# What is General relativity: Definition and 999 Discussions

General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay and singularities/black holes. The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. Unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity; and how gravity can be unified with the three non-gravitational forces—strong, weak, and electromagnetic forces.
Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
Widely acknowledged as a theory of extraordinary beauty, general relativity has often been described as the most beautiful of all existing physical theories.

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1. ### I Can there be structures made from neutrinos with angular momentum?

Would it be possible to eventually have structures made from neutrinos somewhere in the universe, as it is indicated in this question (https://physics.stackexchange.com/questions/80390/are-neutrino-stars-theoretically-possible), like halos of neutrino gas surrounding the center of galaxies...

3. ### Programs Should I do a math or an astronomy double major for general relativity?

Hi! I'm going into college during the fall, (Stony Brook University in the US) and I want to research general relativity in the future. I can choose to do an astronomy or math double major alongside my physics degree, and I want to know which degree will best prepare me for a graduate program in GR
4. ### I Handshake paradox involving the Starship Enterprise

suppose the enterprise departs from planet earth on a mission the the other side of the milky way at 90% of the speed of light; since time is dilated while cpt Kirk drinks coffe on planet earth some time passes (let's say 1h). Approaching mars captain Kirk orders dt. Spock to land on Mars with...
5. ### I Meaning of the distance between galactic objects in GR

Hi, I was thinking about the claim that for instance Sagittarius A* (Sgr A*) black hole is a at 26996±29 light years from the Earth from a GR point of view. Assuming a FLRW model for the Universe, maybe the above meaning is that at a given cosmological time ##t## (the "present" time) the proper...
6. ### I Can there be slowly-falling accretion disks in black holes?

Black holes accrete mass around them and it falls gradually up to the even horizon where mass is trapped by the black hole forever. However, the rate of mass falling from the accretion disk to the black hole ranges from being very fast to very long-lived, depending on various conditions...
7. ### I Israel Junction Conditions: Finding Continuous Metric Across Shell

A Relativist's Toolkit (2004) lists the Israel junction conditions as: ##1. [h_{ab}]## ##2. S_{ab}=[K_{ab}]-[K]h_{ab}## Where ##S_{ab}## is the stress-energy tensor of the shell only, and ##[K_{ab}]## and ##[K]## are ##K_{ab}^--K_{ab}^+## and ##K^--K^+## respectively. My understanding is that...
8. ### I Does Kerr's argument against singularities apply to all black holes?

Roy Kerr has recently written a preprint (https://arxiv.org/abs/2312.00841) in which he strongly argues against the possible existence of singularities inside Black Holes. I've read that his arguments are really powerful and that he is most likely right. But, does it mean that Kerr has...
9. ### A Coupling torsion to electromagnetism and torsion tensor decomposition

When extending general relativity to include electromagnetism, several authors (e.g. Novello, Sabbata ecc.) assume that the traceless part of the torsion tensor vanishes or is deliberately set to zero. Then, either the trace or axial part of the torsion is used in association with the...
10. ### I Galaxy recession and Universe expansion

Hi, I'm aware of the measured recession of the galaxies in our universe and the universe expansion itself cannot be understood as an "ordinary" velocity/speed (for instance in the FRW solutions of Einstein's equations). Can you kindly help me clarify this topic ? Thank you.
11. ### I The Evolution of Galactic Scale Cosmic Voids

According to some papers I've found [1], [2] expanding voids can be found inside clouds of denser materials that can cause them to eventually collapse. I have a question about this: Overdensities generally expand up to a given turnaround radius and then collapse. However, as the elements in the...
12. ### I Can the integrated Sachs-Wolfe & the Rees-Sciama effects have any influence on matter?

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...
13. ### I Why doesn't relativity of simultaneity lead to a contradiction?

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...
14. ### Problems with the Riemann tensor in general relativity

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...
15. ### I Question about Einstein's famous elevator experiment

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...
16. ### I Separation angle between pulsars detecting Gravitational Waves

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...
17. ### I Energy conservation in general relativity

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...
18. ### A Correspondence between areal radius differences and proper distances

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...
19. ### I Variation of the lightning train thought experiment

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...
20. ### I Invariant definition of acceleration in Newtonian physics vs proper acceleration in GR

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...
21. ### I Does dark-energy require a source of energy?

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...
22. ### I A mirror behind the event horizon

Thought experiment: What will happen if you place a mirror behind the event horizon and turn on the light in its direction?
23. ### A A question about tensor calculus in Von Neumann algebra (W*)

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...
24. ### A The Emergence of Space-time in String Theory

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...
25. ### Poisson, relativists toolkit, problem 1.3: Timelike geodesic parametrised by a non-affine parameter

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...
26. ### Physics Mediocre, But Passionate Physics Student--Jobs in General Relativity?

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...
27. ### I General Relativity and the precession of the perihelion of Mercury

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.
28. ### I Wald synchronous reference frame proof

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...
29. ### I Special Relativity: an ideal experiment

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...
30. ### I Not at all clear examples of special relativity (rectangle in motion and coming to rest)

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...
31. ### I Using GR to predict the shape of the entire universe?

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...
32. ### I How many meter sticks are there in this length contraction reasoning?

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...
33. ### I Suggestion for 2 more GR tests

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...
34. ### I A question about static spacetime in GR

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...
35. ### I The boundary conditions at infinity

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...
36. ### I What are the effects on a stationary observer for Kerr metric?

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...
37. ### I Noether's second theorem: two questions

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...
38. ### I Was Born rigidity key for Einstein's understanding that spacetime must be curved?

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...
39. ### I Observer on Earth watching a spaceship traveling at c/2

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...
40. ### B A scenario to help understand the twin paradox in SR

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...
41. ### Why is it thought that black holes could make us travel to the past?

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?
42. ### Calculating the components of the Ricci tensor

(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...
43. ### I Forces and gravitational time dilation

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...
44. ### A Exploring a QM particle in Motion with GR

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...
45. ### A Continuation of Coordinates Across Black Hole Horizons

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...
46. ### Relativity Suggestions for graduate studies in General Relativity

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...
47. ### I Invariant Mass-Energy in FRW Spacetime

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...
48. ### I Adler's New Book on Relativity: Misprint on Page 16?

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...
49. ### B What is the metric for a bag-of-gold spacetime?

What is the metric for a bag-of-gold spacetime?
50. ### B How do Black Holes Grow? A Far-Away Observer's Perspective

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...