# Tagged Questions

1answer
76 views

### Killing vector argument gone awry?

What has gone wrong with this argument?! The original question A space-time such that $$ds^2=-dt^2+t^2dx^2$$ has Killing vectors \$(0,1),(-\exp(x),\frac{\exp(x)}{t}), ...
2answers
108 views

### Geodesic equations

I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...
1answer
42 views

### “WLOG” re Schwarzschild geodesics

Why, when studying geodesics in the Schwarzschild metric, one can WLOG set $$\theta=\frac{\pi}{2}$$ to be equatorial? I assume it is so because when digging around the internet, most references seem ...
1answer
64 views

### Why four velocity under covariant differential is considered to be zero?

In Einstein's general theory of relativity the elements of four velocity $U^{\mu} (\gamma c, \gamma v)$ under covariant differential is considered to be zero, why? $$\mathcal{D} U^{\mu}=0$$ in other ...
2answers
63 views

### What is path of light in the accelerating elevator?

Mathematically, (by mathematically I means by equations) what is path of light in the accelerating elevator? What is the difference between an ordinary derivative and covariant derivative (which is ...
1answer
69 views

### The role of the affine connection the geodesic equation

I apologise in advance that my knowledge of differential geometry and GR is very limited. In general relativity the equation of motion for a particle moving only under the influence of gravity is ...
0answers
45 views

### Naked singularity and null coordinates

I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
0answers
48 views

### Naked singularity and extendable geodesics

I'm currently trying to understand the notion of a naked singularity. After consulting books by Wald and Choquet-Bruhat, it seems that for a naked singularity one must have that the causal curves can ...
1answer
52 views

### Can you enter a timelike hypersurface?

As I understand it, a timelike hypersurface is one that has only spacelike normal vectors. But does this not imply that a the geodesic of a particle crossing it must be spacelike at that point? But ...
1answer
356 views

### Physical significance of Killing vector field along geodesic

Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter. What physical significance do the scalar quantity ...
0answers
54 views

### Gravitational effects and metric spaces

Could somebody please explain something regarding the Nordstrom metric? In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies. My ...
1answer
115 views

### Homogeneous gravitational field and the geodesic deviation

In General Relativity (GR), we have the geodesic deviation equation (GDE) ...
4answers
330 views

### To which extent is general relativity a gauge theory?

In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
2answers
272 views

### Action for a point particle in a curved spacetime

Is this action for a point particle in a curved spacetime correct? $$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$
1answer
229 views

### Potential Energy in General Relativity

I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions: In ...
1answer
255 views

### Problem with convergent geodesics at 2D sphere

There is a chapter on general relativity in the book Spacetime Physics Introduction To Special Relativity by Taylor and Wheeler, which qualitatively explains how attractive gravitational force can be ...
0answers
47 views

### Cauchy Problem in Convex Neighborhood

While reading the reference Eric Poisson and Adam Pound and Ian Vega,The Motion of Point Particles in Curved Spacetime, available here, there is something that I don't quite understand. ...
2answers
237 views

### How to think of the harmonic oscillator equation in terms of “acceleration = gradient”

This is related to another question I just asked where I learned that the equation of motion of a harmonic oscillator is expressed as: $$\ddot{x}+kx=0$$ What little physics I grasp centers on ...
1answer
618 views

### Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
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