. The acceleration of the particle in the direction of the positive x-axis is a= 6t-c for some constant c. The particle is initially stationary and it is stationary again when it is at the point with x coordinate = -4. Find the value of...

In q(c) I calculated the distance using t= 4.25 S . I get S=-3.23×10^-3 I added 5.78m to this which is the distance between A and B, I get 5.78m. Is this the correct method to prove that the bird returns to A. Pls help

I don't understand q(e) . Am I not supposed to calculate the distance between the interval 0 to 2? The textbook ans only shows the interval between 0 and 22. Should I calculate the distance taming only the second equation of velocity?

A particle moves in a straight line. The velocity of the particle, v m/s, at time t s is given by v= -t^3+9t m/s for 0<t<5 a) Find the displacement of the particle from its original position, when t=5s I got the ans for this by integration and limits 5 and 0 =- 43.8 b) work out the distance...

I calculated q(a)=1s q(b)=7cm I don't understand q(c)

S for 0 to 2s = 20m From 2s to 2.5s, I integrated v with limits 2.5 and 2 and got s=8.875m So total distance would be 28.9m but the textbook ans is 29.9m. Iam not able to get 29.9 m

I don't understand how to find the distance that robot travels in 10s.