Question

Cosmology weele 1 Chapter 2 Dodelson First we need some basic GR First of all, the metric \[ d s^{2}=g_{\mu \nu} d x^{\mu} d x^{\nu} \quad \mu, \nu \in 0,1,2,3 \] which defines clistance between spacetime points. In special velativity the metric tensor guv is \[ g_{\mu \nu}=\eta_{\mu \nu}=\left[\begin{array}{llll} -1 & & & \\ & 1 & 1 & \\ & & 1 & 1 \end{array}\right] \] So that \( d s^{2}=-d t^{2}+d \bar{x}^{2} \) (this also provides the well known result that photons move on null geodesics \[ c s^{2}=\left.0\right|_{m=0} \] In general \( d s^{2}<0 \) means "timelike", i.e. points which can be reached while noving with \( |v|<c \). (1)

          Cosmology weele 1
Chapter 2 Dodelson
First we need some basic GR
First of all, the metric
\[
d s^{2}=g_{\mu \nu} d x^{\mu} d x^{\nu} \quad \mu, \nu \in 0,1,2,3
\]
which defines clistance between spacetime points.

In special velativity the metric tensor guv is
\[
g_{\mu \nu}=\eta_{\mu \nu}=\left[\begin{array}{llll}
-1 & & & \\
& 1 & 1 & \\
& & 1 & 1
\end{array}\right]
\]

So that \( d s^{2}=-d t^{2}+d \bar{x}^{2} \)
(this also provides the well known result that photons move on null geodesics
\[
c s^{2}=\left.0\right|_{m=0}
\]

In general \( d s^{2}<0 \) means "timelike", i.e. points which can be reached while noving with \( |v|<c \).
(1)

Cosmology weele 1
Chapter 2 Dodelson
First we need some basic GR
First of all, the metric

d s^2=gμν d x^μ d x^ν μ, ν∈ 0,1,2,3

which defines clistance between spacetime points.

In special velativity the metric tensor guv is

gμν=ημν=[
-1
1 1
1 1
]

So that d s^2=-d t^2+d x̅^2
(this also provides the well known result that photons move on null geodesics

c s^2=.0|m=0

In general d s^2<0 means "timelike", i.e. points which can be reached while noving with |v|<c.
(1)

Added by Elizabeth M.

Question

Please give Ace some feedback