All Questions
100
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Does gravity accelerate you towards the geodesic of light between you and the mass?
If there's a planet far away, you will accelerate straight towards it due to gravity. If you place a Schwarzschild black hole right in the middle between you and the planet (the distance between the ...
- 171
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0
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87
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Nature of the spacetime trajectory (worldline) described by $\frac{d^2x^\mu}{d\tau^2}=0$
The covariant equation of motion of a free particle, in flat Minkowski spacetime and Cartesian coordinates, reads
$$
\frac{d^2x^\mu}{d\tau^2}=0, \tag{1}
$$
with $\mu=0,1,2,3$, and has the solution
$$
...
- 11.7k
1
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32
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Example of lightlike curve that's not a geodesic in Lorentz spacetime [duplicate]
Let $(M,g)$ be a 4 dimensional Lorentz spacetime. A smooth curve $\alpha:\ I\to M$ is called lightlike if $\alpha'(s)\in TM_{\alpha(s)}$ is lightlike for all $s\in I$, which means
$$g_{\alpha(s)}\big(\...
- 143
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1
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110
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Geodesic beeing inextendible and incomplete
We say that a geodesic is (future ) inextendible if there exist no (future) endpoint for example. Wouldnt that imply the domain of the geodesic is $[p, \infty)$ with some beginning point $p$? And it ...
user390166
0
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60
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How would you reparametrize a worldline in terms of proper time in 2-dimensional Minkowski spacetime?
In a 2-dimensional Minkowski spacetime i.e. $x^\mu=(t,x)$, you can define the metric simply by the Minkowski metric, $ds^2=-dt^2+dx^2$, and the Christoffel symbols vanish. If you have a worldline ...
- 51
1
vote
1
answer
99
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The apparent dilatation of time in General Relativity
Maybe this a dumb question, but, is the gravitational dilatation of time caused because a particle travelling through a geodesic in a curved space-time must cover a larger distance than the one ...
- 1,525
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53
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Question on gravity and spacetime curvature [duplicate]
In General Theory of Relativity, it is explained that the fabric of reality i.e. spacetime bends around objects with mass, and that curvature causes other objects to come close to/ fall towards the ...
-1
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1
answer
117
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Why does the 1/2 coefficient in the geodesic equation cancel the 2 in the $\partial_{r}g_{tt}$ term but not the 2 in the $g^{rr}$ term?
In the Newtonian limit, the Christoffel symbol $\Gamma^{r}_{tt}=-\tfrac{1}{2}g^{rr} \partial_{r}g_{tt}$ in the geodesic equation reduces to $$\frac{d^2r}{dt^2} = -\frac{1}{2}\left(\frac{2GM}{c^2r}-1\...
- 335
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131
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I need help with a proof in Hawking & Ellis [closed]
Here's a proof in Hawking and Ellis (1973) of proposition 6.4.6:
The definition of "strong causality" used in the book is that for every point $p$ and every neighborhood $U$ of $p$, there ...
- 863
13
votes
3
answers
2k
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In general relativity, why is Earth able to accelerate?
I was told and convinced that gravity is not a force, and in free fall you're an inertial frame and experience no force, and when on the surface of Earth you would be accelerating upwards.
What I ...
- 320
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50
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Which curve has the maximum proper length? [closed]
Below is a spacetime diagram in the rest frame of a lab on Earth (with a gravitational field). Which of the worldlines shown below has the greatest proper time?
My attempt: B, because $d\tau=\sqrt{1-...
- 131
0
votes
1
answer
92
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Are photons affected by "temporal gravity?"
Since objects follow geodesics in spacetime, that is the locally shortest path, it would seem to me that unless objects move, they do not trace any path at all. In other words, if I'm stationary on ...
- 47
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146
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Equivalence Principle: Uniform to Non-uniform gravitational fields
2Einstein in his 1916 GR paper describes the equivalence principle and makes a case for general relativity i.e a person in a non-inertial frame is equivalent to a person in a uniform gravitational ...
- 141
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3
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2k
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What is timelike geodesic?
I have searched the internet for the definition of timelike geodesic curves. But I am not getting a consistent definition. In some places I saw the geodesic maximises the proper time and in some ...
- 399
5
votes
2
answers
164
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Geodesic: maximal aging versus extremal aging
From Exploring Black Holes, by Taylor and Wheeler, page 1-7:
Purists insist that we say not maximum reading but rather extremal reading: either maximum or minimum. This book contains only examples of ...
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