General relativity Definition and 999 Threads

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...

Our current model (FLRW) is clear that the universe has a continuous temporal asymmetry. This is seen as the expansion factor grows with time, and thermodynamically with entropy. A continuous transformation in the current model ##t \rightarrow t + dt## is not the same as ##t \rightarrow t - dt...

Hello, In the Wikipedia article on "Inflaton" there appears the following formula: ##S=\int d^{4}x \sqrt{-g}[ \frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ 1 }{ 2}\xi R \Phi^]## with ##\xi## representing the strength of the interaction between R and...

I'm wondering if there is a way to find the proper volume of the warped region of the Alcubierre spacetime for a constant ##t## hypersurface. I can do a coordinate transformation ##t=τ+G(x)##, where ##G(x)=\int \frac{-vf}{1-v^2f^2}dx##. This eliminates the diagonal and makes it so that the...

Hi PFs, I am reading this paper written by carlo Rovelli: https://arxiv.org/abs/1010.1939 there are many things that i fail to understand, but i would like to begin with a simple thing. Rovelli write that: It is locally Lorentz invariant at each vertex, in the sense that the vertex amplitude...

Suppose you have the following situation: We have a spacetime that is asymptotically flat. At some position A which is in the region that is approximately flat, an observer sends out a photon (for simplicity, as I presume that any calculations involved here become easier if we consider a...

I have read about the spaghettification of objects due to tidal forces as they get close to the singularity. Gravity at your feet is stronger than at your head, so you get stretched and pulled apart. In this case, the singularity is a point in space. But I also read about the time coordinate...

A new group of investigators are attempting something similar to Deur's work, which seeks to explain dark matter phenomena with general relativity corrections to Newtonian gravity is systems like galaxies. Deur's most similar publication to this one along these lines was: One thing that makes...

Schwarzschild Geometry-proper distance. From what I have studied when the Schwarzschild line element is evaluated at constant time and at a constant radius , proper distance becomes a Euclidean distance on the surface of a sphere. What I don't understand is how to evaluate the integral...

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

Shape Dynamics implements nicely Mach's principles. But how well does it fare when it comes to Quantum Mechanics? How can it be experimentally distinguished from other theories?

And if there are an infinite amount of frequencies, doesn't that mean that an extraterrestrial civilization could be reaching out without us being able to receive their signals. And even if we did receive their signals, how would we understand their form of communication? What if they...

Hope this question can be quickly clarified: There was a statement that the General Relativity can be interpreted by speaking of an ether whose state varies from point to point. Is this correct?!

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...

I have been learning gr on YouTube for the last few months. Most of the videos and the book I have focus on high level understanding. I can do all of the tensor calculus proofs. However simple questions like how you set up a velocity vector or measure proper time in schwarzschild are beyond me...

I just need to compare my results of the Ricci and Riemann Tensors of FRW metric, but only considering the spatial coordinates.

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...

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...

I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...

According to Wikipedia, the definition of the Riemann Tensor can be taken as ##R^{\rho}_{\sigma \mu \nu} = dx^{\rho}[\nabla_{\mu},\nabla_{\nu}]\partial_{\sigma}##. Note that I dropped the Lie Bracket term and used the commutator since I'm looking at calculating this w.r.t. the basis. I...

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 ...

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...

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...

So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...

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...

This thought surprisingly came from thinking about the definition of temperature and the symmetry breaking that separated time from temperature. Which led to thoughts about symmetry breaking that separated QM from GR. Which led to to the symmetry breaking that separated dark energy from baryonic...

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.

Recently I have seen a number of General Relativity visualisations that show spacetime flowing towards any mass, similar to water flowing into a sink hole. ScienceClic's video is an example. That model is also used in the "waterfall model" to explain the event horizon of a black hole, as the...

In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ] Since Einstein equation is G = 8πGT, I am...

Is energy really not conserved in a constantly expanding universe?