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.

Filter by
Sorted by
Tagged with
0 votes
1 answer
36 views

Electromagnetic tensor in a FRW metric

In some papers [like https://arxiv.org/pdf/2204.06883.pdf, eq. (31) ], I see that the Electromagnetic tensor field, for a FRW metric (written in a conformal way) \begin{equation} ds^{2} = a^{2}(\tau) \...
user avatar
2 votes
1 answer
94 views

Relativistic Euler-Lagrange equation

I am confused from the equation 6, why we get Euler-Lagrange equation from equation 8 but not from equation 6? Why we need to use $\zeta$ as invariant parameter in equation 8 even we already have ...
user avatar
1 vote
3 answers
63 views

Does Mach's principle imply that the gravitational field has a non-zero curl?

I would normally visualize the gravitational field as "radial", i.e., one whose curl is zero. However, while thinking about Mach's principle, particularly the notion of frame-dragging (as ...
user avatar
  • 1,195
0 votes
0 answers
35 views

Anomalies in physics [closed]

My question is when to take anomalies seriously and when not to.(Neutron muon $g^-2$ anomaly just disappeared)
user avatar
  • 285
0 votes
0 answers
26 views

Doubt on the continuity factor of Dyson mega-spheres

I) Dyson Mega-Spheres In a nice and cool recent paper, $[1]$, the authors constructed another interresting solution of general relativity; they constructed a thin-shell around a star: a dyson sphere ...
user avatar
  • 2,727
3 votes
1 answer
47 views

Black hole metric of reflected shell of incoming light

At this point in Leonard Susskind's eighth lecture on general relativity, he begins a discussion about finding the metric of a black hole formed by an incoming, spherically symmetric shell of light. ...
user avatar
1 vote
0 answers
19 views

Geodesics Equation from Lagrangian [duplicate]

In the book Introduction to General Relativity Blackholes and Cosmology by Yvonne Choquet-Bruhat, she defines the length of a causal curve as $$\ell\equiv \int_a^b \left( -g_{\alpha \beta} \frac{d \...
user avatar
  • 29
1 vote
1 answer
58 views

Time-dependent Christoffel symbols

I was studying the Schwarzschild metric, and I found out that all of the Christoffel symbols aren't time-dependent. This is because the nonzero Christoffel symbols of the Schwarzschild metric are: $$\...
user avatar
1 vote
0 answers
42 views

Mach's Principle as an initial value problem?

So in this fascinating interview Abhay Ashtektar claims there is a technical formulation of Mach's principle as an initial value problem. At 1:44:22 and the main point is that the only way to ...
user avatar
0 votes
1 answer
37 views

Why does a non-gaussian distribution imply noise in LIGO?

So I'm trying to understand why do we expect a non-gaussian distribution to imply correlation in LIGO? Like how do we know the default noise distribution is gaussian? I am concerned about coordinate ...
user avatar
0 votes
1 answer
15 views

Cosmic expansion from De-Sitter global coordinates metric

Can we show cosmic expansion from this dS metric? \begin{equation} ds^{2} = -d\tau^{2} + R^{2}\cosh^{2}(\tau/R) d\Omega^{2}_{3} \end{equation} I understand that in this background, matter can be set ...
user avatar
0 votes
0 answers
23 views

Deriving Euler-Lagrange equation for vector field in curved spacetime

I'm trying to derive covariant Euler-Lagrange equations for a vector field. The variation of the action should be \begin{gather*} \delta S = \int \text{d}^n{x} \sqrt{|g|} \left( \delta\phi^\mu \frac{\...
user avatar
  • 596
-2 votes
0 answers
25 views

Does the Higgs particle constitute the physical vacuum space? [closed]

If there was no Higgs particle besides of matter not being possible does this mean that there would be no physical space also?
user avatar
  • 3,202
0 votes
1 answer
32 views

Confusions about Schwarzchild Geodesic Deviation

In schwarzchild metric space gets bigger as you approach the horizon, if you build shells around a black hole infinitesimally small distance apart you can build an infinite number of such shells. ...
user avatar
  • 465
-2 votes
0 answers
23 views

Why do objects in Curved Space-Time follow the curved path? [duplicate]

Why does it follow the curved path? If the moon follows the curved space-time of the earth why doesn't it just fall towards the earth, or person 'A' standing on the other side of the world still ...
user avatar
1 vote
0 answers
45 views

Non-minimally coupled inflation — expansion

In the Wikipedia article on "Inflaton" there appears the following formula: $$S=\int d^{4}x \sqrt{-g} \left[\frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ ...
user avatar
  • 11
0 votes
0 answers
40 views

How to tell if the covariant derivative of something is timelike or spacelike

How can I tell if the covariant derivative of something is timelike or spacelike?
user avatar
0 votes
1 answer
46 views

What are the properties of metric tensor? [duplicate]

It's frequently said that graviton has spin-2, so its wave function should have $5$ independent components. The metric tensor has $n^2=16$ components, but it obeys the following property: \begin{...
user avatar
4 votes
0 answers
45 views

Reference for list of the non-zero, unique components of the Riemann tensor for the Kerr metric

Does there exist textbook or webpage which has a list of the unique components of $R^{\mu}_{\nu \alpha \beta}$ for the Kerr metric? Such a reference is easy enough to find for Schwarzchild (including ...
0 votes
1 answer
61 views

Can we use entangled particles to find out what is going on inside a black hole?

If you throw one entangled particle inside a black hole can we know what is happening with it from looking into another entangled particle outside the black hole?
user avatar
  • 285
0 votes
0 answers
25 views

Does photon energy affect deflection of a beam of light in a gravitational field? [duplicate]

Does photon energy affect deflection of a beam of light in a gravitational field? According to general theory of relativity angular deflection of a beam of light in a gravitational field is $$φ = \...
user avatar
  • 101
13 votes
3 answers
248 views

Why would GR's prediction for galaxy rotation curves differ from Newtonian gravity's in spite of prevailing intuition from dimensional analysis?

Until recently, I had assumed that the predicted (non-dark matter) galaxy rotation curves shown in plots such the one on the Wikipedia article were calculated with general relativity. However, I now ...
user avatar
1 vote
0 answers
23 views

GW gauge choice shortcut

When solving the linearised Einstein field equations for gravitational waves, we define the trace reversed metric $\bar{h}_{\mu\nu}$ for which we write the coordinate transformations $x^\mu \...
user avatar
2 votes
0 answers
31 views
+50

Measured Data Question regarding Galaxies with or without Dark Matter and Supermassive black holes

My understanding is that all Ultra Diffuse Galaxies (UDGs) have no Dark Matter nor do they have Supermassive Black Holes. It is also my understanding that all other galaxies have both Dark Matter and ...
user avatar
1 vote
2 answers
111 views

Rotation of astrophysical black holes

It's usually stated that "astrophysical black holes are expected to have non-zero angular momentum, due to their formation via collapse of rotating stellar objects". In other words: rotating ...
user avatar
3 votes
2 answers
53 views

Vector $V^\mu$ vs the Lorentz contravariant components $V^a(x)$

The vector $V^\mu$ was related to the Lorentz contravariant components $V^a(x)$ \begin{equation} V^a(x)=e^a_\mu(x) V^\mu \end{equation} where $V^\mu$ was contravariant under the general coordinate ...
user avatar
3 votes
1 answer
62 views

Is it possible to have a spacetime described by a piecewise metric? [closed]

For example (in $1+1D$): $$ ds^2 = \begin{cases} -dt^2 + dx^2 & \text{if } x > 0\\ -dt^2 + Adx^2 & \text{if } x \leq 0 \text{ and } A \neq 1 \end{cases} $$ What ...
user avatar
  • 33
3 votes
0 answers
34 views

Twistor equation and Killing equation

Yesterday was the birthday of Roger Penrose. And reading again about twistors I realized that twistor equation is strikingly similar to a Killing equation. My question is, are they "equivalent&...
user avatar
  • 5,579
2 votes
1 answer
113 views

Lie derivative acting on a function

I'm a little confused about Lie derivatives. In fact all that definitions of pull-back and push-forward and one-parameter family of diffeomorphisms and integral curves and so on seems strongly ...
user avatar
0 votes
3 answers
97 views

Do massless particles have gravity? [duplicate]

What I know so far is that according to the general theory of relativity, gravity is not the force of attraction between two objects; instead, it is a consequence of the curvature of space-time. And ...
user avatar
  • 175
1 vote
0 answers
67 views

Local conformal group of the Euclidean plane and the (local) diffeomorphism group of locally Lorentzian 4-manifolds

Maybe this question is rather too general to mention, but I hope the community can help to make it more precise in case it's needed. The question is: if there's any link between the local conformal ...
user avatar
8 votes
2 answers
399 views

Throwing and catching a clock in general relativity

I'm new to this Q&A site, so sorry if my formulas don't look great! I'm trying to create a function that shows the time on a clock B that's been thrown up from and caught in position A, with ...
user avatar
  • 83
5 votes
2 answers
161 views

What is the relative acceleration composition law in General relativity?

In Euclidean geometry we have the following relative acceleration composition law: $$ \vec a_{DE} + \vec a_{EF} = \vec a_{DF} $$ Where the relative acceleration between $i$ and $j$ for any $i$ and $j$ ...
user avatar
1 vote
1 answer
31 views

Geodetic Precession of a Gyroscope in Hartle's GR Book

In 14.3, Hartle deduces the geodetic precession angle per orbit of a gyroscope in Schwarzschild geometry. Immediately after eq.(14.18), the book reasons that the angle deduced is physically measured ...
user avatar
  • 21
4 votes
1 answer
98 views

When connections are fundamental objects, is LQG the only possible theory?

In an interview Abhay Ashtekar claims: if you have a background independence and if you want to have Einstein connections this (Loop Quantum Gravity) is the only thing you can write down. Where the ...
user avatar
0 votes
1 answer
38 views

Cross product of basis vectors in general relativity

Say I wanted to find an expression for the differential surface trapped between two basis vectors (in 4-dimensional curved coordinates), one approach would be to take their cross product, and take the ...
user avatar
  • 539
1 vote
1 answer
71 views

"Lorentz gauge" or "Lorenz gauge"?

In electrodynamics there is a gauge condition named after Ludvig Lorenz: $$\partial^\mu A_\mu = 0.$$ In general relativity we also have a gauge condition defined as follow: $$\partial_\mu \gamma^{\mu\...
user avatar
  • 11
1 vote
1 answer
58 views

What is the average recessional velocity of an object in the universe?

I’m trying to get a better grasp on cosmological horizons and have a question regarding recessional velocity. In particular: What is the average recessional velocity of a cosmological object (...
user avatar
0 votes
2 answers
47 views

The Same Origin Requirement of Reference Frames

Currently learning special relativity: My understanding is that Lorentz Transformations are the motions of Minkowski space that preserve the spacetime interval - and the same origin point. That is two ...
user avatar
1 vote
0 answers
50 views

Path integral of Quantum Gravity while keeping Einstein's relation satisfied

Suppose we have a field $\phi(x)$ and the metric field is $g_{\mu \nu}(x)$. The action is the functional $S[\phi (x) , g_{\mu \nu } (x)] $. We want to do the path integral: $$\int d[\phi (x)] d[g_{\mu ...
user avatar
  • 2,929
0 votes
0 answers
55 views

Valid tensor expression?

The following given tensor expression is:$$A^i=B_i+C_i\tag{1}$$ which is invalid expression since the free index on L.H.S is in upper part and on R.H.S it is in lower part so to make valid tensor ...
user avatar
5 votes
3 answers
3k views

What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?

I have read this question: Now it's not actually true that general relativity obeys a law of superposition, but it is an extremely good approximation for a small-amplitude gravitational wave passing ...
user avatar
-1 votes
0 answers
38 views

Spacetime fabric questions [duplicate]

Below is a pic of mass-energy curving spacetime. There is no up and down in space. So who decides that the black planet in the pic is weighing down on the spacetime fabric? It might as well be '...
user avatar
1 vote
0 answers
48 views

Black $p$-brane solution

Im trying to confirm that the metric (11) in the paper below is a solution to Einstein's equations (6). I tried to use the metric and extract $\lambda=(1-(r_+/r)^{D-3})^{1/2-\gamma/2(D-3)}$ and $R=r(1-...
user avatar
  • 11
1 vote
0 answers
53 views

What is the dimension of cosmological constant $\Lambda$

I came across two forms of the Friedmann equation. Those are as follows: $$H^2=\frac{8\pi G \epsilon}{3c^2}-\frac{\kappa c^2}{R_{0}^2 a^2}+\frac{\Lambda}{3}\tag{1}$$ $$H^2=\frac{8\pi G \rho}{3}-\frac{...
user avatar
  • 25
-3 votes
0 answers
57 views

What's the spacetime metric in the frame freely falling to and into a black hole?

The normal frame used in black hole physics is the Schwarzschild metric. But how does the metric look like if you fall freely into it from far away? Initially flat and time dependent components? Wil ...
user avatar
  • 312
0 votes
0 answers
23 views

Time in Quantum Mechanics [duplicate]

From my understanding, time does not flow in general relativity and the flow of time is just a construct of our perception. All moments in the past, present, and future are equally real in this model ...
user avatar
1 vote
2 answers
78 views

How can the ratio of a black hole's (or any object's) angular momentum to its mass be less than one?

In the latest Quanta Magazine article, about Kerr black holes, the researchers say their new solution for these objects only works, so far, for Kerr black holes with a ratio of angular-momentum-to-...
user avatar
  • 3,675
0 votes
0 answers
31 views

Where can I find examples of how to use the Schwarzschild solution and the "time delay of light" effect? [closed]

I'm reading Wald's book on General Relativity, and I can't find any examples online of how to use these equations. The "time delay of light" effect is on pages 146–147. The examples would be ...
user avatar
-1 votes
0 answers
88 views

Creating The Sun [duplicate]

I am a high school student and just came to know about Einstein famous formula for relativity $$ E = mc^2 $$ I was wondering if somehow I was able to throw a considerably heavy object with a speed ...
user avatar

1
2 3 4 5
239