All Questions
23
questions
2
votes
1
answer
143
views
Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes [closed]
Is there a way to conceive a TOV equation, and therefore the stability analysis for a metric like:
$$ ds^2 = -dt^2 + a^2(t,r)\big(dr^2 + r^2d\Omega ^2\big)~?\tag{1}$$
- 3,085
1
vote
0
answers
49
views
Initial-value problem for gravitational waves
Gravitational waves have been very much in the news recently and I would like to understand them better. I know vaguely that they cause transverse changes to the geometry of matter as they pass by. ...
- 593
2
votes
1
answer
69
views
Question on the spacetime outside Earth
The general metric for a slowly rotating body is $[1]$:
$$ds^{2} = -B(r)dt^{2}+A(r)dr^{2}+r^{2}[d\theta^{2}+sin^{2}\theta(d\phi-\Omega(r,\theta)dt)^{2}]\tag{1}$$
My question is:
Considering $\Omega = \...
- 3,085
0
votes
1
answer
132
views
Junction Conditions: In what cases is matching the extrinsic curvature at a boundary tantamount to matching metric derivatives at the boundary?
My understanding of the Israel junction conditions are as they are laid out in Poisson's "A Relativist's Toolkit", namely that if one wishes to join 2 different spacetimes across some ...
- 19
0
votes
1
answer
98
views
How exactly did Einstein check if his equation on general relativity was correct? [duplicate]
I saw the equation on general relativity and then I wondered: how did Einstein check if his equation was right or wrong?
- 625
0
votes
4
answers
408
views
Why does a particle move in space in a curved spacetime?
I understand that all the particles move in spacetime at $c$. A massive particle affects the spacetime, rendering it bent or curved.
In the absence of a massive particle, the said particle (in unbent ...
- 196
2
votes
1
answer
119
views
Would something in the center of a supermassive shell be pulled apart or remain stationary?
Imagine a supermassive hollow shell in space, and also imagine there is an object at the center of this shell.
How does the force of gravity affect the body inside the shell?
My reasoning is that the ...
- 145
1
vote
0
answers
120
views
Why do the ADM-energy, mass and linear momentum work?
In asymptotically flat spacetimes, the ADM-energy, linear momentum and mass are defined as
$$E:= \frac{1}{16\pi}\lim_{r\to\infty} \int_{S^2_r}\sum_{i,j}\partial_ig_{ij}-\partial_jg_{ii}\frac{x^j}{r}\...
- 113
1
vote
1
answer
153
views
Understanding Birkhoff's theorem
I was seeing the generalisation of Newton's shell theorem to GR, including the answer given here:
Is spacetime flat inside a spherical shell?, but I don't understand why proving that the metric inside ...
- 1,124
1
vote
0
answers
154
views
Am I seeing a particle orbiting a Morris-Thorne Wormhole?
I tried to calculate the time-like geodesics of the Morris-Thorne Wormhole $[1]$, $[2]$, $[3]$ for redshift function $\Phi(r) = 0$ and $b(r) = \sqrt{r_{0} r}$. But I don't know for sure if all the ...
- 3,085
0
votes
2
answers
223
views
What is the physical interpretation of the equation for the invariant interval in general relativity?
In my GR lecture I was given the following equation for the spacetime interval (signature $(+,-,-,-)$):
$$ ds^2=(1+\frac{2\phi}{c^2})c^2 \, dt^2-(1-\frac{2\phi}{c^2})\delta_{ij}\, dx^{i}dx^{j} \tag{1}...
- 1,037
1
vote
0
answers
75
views
Spacetime metric as an order parameter?
I've been reading on Sean Carroll's ideas ([1], [2]) on space from Hilbert space and bulk entanglement gravity in which he tries (and succeds) to derive the linearized Einstein equation directly from ...
- 133
1
vote
0
answers
159
views
Abel deprojection formula in static and spherically symmetric spacetimes
Given a fluid spherically distributed with density $\rho(r)$ in 3-dimensions in flat-spacetime; the projected surface density $\sigma(R)$ (onto two dimensions) can be obtained by the well known ...
1
vote
1
answer
118
views
Direction of gravity
General Relativity explains the path a falling body makes (ex. An apple falling toward the center of the Earth) as a geodesic in curved spacetime. What explains the direction the apple falls? In other ...
- 11
7
votes
1
answer
366
views
How does time behave inside a massive spherical shell?
According to General relativity the clocks in our satellites in the atmosphere tick faster than those on Earth, as they are farther from the gravitational well of Earth and are free falling.
...
- 5,568