# Questions tagged [general-relativity]

A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

8,453 questions
Filter by
Sorted by
Tagged with
42 views

### What happens to light in the middle of a BH binary?

A BH binary is a system of two black holes orbiting each other in close orbit. https://en.wikipedia.org/wiki/Binary_black_hole Now on this wiki page, there is a simulation of the merging black holes,...
40 views

### Why does relativity first slow down time for the object as it approaches lightspeed, and then reverse time for the world if it passes lightspeed?

When looking into relativity I see a lot of assumptions thrown about about the knowledge of the reader, even the primers that are supposed to help newbies like me try to learn what it's about often ...
16 views

### Derive the conversion factor for electric charge from SI to Geometric units [closed]

In the Geometrized system of units, $G = c = 1$. This directly gives us the definitions for second and kilogram in the geometric system, as $1\:s = c_0\:m$ and $1\:kg = G_0c_0^{-2}\:m$, where I have ...
44 views

### Why Einstein's GR considered perfect theory of gravity even though it has geometrical base? [closed]

In my view, GR is imaginary geometrical explanation of how gravity works and fundamental science behind why gravity works is still unknown.
59 views

### What are Connection Forms in General Relativity?

I'm trying to follow an article by H. Ellis (1973), where he developed the first ever metric of a traversable Wormhole (more info here). In pages 105-106 (the end of the 3rd page in the linked file ...
22 views

60 views
+150

### Past boundary of $\mathcal{I}^+$ and future boundary of the hyperboloid resolving $i^0$?

Let us consider Minkowski spacetime. Let $(u,r,x^A)$ be retarded coordinates with $x^A$ coordinates on the sphere. Future null infinity is described here as the $r\to \infty$ limit with $(u,x^A)$ ...
99 views

### Is there anything wrong with this modified Einstein-Hilbert action of first order?

The Einstein-Hilbert Action: $$S_{EH}=\frac{1}{2\kappa}\int \sqrt{-g}g^{ab} \left({\Gamma^c}_{ab,c} - {\Gamma^c}_{ac,b} + {\Gamma^d}_{ab}{\Gamma^c}_{cd} - {\Gamma^d}_{ac}{\Gamma^c}_{bd}\right) d^4x$$ ...
31 views

### Linearised Gravity and Motion of Particles in Background Metric

Let's say we have two point particles as our matter source. Suppose we want to solve Einstein Equation Perturbatively and obtain the gravitational wave at the linear order. Let us expand around ...
64 views

### Concept of parallel transport and its physical intuition

I am currently reading Foster and Nightingale and when it comes to the concept of parallel transport, the authors don't go very deep in explaining it except just stating that if a vector is subject to ...
84 views

### An identity with the second covariant derivative [closed]

My question is simple and is placed in the context of GR. Let $X^{\mu\nu}$ be any rank-2 tensor, and $\nabla_\mu$ be the metric compatible, torsion-free, covariant derivative. Does the following ...
29 views

### Is Space-time compression a better explanation than warping? [closed]

Has anyone else come to the conclusion that Mass shrinks (compresses) space-time and that is what we perceive as gravity.
36 views

### Finite computational power of universe vs continuous nature of unbounded particles

I am not a physicist, but I've worked to make this an intelligible question for SE. What information is exactly and how it is stored in the universe is still being studied, but here Seth Lloyd gives ...
44 views

### Is the Cross Product of two vectors in General Relativity on a 3-Space the same as in “Non-Relativistic” Physics?

Considering the covariant tensor $$C = e_{ijk}A^j B^k = A \times B$$ in a 3 spherical-space diagonal metric $$ds^2 = g_{i,i}dx^{i}\cdot dx^i$$ Isn't $C$ the same as "Classical/Newtonian" physics? (...
70 views

### Is this an alternative Dirac Equation in curved space?

The usual covariant derivative for the Dirac equation in curved space is: $$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$ However, I think I found another ...
51 views

### Doesn't spin-spin interactions in gravity disobey Galilean relativity?

In gravity (GR) apparently there are forces which occur which are related to the spin of two masses. For example if we had a rotating gravitational source and dropped, say, some particles into it ...
39 views

### How is Schwarzschild metric asymptotically flat for large $r$?

The Schwarzschild line element is: $$ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 +r^2(d\theta^2 +\sin^2\theta d\phi^2).$$ As $r \to \infty$, this is supposed to ...
116 views

### Could gravitons be dimensionless?

If the metric $g_{\mu\nu}$ is dimensionless (i.e. does not have associated dimensional units) and gravitons are quantum excitations of the metric does that mean that gravitons themselves are ...
In Landau-Lifschitz (Volume II): Actually, it is not difficult to bring $T^{ik}$ to this form. To do this we start from the field equation $$T^{ik}=\frac{1}{8\pi\kappa}\left(R^{ik}-\frac{1}{2}g^{ik}... 1answer 50 views ### Path of a curve Consider \textbf{R}^3 as a manifold with the flat Euclidean metric, and coordinates {x,y,z}. Introduce spherical polar coordinates {r,\theta,\phi} related to {x,y,z} by x = rsin(\theta)cos(\... 1answer 36 views ### Why the imaginary constant on the spin-connection? I have been studying the spin-connection for the Dirac equation. The covariant derivative is defined as:$$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$where \... 2answers 72 views ### Apparent coincidence of spin-connection term and Higgs field? In curved space time, there is a spin-connection term \overline{\psi}\gamma^\mu\sigma^{ab}\omega^{ab}_\mu\psi. Here's my apparent problem. If there were no Higgs field and no gravity, all particles ... 1answer 37 views ### Gravity creating other dimensions [duplicate] It is a well known fact that gravity can bend space, kind of like a rock placed on a sheet of paper, bending the paper. But, doing this will make another third dimension, that the marble actually ... 1answer 53 views ### Does General Relativity actually satisfy the General Principle of Relativity? The “General Principle of Relativity” being “All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics”. To my knowledge, this is related historically ... 2answers 135 views ### Why is Schwarzschild metric taught at all? It seems like the Schwarzschild metric only has historical relevance. Since other coordinates like the (ingoing) Eddington-Finkelstein coordinates are far superior. It seems like the condition on the ... 1answer 16 views ### In Eddington–Finkelstein coordinates how do we show a projectile appears to slow down near the horizon? In the Schwarzschild coordinates it is stated that it is clear that an object appears to slow down near the horizon form the perspective of an outside observer. How do we do this calculation in in ... 0answers 35 views ### Differential of a metric determinant In Landau Lifschitz (Volume II): We now derive an expression for the contracted Christoffel symbol \Gamma_{ik} which will be important later on. To do this we calculate the differential dg of the ... 0answers 30 views ### Can anyone refer me to a good study material to study Petrov Classification from? I am currently trying to study Petrov Classification so I may start my research in the summer. I have completed a year of GR course at the level of sean Carroll. 0answers 58 views ### Would the nightsky be bright (filled with starlight) without accelerating space expansion? As I currently understand, if a photon was emitted from a far away point in the Universe, beyond the event/particle horizon, so that the space inbetween the emitter and us is expanding faster then ... 0answers 49 views ### Are the spacelike foliations of a non-static spacetime topologically equivalent? Assuming a stationary, globally hyperbolic spacetime, I can imagine that all spacelike foliations are topologically equivalent though not all will be identical since the spacetime is not static. Is ... 0answers 21 views ### Does Birkhoff's theorem generalize to higher dimensions without additional assumptions? In the Newtonian theory of gravity, the shell theorem says that the gravitational field inside a massive and spherically symmetric shell is zero. The conclusion is the same in general relativity, as ... 0answers 58 views ### Is the reason of relativity circular? [closed] I would like to ask a question related the stages of a star's life and relativity. We know that times runs slower in regions where the gravitational potential is high, if we apply this to a star it ... 1answer 41 views ### About variation of Ricci tensor I have been doing some calculation on variation of Ricci's tensor with respect to the metric, that, according with S. Carroll (An Introduction to General Relativity: Spacetime and Geometry, equation 4.... 2answers 65 views ### Does light have gravity or Gravitomagnetism? We all agree that light has no mass yet it is affected by gravity. According to accepted theories I have seen light itself is also said to bend space meaning that it causes gravitation. This would ... 3answers 4k views ### Can a wormhole be created if it has not always existed? I know there are solutions to Einstein's field equations that give a wormhole geometry. But they are time independent. They are static. Is there a process where empty flat spacetime can evolve into a ... 5answers 4k views ### Do planets orbiting stars emit gravitational waves? I have heard it said that charged planets could not orbit a massless (low mass) oppositely-charged star based on electromagnetic attraction the same way they can with gravitational attraction, because ... 0answers 51 views ### Deduction of the action of f(R) gravity From$$S=\int{d^4}x\sqrt{-g}f(R)$$I want to deduce the f(R) field equations which are:$$f'(R)R_{\mu\nu}-\frac{1}{2}f(R)g_{\mu\nu}-[\nabla_{\mu}\nabla_{\nu}-g_{\mu\nu}\Box]f'(R)=\kappa T_{\mu\nu} ,\$...
The Einstein tensor given by: $$G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}$$ Can be shown using Bianchi identity?