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.
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...
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...
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...
I started by expanding ##dx## and ##dt## using chain rule:
$$dt = \frac{dt}{dX}dX+\frac{dt}{dT}dT$$
$$dx = \frac{dx}{dX}dX+\frac{dx}{dT}dT$$
and then expressing ##ds^2## as such:
$$ds^2 =...
I have some questions regarding the expected exchange particles for gravitation.
From my understanding the following was valid:
We can linearize the equations of GTR for weak fields
"Quantum mechanics" (Schrödinger, Dirac equations) are linear
Those linear equations allow eigenstates and...
Hi, I am reading through my lecture notes - I haven't formally covered killing vectors but it was introduced briefly in lectures.
Reading through the notes has highlighted something I am not sure about when it comes to co-ordinate transformations.
Q1.Can someone explain how to go from...
In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries?
I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...
In Dirac's "General Theory of Relativity", at the end of Ch. 25 (p. 47), right after deriving the full Einstein equation ##R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R = -8\pi\rho v^\mu v^\nu = -8\pi T^{\mu\nu}##, he makes a reference to the conservation of mass (Eq. 25.3):
$$0 = (\rho v^\mu)_{:\mu} =...
This time with General Relativity:
https://www.amazon.com/dp/1541601777/?tag=pfamazon01-20
I got a copy as soon as I noticed it. And it is good - as all his books are.
Notice - number one best seller. Lenny deserves a medal.
There is a genuine thirst for science beyond banal...
Hello, everyone
I am now working on this project quite a while now and I just wanted to share it with this forum, which I was a member for a long time. I am working on a python application about GR and I believe I managed to create a very user-friendly layout.
It's called GTRPy, and it allows...
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...
When arriving at the standard model of cosmology, i.e. the exapnding universe, we assume based on experirmental data that the cosmos is homogenous on large enough scales.
But when we go back in time, when the galaxies are beginning to form, we note that because of the growth of density...
Modeling the time evolution of the sun and earth orbiting each other using ##F = \frac{GMm}{r^2}## is straightforward. However, it appears that modeling the time evolution of the same 2 body system using general relativity seems to be a hard/intractable problem?
There was in depth discussion by...
Einstein showed (via general relativity) that spacetime is curved by mass, mass moves in relation to this curvature, and that gravitation arises as secondary effect. Why then are we looking for quantum gravity as some sort of mass<->mass interaction?
Aren't the fundamental interactions better...
I was reading this paper (*Green's functions for gravitational waves in FRW spacetimes:* [https://arxiv.org/abs/gr-qc/9309025](https://arxiv.org/abs/gr-qc/9309025)) and I had a specific question about one statement in the paper that I would like to ask:
At page 6, the author says that...
About a month or two ago I started doing simulations of light physics around black holes and yesterday I got a fast Christoffel symbols function for the Schwarzschild metric in cartesian coordinates, but now the photon ring appears flipped. I feel as though it is wrong. But as I am still pretty...
For some time I was wondering, what would happen if the Sun just disappeared like someone hit the delete button in Universal Sandbox. Specifically, what kind of gravitational waves will be produced in the wake of such an event?
Would the law of conservation of Mass-Energy be miraculously...
It's possible that this may be a better fit for the Differential Geometry forum (in which case, please do let me know). However, I'm curious to know whether anyone is aware of any standard naming convention for the two principal invariants of the Weyl tensor. For the Riemann tensor, the names of...
Does anyone know of a comprehensive list of solutions to GR, their developmental history, and the viability for serving as a practical model for the observable universe?
Once having converted the FLRW metric from comoving coordinates ##ds^2=-dt^2+a^2(t)(dr^2+r^2d\phi^2)## to "conformal" coordinates ##ds^2=a^2(n)(-dn^2+dr^2+r^2d\phi^2)##, is there a way to facilitate solving for general geodesics that would otherwise be difficult, such as cases with motion in...
The Hiscock coordinates read:
$$d\tau=(1+\frac{v^2(1-f)}{1-v^2(1-f)^2})dt-\frac{v(1-f)}{1-v^2(1-f)^2}dx$$
##dr=dx-vdt##
Where ##f## is a function of ##r##. Now, in terms of calculating the christoffel symbol ##\Gamma^\tau_{\tau\tau}## of the new metric, where ##g_{\tau\tau}=v^2(1-f)^2-1## and...
General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timlike curves, or world lines that lead back to the same point in spacetime.
I wondered if these solutions also permits Causal loops? Such as the one...
I was going through this paper where on page 5 they argue that in the given Poincare section:
I am a bit confused by this statement. How does the given saddle point correspond to the black hole horizon and is it necessary that it acts as a source of chaos? Any explanation would be truly...
Hi, mathematically in the F = GMm/r^2 equation r can be very close to infinity (or the size of the universe), but gravitational force always will be some number.
But how is that in the real world? Let's say we have a perfectly empty universe but only with two sun-like stars. If they are away...
So, I have a question.
The time dilation formula is:
t = t₀ • 1 / √(1 - v²/c²)
Let's take a photon that travels at c. In my opinion, for a photon "clock doesn't tick" and its life is just a moment.
But when we calculate time dilation by this formula, then c over c is 1 and the root of 1 minus...
In describing the spacetime around a massive, spherical object, one would use the Schwarzschild Metric. What metric would instead be used to describe the spacetime around multiple massive bodies? Say, for example, you want to calculate the Gravitational Time Dilation experienced by a rocket ship...
The paper is The Volume Inside a Black Hole (0801.1734)
Looking at the abstract, I have a question already.
It is stated: Because the light rays are orthogonal to the spatial 2-dimensional surface at one instant of time, the surface of the black hole is the same for all observers (i.e. the...
I'm reading Tipler's 1976 paper, "Causality Violation in Asymptotically Flat Spacetimes" and he keeps using a symbol which seems to resemble the symbol for Future Null Infinity in a strange font, but it's usage doesn't make sense with what I would expect if that's what the symbol meant. He...
https://arstechnica.com/science/2022/09/einstein-wins-again-space-satellite-confirms-weak-equivalence-principle/
See also http://dx.doi.org/10.1103/PhysRevLett.129.121102 (limited access)
Considering the FLWR metric in cartesian coordinates:
##ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2)##
With ##a(t)=t##, the trace of the extrinsic curvature tensor is ##-3t##. But why is it negative if it's describing an expanding universe, not a contracting one?
In texts on General Relativity, the proper time ##d\tau^2 = -ds^2## (with an appropriate choice of metric signature) is commonly said that the time measured by a timelike observer traveling along a path is given by the integral of ##d\tau## along this path. Of course it's possible to construct a...
Could one derive a set of coordinate transformations that transforms events between different reference frames in the de Sitter metric using the invariant line element, similar to how the Lorentz Transformations leave the line element of the Minkowski metric invariant? Would these coordinate...
On pages 106-107 of Spacetime & Geometry, Carroll derives the geodesic equation by extremizing the proper time functional. He writes:
What I am unclear on is the step in 3.47. I understand that the four velocity is normalized to -1 for timelike paths, but if the value of f is fixed, how can we...
I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such:
where the action is given by
However, I...
In Newtonian mechanics, G is simply a proportionality constant or the force with which two bodies of unit mass attract each other. However, GR doesn't treat gravity as a force. So how is G defined in GR? Is it a property of spacetime or just some useless mathematical artefact? What does G...
hello I'm korean high school student and sorry for my poor English.
I saw ## t_0=t_f\sqrt{1 -\frac{ 2GM}{rc^2}} ## in wikipedia.
does ## \sqrt{1 -\frac{ 2GM}{rc^2}} ## of this equation have name like lorentz factor ## \frac{1}{\sqrt{1 -\frac{v^2}{c^2}}} ##of ## t=\frac{t_0}{\sqrt{1...
Sean Carroll has an article (https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/) where he explains that matter can gain energy from spacetime expansion.
At the end of the article, he says: In general relativity spacetime can give energy to matter, or absorb it from...