General relativity Definition and 999 Threads

CMB photons can be affected by the expansion of the universe through the linear integrated Sachs-Wolfe effect (ISW) [1] and the non-linear ISW effect or also called Rees-Sciama effect [1]. In particular, according to the ISW effect, the photons crossing superclusters would leave them having a...

I cannot get the following out of my head. Suppose this situation. Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon...

After Taylor expansion and using equations (2), I have no problem getting to equation (1). Now obviously I have to somehow use (3.71) ,which I do know how, to derive to express the second order derivative. On the internet I found equation (3), and I have tried to understand where this comes from...

Hi, In Einstein's famous elevator experiment, someone in the elevator cannot tell if the acceleration they experience is from the gravity of a nearby large mass, or from their own change of velocity under the influence of some external force. But if there is an external force accelerating...

I’m trying to understand the Hellings and Downs curve that is being used to argue for the existence of a gravitational wave background ([NANOGrav article][1]). How can it be that the angle between two pulsars is the only variable that determines if the gravitational waves will interfere...

Is energy conserved in general relativity? I have read most of the posts here that address this. But it isn't clear to me, what most people say is that energy is conserved locally but it can't be defined globally, some people say this means that energy is not conserved in GE while others argue...

Other ways of wording this finding about the extended SC (Schwarzschild) spacetime: - in the local frame of a free faller, radial distance is given r coordinate difference - in either Fermi-normal coordinates, or Riemann-Normal coordinates built from a free faller at an event, coordinate...

Hi all, I've been going over some special relativity as it's a topic I never really studied during my younger years and wanted to get to grips with it, especially since it's such a fundamental part of our understanding of the cosmos. I was reading about Einsteins train lightning thought...

Does it exist an invariant way to define acceleration in Newton physics like the proper acceleration in GR ? In Newton physics if an accelerometer attached to an object reads 0 it does not mean it is actually not accelerating (since gravity is a force). To define inertial motion the concept of...

In the Lamda-CDM model of cosmology, dark-energy is explained by a Lamda like curvature of space-time. In this description, space-time is curved in such a way as to cause a gentle outward repulsive force on the large scale, expanding all of the universe over time. This is one cause of the...

Thought experiment: What will happen if you place a mirror behind the event horizon and turn on the light in its direction?

Hi there, have a wonderful next year! I'm here because I have a doubt. I was trying to generalize the Einstein Field Equation for Von Neumann W* Algebra, which is related with non-integer, non always positive degrees of freedom. In particular, with the sum of positive and negative fractal...

A few yesrs ago now I read a First Course in String Theory. In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR. I didnt think anything of it at the time (pun intended), but I recently saw a...

For (a) and (b), since the geodesic is not affinely parametrised, we have that ##t^a\nabla_a t^b = f(\lambda) t^b##, for some function f. As a results, for (a) I get that ##t^a \nabla_a \epsilon = 2 f(\lambda) \epsilon##. And for (b) I get that ##t^a \nabla_a p = f(\lambda) p##. (I can write...

I'm a mediocre physics student (at best) at an Ivy League institution, and I'm passionate about general relativity. My dream is simply to do research in the field, even though I will never be a superstar or pioneer. Finally, I'm planning to complete a Master's in astrophysics or physics...

Hi, as test of GR I'm aware of there is the "anomalous" precession of the perihelion of Mercury. My question is: in which coordinate system are the previsions of GR verified concerning the above ? Thanks.

Hi, on Wald's book on GR there is a claim at pag. 43 about the construction of synchronous reference frame (i.e. Gaussian coordinate chart) in a finite region of any spacetime. In particular he says: $$n^b\nabla_b (n_aX^a)=n_aX^b\nabla_b \, n^a$$Then he claims from Leibnitz rule the above equals...

Let me preface this by saying that I do not claim to dismantle relativity. That said, in reading the Feynman I came across an ideal experiment that is not entirely clear to me. The context is the usual two spacecraft moving at relatively constant speed. With the reasoning I give below Feynman...

I have always had certain difficulties in correctly understanding the theory of special relativity; I often apply it to certain situations and they fall apart... Imagine there is a rectangular object placed with its long sides parallel to the ground and its short sides perpendicular to it...

So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this. The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...

I have a question about the concept of length contraction. The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t. The green axes represent the coordinate system of a moving...

Although there are tons of experimental tests/confirmations for General Relativity, I noticed that most of them are made on/from Earth, or very close to Earth, so in this thread I'll suggest 2 extensions of past experiments: 1. GSM GPS satellite (preferably with an unmodified atomic clock) far...

Hello, I'm studying General Relativity using Ray D'Inverno's book. [Moderator's note: link deleted due to possible copyright issues.] . I don't understand what the author writes in paragraph 14.3 ("Static solutions") where he demonstrates that for a static spacetime there are no cross-terms...

Section 5 (pg. 29) of the Michel Janssen's paper EINSTEIN’S QUEST FOR GENERAL RELATIVITY, 1907–1920(*) says: 1. From the above I understand that the application of general relativity to an infinite universe was considered problematic. 2. On the other hand, I understand that it is currently...

A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I...

A technical subject, well above my level it seems (I'm still learning about quantum physics and special relativity), but one about which I absolutely must get some clear ideas as soon as possible. From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry...

I'll set out by saying that I have no real formal training in physics or maths. However, I have been keen to try to understand what exactly convinced Einstein that spacetime must be curved. As I understand it, the bending of star light was already explained by Newtonian physics, although of...

i have just started on relativity, so be simple. you are going to travel 1 lightyear at half the speed of light. therefore, it would take 2 years to travel 1 lightyear. on Earth, you would see me going half the speed of light, so it should take two years as well? i calculated gamma as being...

I am looking at some of the threads on the twin paradox, and getting even more confused. I have been trying to run through the details of what each twin is seeing, and was wondering if I could get some help. I am just trying to imagine how each twin is “seeing” the other twin at each step as the...

I very often see in movies and works of fiction that scientists explain that with a black hole you can travel in time and how the characters use black holes to travel in time, more precisely to the past Do scientists really believe that time travel through black holes is likely? If so, why?

(I) Using the relevant equation I find this to be ## \frac{e^{x}}{2} ##. (II) Using the relation for the Ricci tensor, I find that the only non-zero components are...

The following is more of an interesting example and observation than a question that I am presenting for public comment. It's somewhat related to a recently thread, which was closed for moderation, but I think it's different enough not to fall under the ban of reposting threads that have been...

I encountered a problem in reading Phys.Lett.B Vol.755, 367-370 (2016). I cannot derive Eq.(7), the following snapshot is the paper and my oen derivation, I cannot repeat Eq.(7) in the paper. ##g^{\mu\nu}## is diagonal metric tensor and##g^{\mu\mu}## is the function of ##\mu## only...

Studying and tinkering with some solutions, I've come to some realizations and questions regarding the regularization of coordinate singularities, so I'd like to see if my conclusions are good, and I guess I have some questions as well. There are two questions/conclusions, but since they...

Hello everyone, I am a couple of months away of starting my PhD in Numerical Relativity and I am seeking recommendations for references to get a batter understanding on the mathematical foundations of GR and topics of Numerical Relativity. So far I have had an undergraduate introductory course...

GR has very limited situations in which a total mass-energy can be defined. The Komar mass, for example, requires the presence of a timelike killing vector field and an asymptotically flat spacetime. Basically, if the metric change with time or it's spacelike curvature does not flatten out...

I bought a copy of Adler's new book on relativity. Is there a misprint on page 16 regarding the Lorentz metric = diag (-1,-1,-1,-1) or am I missing something? The text itself after the equation suggests it is the same metric as on the earlier page so that index placement, two lower indices vs...

What is the metric for a bag-of-gold spacetime?

Black holes are everywhere in astrophysics. There are numerous discussion about how black holes look like, what happens to gas falling into black holes, how light bends around black holes, whether there is loss of information when mass or energy falls in, etc. There is thought to be a black hole...

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...

Are there any metrics for intra-universe wormholes?

I found this interesting discussion here in Physics Forums (https://www.physicsforums.com/threads/are-all-symmetries-in-physics-just-approximations.1005038/) where the topic of all symmetries being approximate is discussed Is there any model (for instance, some type of spacetime metric or...

In the book general relativity by Hobson the gravitational wave of a binary merger is computed in the frame of the binary merger as well as the TT-gauge. I considered what components of the Riemann tensor along the x-axis in both gauges. The equation for the metric in the source and TT-gauge are...

I am studying metrics that exhibit CTCs. I was looking at a few different metrics... Tipler's solution Godel metric Kerr metric For starters to compare them, I am trying to convert said metrics into cylindrical coordinates. Thanks in advance for any help😃

Hi, I am looking to study general relativity at my own steam (currently finishing 1st year physics at Warwick) during the summer. What textbook(s) would you recommend? I've heard good things about A. Zee's 'Einstein Gravity in a Nutshell'- is that worth it, and would it be suitable for someone...

Is it generally the case even with light like paths that ##\dot t>0##?

I know nothing about physics, to be clear. My friend was saying due to general relativity, the faster you move through space, the slower you move through time. Objects with a heavy mass (like a blackhole) can distort the fabric of space time and being near its gravitational pull means that you...

I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned. There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...

A minimally coupled scalar field can model a cosmological fluid model where And where the equation of state can be the standard ## \omega = \frac {p} {\rho}## I can see how this does a fine job modeling matter, because as the scale factor increases, the density will go as ##\frac {1} {a^3}##...

Let's say we have some observer in some curved spacetime, and we have another observer moving relative to them with some velocity ##v## that is a significant fraction of ##c##. How would coordinates in this curved spacetime change between the two reference frames? For example, imagine a...