Relativity

Hello, I am trying to understand the Einstein Field Equations, but the only problem is that I cannot figure out how the einstein tensor describes the curvature of spacetime. There seems to be no good references or nifty little pictures showing the components like the one shown below for the stress-energy tensor. I have seen one good thing that helps me understand some things, but it does not do much for explaining the components of the einstein tensor. (Pdf shown below) Pdf explaining the einstein field equations. Merry Christmas.

So, I have been trying to understand the Einstein field equations to better understand general relativity. I figured out the stress-energy tensor but the einstein tensor puzzles me. There are no fun little diagrams showing me what the different parts of the tensor represent. Another thing is I cannot find the value of the cosmological constant. Can anybody help me?

There have been several threads recently where some dubious statements about the distinction between constant and invariant have been made. I am therefore posting this thread to examine this issue by discussion. I am kicking off with a question An observer is watching the rear end of a train which is receeding a high speed , but not accelerating. Hanging on the back of the train by a long coil spring is a lamp which is oscillating up and down. What is the relativistic effect on the spring constant, ie what is the difference, if any, between the spring constant according to the train guard and the observer ?

The concept of relativity was quite the revolution for physics back in the day. But is it really something entirely new without any classical analoge? What i am struggling with is that Lorentz invariance is not particularly special to light/Maxwell, but is a rather a basic property of any linear wave equations. Let's consider a simple old classical model of an ideal uniformly distributed gas at rest in the lab frame and let's have a look at the acoustic wave equations we have for that case. Within this approximation the equation is a linear 2nd order PDE. Let's keep our minimal physical model limited to acoustics alone for now. Formally looking at the equation…

A thought experiment Let's say that the Earth is 14 billion years old today and that 2 photons from a light source 14 billion light years from us sent 2 photons towards the Earth 14 billion years ago. (4.41504e17seconds) Both photons followed exactly the same path. Allice received both of these photons today. – She reflected the one photons to Bob. Alice lives on top of a skyscraper which is 1000 meters high. Bob lives on the first floor. Bob's clock loses 1e-15 seconds every second compared to Alice's clock. Alice agrees with the theory of relativity that the speed of light is 3e8 m/s and she also agrees that the distance that the photo…

What if the speed of causality is the way it is because space is quantizable. Space is like a patchwork of chessboard. Light is the queen and she moves unimpeded through one chess board at a time. Can physicists chime in on this?

Maybe someone can quickly clear up a problem I have with the possibility that gravity is mediated by an elementary particle, the Graviton, that is massless and propagates at the speed of light. As I understand it, it's considered hypothetical at the moment, meaning it's considered as one possibility. I can't see how it's possible. My reasoning is pretty simplistic. Take a black hole at the centre of a galaxy. It's gravity clearly affects the stars and materials that are orbiting it. We can calculate the mass of the black hole by how it's gravity affects everything else. But how can a boson escape a black hole, and affect the surrounding stars? As I understand it, n…

This is the bit what i am currently struggling with in physics. Relativity is a concept deeply rooted in the nature of geometry itself because we must always account that space and time are never measured absolutely but in units - and those are always relative to some local and frame dependent reference. For the SI second this is a specific Caesium transition frequency at the observers frame and location. When something is said to be constant it merely means it changes exactly the same as the reference in units of which it is measured. Because all measurement is relative, it is impossible/meaningless to determine if something changes in an absolute sense, hence it is cruc…

There are two ways to visualize tensors as coordinate independent, "geometric" objects (that I know of). One way is what I'd call, "dynamic": tensor is a linear function that takes in vectors and 1-forms and puts out numbers. "A tensor is a machine", Gravitation by Misner, Thorne, Wheeler. Another way is what I'd call, "static": tensor is an equivalence class of sets of components that transform into each other with a coordinate transformation. "A tensor is something that transforms like a tensor", Einstein Gravity in a Nutshell by Zee. To me, the "static" definition is easier to visualize and to use. What is your preference, if any?

Imagine a uniformly cooling white dwarf of uniform temperature. A cosmic ray is flying through it. Will the ray observe it cooling faster, slower, or with the same rate as a rate observed by an external observer which is at rest relative to the dwarf?

I have a question from the following statement in this article that I can't understand. How can our speed traveling in time be the speed of light? I realise our measure of time, such as seconds, minutes, is purely artificial, so how is our movement through time measured? For anything travelling at the speed of light, you would need infinite energy to accelerate the object to light speed. I don't see an infinite energy propelling my desk or me to light speed. What's going on here? "We know through the physics of Einstein's special theory of relativity that you can trade motion in space for motion in time. If you're standing perfectly still, you're moving t…

Historically, after Newtonian formulation of mechanics, alternative formulations were developed, i.e., Lagrangian and Hamiltonian. In QM, after wave mechanics, matrix mechanics was developed. In QFT, there are S-matrix and path integral formulations. Which alternative formulations of GR are known today? PS. I think, in SR the parallel examples are Einstein and Minkowski formulations.

Variations of this phrase in description of black holes are endlessly repeated: (Black hole - Wikipedia) (Black hole | Definition, Formation, Types, Pictures, & Facts | Britannica) (What Is a Black Hole? | NASA) Etc. My question is, why they use the phrase "even light" as some kind of extreme, as if light is expected to escape from everything and everywhere? What is it about light that if IT cannot escape then NOTHING can? (I am not asking about the physics of it, but about the use of this phrase in the layman descriptions.)

I'll try to keep this concise: Elementary particles have very different relative velocities, with quarks and gluons moving at or near C, and electrons being much slower (eg sometimes ~0.7% C). With this in mind, an atom or larger mass is typically considered to be in its own reference frame, despite its components being at very different relative velocities. Why is this? For example, a human does not perceive any time dilation or length contraction between the particles of their own body. Is this because the experience of a larger mass is more or less the average of its component particles? Would it be true that if a quark or electron could perceive the world, t…

An object is going to travel 1,207 light years. It accelerates at a steady rate until the halfway point, where it reaches its maximum velocity of 18.75% of light speed, before starting to slow down at the same rate at which it accelerated. Once the object reaches its destination, how much time will have passed for the object and how much time will have passed for a stationary observer? Thank you.

What are the least possible requirements of such conditions?

Suppose we take two points on a Minkowski spacetime diagram and "connect" them with different pairs of physical events. So one if the points is the origin and the other is any arbitrary point The first pair of physical events is a massless object fired,* from the origin through a vacuum and leaving a physical mark ** at the site of the second point on the Minkowski map. The second pair of physical events is a spaceship travelling at c/2 and arriving at the site of the mark made by the massless object.(at a different time and spatial distance) The third pair of events is just a bullet following a similar trajectory. So there…

Were there any processes occurring in the Inflation epoque ? If there were ,was there a maximum speed limit different to c? I am guessing that there were no processes we know of and ,if there were the speed limit would have been c. btw ,did the Inflationary period precede the BB or (as I think ) come after it?

youtube link deleted

Two V shaped bodies are moving towards one another. One is moving up and the other is moving down. The two V’s are in relative constant linear motion. When two bodies are in relative constant linear motion, the one body could be at rest while the other body is in motion, or the other body could be at rest while the one body is in motion. The moving body length contracts. The moving body length contracts in its direction of motion. In the one inertial frame of reference the other moving V length contracts and becomes obtuse while the one resting V remains a right angle. And in the other inertial frame of reference the one moving V length contrac…

How come? Let's say events A and B are spacelike separated. Then there are observers moving with a normal, i.e., < c, speed for whom event B occurs before event A. If A is sending a signal and B is its receiving, then for these observers, the signal is received before it is sent. Isn't it a causal paradox?

We have an object approaching the surface of the Earth (no atmosphere) and instead of crashing into the surface it enters a hole/tunnel in the "gruyere" that is by luck or design the exact spiral shape that allows the object to spiral into the centre of the Earth without physical contact. The next step is to "melt all the cheese " so that all the mass is together in a very small region of the centre of the "Earth" Another object (same size,same mass,same shape etc etc) approaches this second "Earth" at the same angle and speed of approach. Do the two objects follow more or less identical trajectories in GR? I think ,but could be wrong that th…

Does the Earth generate gravitational waves as a result of all the em attractions/repulsions within it? Are the atoms in constant accelerated motion and does that cause gravitational waves in the same way as em radiation is caused? I have been thinking about what happens when 2 objects come close to each other and their motion is changed by ,eg electric repulsion. It seemed to me that there might also(in addition to the em wave) be a gravitational wave as a result of the acceleration.

Suppose we have a trampoline moving through the vacuum of space At any snapshot in time (so not 4d) the trampoline will look to us in it's normal flat shape Now let us say that a region of the trampoline is subject to an acceleration (for simplicity perpendicular to the surface) so that that region is stretched into the shape all trampoline analogists are familiar with except that there is no heavy metal object producing the "well" but rather the shape is produced "internally " by the local acceleration.** So an observer at a remove from the "flying trampoline" will see a flat surface with a protrusion a bit reminiscent of Sigourne…

Suppose we have two massive spherical objects and they are moving wrt each other. They pass each other at one point . Do their respective momentums (in addition to their mass) combine to curve spacetime at that point? Again (a different scenario) ,if the same two massive objects follow the same trajectory as each other do the pair also curve spacetime ,but differently from the earlier scenario? Ps Am I barking up the wrong tree to try and separate curvature effects due to mass from curvature effects due to momentum and are they perhaps two sides of the same coin?