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.

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5answers
848 views

Does local mean infinitesimally small?

I have studied General Relativity and there is one thing that I have trouble comprehending. What does local really mean? I will give some examples: The Hessian The Hessian is a way to compute the ...
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53 views

Do cosmological event horizon evaporates like black-hole horizon?

While the inflation phase of the universe, expansion was exponential and so the universe was de Sitter-like. So, for a point-like observer, there was a cosmological event horizon. Do this horizon ...
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1answer
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Why is there a third extremum radial coordinate for “rosace-like” trajectories in the Schwarzschild geometry?

I drop a test-particle in the Schwarzschild geometry, at an initial radial coordinate $r_0 > a \equiv 2 G M$ ($a$ is the Schwarzschild "radius"), with initial velocity $v_0 < 1$ ...
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1answer
27 views

Can the properties of a volume of space-time vacuum be determined by measurements just on its surface?

In classical electromagnetics, static electric and magnetic fields in a given volume in a vacuum are completely determined by measuring the fields on the surface that bounds the volume. The fields at ...
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27 views

How does gravity leak to other dimensions, if extra dimensions existed?

There was research article that showed the gravitational waves and electromagnetic waves propagated through the universe the same way, loosing energy by the inverse square law. The researchers ...
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1answer
47 views

Killing vectors and isometry

Let $X=x\partial_{t}+t\partial_{x}$ and $Y=y\partial_{t}+t\partial_{y}$ be Killing vectors on Minkowski $(-,+,+,+)$. It can be shown that $[X,Y]$ is also Killing. I get the following: \begin{equation} ...
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1answer
56 views

Coordinate changing in general relativity [closed]

I'm a bit confused about the transformation $x^{\mu} \rightarrow \tilde{x}^\tilde{\mu}$. How do the following quantities change for any given metric: A vector component $V^\mu$. A vector $V^{\mu}\...
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2answers
116 views

Is the Unruh effect a special relativistic effect or a general relativistic effect?

If an observer moves in an accelerated frame in flat spacetime, the vacuum looks like a thermal distribution of particles to that observer. This is the Unruh effect. Is it a special relativistic (SR) ...
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1answer
56 views

Advanced/Retarded Eddington-Finkelstein coordinates & Black/White Holes

The Schwarzschild spacetime is described by $$ds^2=-(1-\frac{r^*}{r})c^2dt^2+(1-\frac{r^*}{r})^{-1}dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2,$$ where $r^*$ is the Schwarzschild radius. The advanced ...
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1answer
55 views

Why is null geodesic in Eddington-Finkelstein coordinate system a $45^\circ$ straight line?

In the book Relativity, Gravitation and Cosmology by Ta-Pei Cheng, page 106-7, the Eddington-Finkelstein coordinate system is described as a coordinate system set up using a photon falling radially ...
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Leibniz Rule for Covariant Derivative Question [duplicate]

I am watching a series of lectures about General relativity by F. Schuller. In the Lecture 7 - Connections ( https://youtu.be/nEaiZBbCVtI?t=1245 ) he gives the properties for a covariant derivative ...
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Is centripetal force relative based on location in space time?

Would an object rotating in orbit 2,000 miles above the Earth be expected to generate the exact same centripetal force as an identical object with identical spin velocity in orbit 20,000 miles above ...
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2answers
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Is spacetime multilayerd? [closed]

They say celestial objects like Earth make a curve on spacetime due to their heavy mass. Well what about any object just above Earth? They do poses mass then they make a curve in spacetime. So, isn't ...
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1answer
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1) When can a time coordinate be separated in the interval (General relativity) ? 2) Unclear proper time expression

One has that $ds^{2} = g_{ij}(x)dx^{i}dx^{j}$. I often see that the interval is re-expressed with a time "seperation" of the form: $$ ds^{2} = g_{00}(x)dt^{2} + \tilde{g}_{ab}dx^{a}dx^{b} \;...
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2answers
68 views

How certain are we that and objects spacetime speed is constant

I just recently realized - through the aid of a simple yet effective video - that mass curves not space, but spacetime. This has lead me to finally understand why we use geodesics to explain the ...
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1answer
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If you drop a slinky into a black hole, does it stretch out? [closed]

If so, where does the energy come from?
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Linearization of the action

I am taking an introductory course in general relativity and the guy who gives the recitation uses the following relation but fail to explain to my satisfaction why it is eligible. I hope that here I ...
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3answers
90 views

Does time dilate at all in freefall depending on gravitational field?

Given the equivalence principle, I would expect any object in freefall to have the same frame of reference, which would mean the same time dilation. I'd like to verify my understanding of this. For ...
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1answer
26 views

Tensors index notation Symmetrisation/antisymmetrisation

I am having trouble figuring out what is the development of the following equation due to its notation Its a definition for the <> notation, and all that was previously stated was that $u^{(ab)...
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1answer
52 views

Multi-Black Hole Solutions and No-hair theorem

There is famous No-hair theorem: The no-hair theorem states that all black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely ...
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27 views

Diffeomorphisms of tetrad and spin connection in a general Einstein background

How does a tetrad field and the spin connection transform under diffeomorphism, in an arbitrary general background? Shall one use the usual covariant derivative with respect to Levi-Civita connection ...
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0answers
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Magantism vs Gravity with Special Relativity [duplicate]

According to relativity, gravity is not a force, and an item doesn't fall, so much as travel through a straight line (geodesic) through space time which is warped. Because the geodesics converge, it ...
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1answer
38 views

Local inertial frames, and locally flat geometry, taylor expanding metric coefficients

In general relativity, if there is a line element of the form $$ds^2 = [f(u, v)]du^2 + [h(u, v)]dvdu + [w(u, v)]dv^2$$ which I believe corresponds to metric coefficients $$g_{00} = f(u, v)$$ $$g_{01} =...
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1answer
24 views

How much does light deflect due to GR over 1 meter at earth’s surface

In other words, how much does gravity curve space at the earths surface? Assuming the earth is “flat” over a distance of 1 meter, how far down is a horizontal beam of light deflected due to general ...
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3answers
101 views

Why does $ds^2=0$ for a light signal's worldline in general relativity?

I know that in special relativity, the invariant interval $ds^2$ for a light signal's worldline is $$ds^2=\eta_{\mu\nu}dx^\mu dx^\nu=0$$ where the flat metric $\eta_{\mu\nu}=\text{diag}(-1,1,1,1)$. ...
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What sets the scale of a free Maxwell theory in $d\neq 4$?

The action for the free Maxwell theory is given by $$S=\int d^dx\sqrt{-g}\bigg(-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}\bigg)$$ The theory is invariant under conformal transformations $g_{\mu\nu}\to\Omega^2(x)...
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2answers
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Geodesic completeness in general relativity

There are well-known definitions of complete geodesic and geodesically complete spacetime: A geodesic is complete if an affine parameter for the geodesic extends to ±∞. A spacetime is geodesically ...
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1answer
96 views

Essence of Time [closed]

When I tried to derive General relativity I realized that in different non-inertial frames we just can't compare anything, including time intervals, because gravity spoils everything thus making ...
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1answer
45 views

Are we gaining or losing time as our planet revolves around the Sun?

I understand that the Earth (or someone standing on our planet) will undergo time dilation due to a number of reasons compared with someone hovering in interstellar space. I would like to focus on two ...
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3answers
198 views

Is the scalar curvature an independent quantity of the manifold?

As I understand it, the scalar curvature is a function that assigns a real number between $]-\infty,\infty[$ to each point $(x,y,z,t)$ of a manifold: $$ R:\mathbb{R}^4\to \mathbb{R} $$ I am having ...
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1answer
36 views

Visualization of time curvature of spacetime

The Flamm's paraboloid is a slice of the Schwarzschild metric by two spatial dimensions. This shows the space dilation, but without the time component doesn't really give much insight into the ...
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Hilbert Space and distribution theory in QFT

When developing Quantum Field Theory, we usually refer to the Minkowski coordinates which cover the whole space in the case it is flat. I don't know how to set distribution theory and Hilbert space ...
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Gravitational space dilation [duplicate]

The time and space dilation might be derived from behaviour of photon entering a gravity well. Its energy increases, so its period and wavelength decrease. But the number of cycles in the light beam ...
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2answers
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How accurate are the wormhole visualizations in Interstellar?

I'm watching Interstellar and as a huge gravity geek I'm loving it. I have some doubts about the accuracy of the wormhole visualizations, but I want to double check because I heard they had physicists ...
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1answer
265 views

Did the luminiferous aether theory aim to define absolute space, or at least a preferred frame of reference?

From what I understand, the notion of frames of reference took precedence over a notion of "absolute space" in classical mechanics. Did the luminiferous aether, aside from attempting to ...
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35 views

Graviton fluctuation suppressed in large $N$ matters

I have a question about semiclassical gravity approximation. For probing Hawking radiation, we usually treat gravitational theory as semiclassical assuming large $N$ matters. However, I do not know ...
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1answer
52 views

Definition of density of black holes

For a blackhole of mass $M$, radius $R$ and Schwarzschild radius $R^*$ (where $R<R^*$), its density $\rho$ is defined as $$\rho=\frac{M}{(R^*)^3}.$$ One reason I read for using the Schwarzschild ...
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2answers
63 views

Derivation of redshift of photon emitted from edge of schwarzschild black hole

It seems that there is no nice derivation (either on this website or elsewhere on the web) of the standard formula for the redshift of a photon emitted in the Schwarzschild metric as observed by an ...
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3answers
136 views

The spherically symmetric metric and the general metric

In Ta-Pei Cheng's Relativity, Gravitation and Cosmology book, pg. 88, it was stated that the infinitesimal invariant interval $ds^2=g_{\mu\nu}dx^\mu dx^\nu$ for a spherically symmetric metric $g_{\mu\...
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0answers
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Thermodynamics from the total energy of a Black hole and its temperature

Given the blackhole temperature formula, $$T =\frac{\hbar c^3}{8\pi k_BGM},$$ can I use $M=E/c^2$ (where $M$ is the mass of the Blackhole) to invert the above equation to express it as $$E=E(T)$$ and ...
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1answer
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Fuzzballs vs. black holes

Now I am trying understand: What are fuzzballs? What is the difference between fuzzballs and black holes? According to this presentation, one can construct fuzzball solution from ordinary BH solution ...
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Continuity equation for the stress-energy tensor in the FLRW metric

I'm trying to compute the continuity equation for the stress-energy tensor $\nabla^\mu T_{\mu\nu}$ in the FLRW metric $$ds^2=-dt^2+a^2(t)ds^2_3$$ where $ds^2_3=g^3_{ij}dx^idx^j$ is the metric for the ...
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Calculating the geometry from a line element and splitting up multiple partial differentials

Lets say you have a line element of the form: $ds{^2} = f(x,y)(dx^2 +dy^2) +g(x,y)dxdy $ and I want to convert it to a more familiar line element. How would I do this? When I was attempting to get it ...
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0answers
26 views

Euclidean Schwarzschild black hole

I am studying the Euclidean Schwarzschild metric and trying to find its isometries. It still has $\partial_{\phi}$ as a Killing vector, but I wonder if the range of $\phi$ is still $0$ to $2\pi$. The ...
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1answer
64 views

Symmetry of geodesic equations under the transformation of Christoffel symbols

I am not asking for a solution of the following problem that appears in my assignment. However, I don't understand the question and I would like someone to explain the what the question actually is ...
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3answers
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Massless Kerr black hole

Kerr metric has the following form: $$ ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 + \left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 + \left(r^2+a^2\cos(\...
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Decoupling higher order actions

I’m dealing with non-minimally coupling Quadratic gravity in the weak field limit, and as a result of the perturbation $g_{\mu\nu}= \eta_{\mu\nu} +h_{\mu\nu}$ I get some kinetic term mixing. On doing ...
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1answer
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Lorentz transformation in GR

I try to do basics computations of SR with the heavier formalism of GR to see if I understand it well. Change of coordinates is spacetime: changes of coordinates in space time are change of coordinate ...
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1answer
39 views

How is causality preserved between observers in a cosmological setting?

Suppose that 2 observers are sending light signals to each other.If each of them are stationary in relation to a nearby galaxy, but each of these are separated by so great distance, they will be ...
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1answer
34 views

Why are shear-stress and momentum-flux the same in the GR?

I am investigeting the meaning of the components of the Stress-Energy tensor: My source also states, that this matrix is always symmetric in the General Relativity. That looks obvious on the image - ...