All Questions
10
questions
3
votes
4
answers
364
views
Regarding the signature of special relativity
in special relativity we add time as a dimension and replace euclidean space $ \mathbb{R}^4 $ with a pseudo-euclidean space $ \mathbb{R}^{1,3} $ of signature $ (1,3) $ by defining a quadratic form $\...
- 309
1
vote
0
answers
20
views
Rescaling the null coordinates
Given a $4$-dimensional spacetime described by four coordinates $(t,r,\theta,\phi)$, we usually define the null coordinates by,
\begin{equation}
u = \frac{t-r}{2}, \quad v = \frac{t+r}{2}
\end{...
- 404
1
vote
1
answer
205
views
Spin connection raise and lower flat indices
The spin connection $\omega^a_{b\nu}$ is used to define the covariant derivative of a spinor in curved spacetime. I want to explicitly calculate the covariant derivative:
$$\nabla_\nu\Psi=(\partial_\...
- 505
1
vote
0
answers
73
views
Signature of the Minkowski metric tensor
In special relativity, events happen in the Minkowski spacetime, with signature $(3,1)$ or $(1,3)$. I was wondering about the need of different sign for temporal and spatial coordinates. Looking ...
- 123
4
votes
1
answer
849
views
Different signatures of the metric in Einstein field equations
Throughout the GR lectures, we have always used (- , + , + , +) signature for the metric tensor but in some chapters it was switched to (+ , - , - , -) and immediately after that Einstein field ...
- 3,464
0
votes
1
answer
572
views
Time-like coordinate vs space-like coordinates in GR
I know the definition of space-like and time-like coordinates in simple geometric, basically, we got:
$$ds^2=dt^2-dx^2-dy^2-dz^2$$
so the coordinate with a positive contribution to the $ds^2$ is the ...
6
votes
4
answers
1k
views
When is the value of spacetime interval $ds$ negative?
The spacetime interval in special relativity, $ds$, is defined as
$$
ds^2=c^2dt^2-dx^2-dy^2-dz^2
$$
with the $(+,-,-,-)$ Minkowski sign convention. The value of $ds^2$ can be positive, zero, or ...
- 1,335
5
votes
2
answers
2k
views
What is the meaning of the negative sign in $\Delta s^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 - (c\Delta t)^2$?
In the equation of the spacetime interval formula $\Delta s^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 - (c\Delta t)^2$ is there meaning for the minus sign before the $(c\Delta t)^2$ or is it just a ...
- 170
2
votes
1
answer
80
views
Is spacetime defined mathematically without using $c$ speed?
Is there a mathematical definition of spacetime that does not use $c$ speed as a conversion factor or involve the spacetime interval? If not why?
3
votes
1
answer
848
views
Friedmann-Robertson-Walker (FRW) metric and scale factor confusion
I'm confused about the different ways of writing the Friedmann-Robertson-Walker (FRW) metric using the normalised and non-normalised scale factor. Peacock, for example, (see equation 3.13) gives
$$c^{...
- 3,059