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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48 views

About periodicity of coordinates given a metric

If I am given a metric how do I decide which coordinate is periodic? Eg. can I look at metric in plane polar coordinates and tell that θ direction is periodic. Also How do I calculate the period of ...
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1answer
56 views

Questions about null geodesic [closed]

Show for the null geodesic in 3D flat spacetime using polar coordinates so the line element is $ds^2=-dt^2+dr^2+r^2d\phi^2$. Do light rays move on straight lines? My question is that I only learned ...
2
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1answer
47 views

Energy conservation around a black hole

In the Schwarzschild black hole, the Killing vector "time translation" $k^a$, so that the following quantity is conserved along a geodesic: $$E = -g_{ab}k^au^b = (1 - ...
4
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1answer
90 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} ...
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1answer
51 views

Difference between Fermi and Riemann normal coordinates

What is the difference between Fermi normal coordinates and Riemann normal coordinates? Which one of them is related to the vanishing of the Christoffel symbols?
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2answers
80 views

What is more fundamental: Geometry and Topology or physical matter? [closed]

Since, there is always an interplay between gravity and the fabric of spacetime. I wonder which is more fundamental: Geometry and Topology or physical matter?
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0answers
24 views

Does a black hole ever fully form to an outside observer? [duplicate]

According to general relativity, I had understood that time appears to slow down when looking into high gravitational fields from afar, so that as a black hole forms, the light from a collapsing star ...
0
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0answers
25 views

Relative motion in particle measurements

I was thinking about measurement of particles at almost-zero energies/temperatures and the movement associated with it. Compared to an observer next to the particle who sees the particle moving at ...
3
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1answer
69 views

What happens if I slowly lower a dangling object into a black hole?

I could've sworn I've seen this question before, but I couldn't find it. Suppose I have an object on the end of a really long string. I can slowly lower it near the event horizon of a black hole, ...
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0answers
32 views

Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
2
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2answers
90 views

Using $\sqrt{-g}$ in integrals of proper volume

I am a little confused over integration using proper volume element. When do we use $\sqrt{-g}$ in calculations? For example, in many calculations involving stars, say when using TOV equation, this ...
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0answers
35 views

Interpreting meaning of coordinates given a metric

I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. $ds^2=-(1+2 \Phi(r))dt^2 + ...
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0answers
36 views

The derivation of the Mass-Energy(including mechanical energy) equivalence principle [duplicate]

(Not duplication! I couldn't find the answer for the general case, instead of the special case that I've already seen in Youtube I hyperlinked.) I will fully satisfy with not only a mathematically ...
1
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0answers
23 views

The mass-energy equivalence is a principle which can not be derived from anything? [duplicate]

Not duplication) I couldn't find the answer for the general case, instead of the special case that I already seen in Youtube I hyperlinked. I will fully satisfy with not only a mathematically ...
1
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1answer
83 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
1
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2answers
52 views

Does the constancy of the speed of light in vacuum hold for any observer in GR as well?

From SR, we know that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. But in GR, does it still hold for all observers? I mean the constancy ...
0
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2answers
129 views

Why would a modern smartphone not work if the theory of general relativity hadn't been discoverd? [closed]

My teacher told me that todays smartphones wouldn't work if the theory of relativity hadn't been discovered, but he didn't explained why.
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1answer
33 views

How are the frequency and wavelength of electromagnetic waves affected within an event horizon?

I apologize if this has been asked previously or if my thinking is way off base, but I am inexperienced with relativity (and this is my first question on the site). I am wondering; as one (not ...
9
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4answers
167 views

How do we know the Schwarzschild solution contains an object of mass $M$?

The Schwarzschild metric is $$ds^2 = - \left( 1 - \frac{2GM}{r} \right) dt^2 + \left(1-\frac{2GM}{r}\right)^{-1} dr^2 + r^2 d\Omega^2.$$ In Carroll's GR book, it is claimed that $M$ is the mass of the ...
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1answer
62 views

Gravitational wave equations worked out

Is there a website where gravitational wave equations are worked out numerically? I would like to experiment with mass configurations but can't find examples.
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0answers
26 views

Non equilibrium black hole radiating away energy and angular momentum, with total energy and angular momentum conserved

The question refers to whether mass (i.e., energy) and angular momentum can be considered to have been carried away by the gravitational radiation in the hole settling down. And whether those entities ...
6
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2answers
188 views

What manifold is spacetime?

In General Relativity, spacetime is a $4$-dimensional manifold with one Lorentzian metric tensor defined on it. In the Special Relativity case what manifold is spacetime is quite clear: it is ...
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0answers
31 views

Geodesic tangent vector in a Riemannian 4-space

I am doing a question in Lewis Ryder's introduction to General relativity. I am very close to the answer but not quite there. The question is: A Riemannian 4-space has metric $$ds^2 = ...
1
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1answer
64 views

On the proof of the existence of geodesics coordinates [closed]

From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is $$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} ...
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1answer
34 views

Eddington-Finkelstein coordinate

The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as \begin{align} u&=t-r^*\\ v&=t+r^* \end{align} where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$ The ...
3
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1answer
50 views

Is this equation $\nabla_a\sqrt{-g}=0$ correct? [duplicate]

Is the equation $$\nabla_a\sqrt{-g}=0$$ correct? Here $\nabla_a$ is the Levi-Civita connection, and $g$ is the determinant of metric $g_{ab}$. Apparently, we have $\nabla_ag_{bc}=0$, but I am not sure ...
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0answers
43 views

Dark matter from general relativity? [duplicate]

We know that there is dark matter due to the observational orbital velocities and mass to light ratio not matching that of expected ones. However the expected orbital velocities of stars in the Milky ...
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0answers
26 views

what is the metric of N-sheeted $AdS_3$?

Suppose the AdS$_3$ metric is given by $$ ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2 $$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications ...
0
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2answers
128 views

Is this analogy of Hawking Radiation correct?

Through reading of textbooks and other research papers, I have settled on the analogy of hawking radiation below (Written completely by myself) Within the ergosphere of the black hole, virtual ...
0
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2answers
108 views

A spin zero graviton?

Why can the graviton not be a spin 0 particle? On a similar note why can it not be a spin 4, spin 6 particle?
0
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1answer
51 views

What are the vacuum Einstein's equations? [closed]

I read on Wikipedia that if the Stress-Energy Tensor is set to zero in General Relativity's Field Equation that it makes the Vacuum Equations. What are these equations, and how are they used?
0
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0answers
17 views

When a dumbbell tumbles, is the gravitational wave amplitude dependent on the frequency?

Normally, we think of gravitational waves as being only created by massive objects, which makes using them infeasible. But if the speed of tumbling affects the amplitude of the waves, then we might ...
0
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0answers
32 views

What is the Metric Tensor? [duplicate]

I was studying Einstein's Field Equation, and this was the most common symbol. Can you explain what it is and how it could be used?
53
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4answers
3k views

GR and my journey to the centre of the Earth

[General Relativity] basically says that the reason you are sticking to the floor right now is that the shortest distance between today and tomorrow is through the center of the Earth. ...
6
votes
1answer
248 views

Null geodesics in uniform gravitational field metric

I'm trying to understand the null geodesics in the metric: $$\mathrm{d}s^2 = -(1+gz)^2 \mathrm{d}t^2 + \mathrm{d}z^2 + \mathrm{d}x^2$$ In particular I'm wondering if the following intuition is ...
3
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3answers
186 views

Why does matter curve space time? [duplicate]

I am under the impression that Einstein never explains in his General Theory of Relativity, why matter curves spacetime; could explanations please be given?
4
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3answers
76 views

Where does the energy of a photon trying to escape a black hole go?

I've heard "light cannot escape a black hole" explained several ways. One is that if a photon inside the event horizon tries to escape a black hole it loses energy to gravity. As it loses energy its ...
0
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0answers
21 views

How are negative energy orbits around a Black Hole defined?

I have read several times that within the ergosphere or a Kerr Black Hole, it is possible to have particles that have an orbital energy value of less than 0. However, I do not understand the concept ...
0
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1answer
78 views

At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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1answer
72 views

When and where to check the formal definition of a manifold

In most texts on GR we are first introduced to a formal and rigorous definition of a manifold. We then learn the point that in GR "any coordinate system" might be used for the 4D spacetime metric. ...
3
votes
1answer
39 views

$f^{\prime}(R)=0$ in $f(R)$ gravity

Suppose in a certain $f(R)$ gravity theory, $f^{\prime}(R)=0$ for some finite value of $R$. (e.g. let $f(R)=R+\alpha R^2$ with $\alpha<0$. $f^{\prime}(R)=0$ at $R=-\frac{1}{2\alpha}$.) Also ...
3
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2answers
596 views

Producing gravitational waves in labs

Can gravitational waves be created on very small region of vacuum with quadruple movement of atom or subatomic particles?
-8
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1answer
90 views

Smallest thing ever measured and quantum mechanic bs [closed]

Is it possible to prove in 2016 that the universe is made up of more discrete units than say an atom or quark? What is the smallest thing we have been able to measure, like not theorize about, but ...
0
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3answers
63 views

Space time curvature and gravity [duplicate]

Is Space time curvature responsible for gravity or Gravity responsible for the curvature in space-time.
1
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1answer
50 views

Orthogonal of tangent vector in Rindler coordinates [closed]

For 2D space time from $(t,x)$ to $(u,v)$ the transformation are $$t = u \sinh(v)$$$$x=u\cosh(v)$$ Asking to show that two families of curves $u = \textrm{constant}$ and $v = \textrm{constant}$ ...
0
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0answers
41 views

Proper Distance and Coordinate Distance in General Relativity

When I started studying general relativity,I was told that the coordinate distance is not covariant and it does not have any physical meaning.I realized that only the proper length is the ...
3
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0answers
22 views

Israel-Wilson-Perjés Solutions

I'm searching for a reference that gives explicitly the field strength (or at least the gauge fields) of the Israel-Wilson-Perjés Solution, using complex harmonic functions for the metric. In ...
4
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2answers
125 views

Why is the covariant derivative of the determinant of the metric zero?

This question, metric determinant and its partial and covariant derivative, seems to indicate $$\nabla_a \sqrt{g}=0.$$ Why is this the case? I've always learned that $$\nabla_a f= \partial_a f,$$ ...
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0answers
26 views

Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields \begin{equation} S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} , \end{equation} ...
3
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1answer
27 views

What is a quasar flux ratio anomaly?

In the context of strongly lensed, multiply-imaged quasar observations, I sometimes hear about "flux ratio anomalies". What are these? Why are they important?