IEVref:
113-07-60
ID:
Language:
en
Status:
Standard
Term:
metric tensor
Synonym1:
Synonym2:
Synonym3:
Symbol:
g
μ
ν
g
μ
ν
Definition:
symmetric
tensor of the second order
defining the geometric properties of
space-time
by the relation
d
s
2
=
∑
μ
,
ν
g
μ
ν
d
x
μ
d
x
ν
, where
d
s
2
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaciizaiaadohadaahaa Wcbeqaaiaaikdaaaaaaa@3671@
is a
squared interval
and
d
x
μ
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaciizaiaadIhadaahaa WcbeqaaiaajY7aaaaaaa@3667@
,
d
x
ν
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaiizaiaadIhadaahaa Wcbeqaaiaaj27aaaaaaa@3666@
are components of a quasi-infinitesimal
displacement four-vector
Publication
date
:
2022-06
Source
Replaces:
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5:
symmetric
tensor of the second order
defining the geometric properties of
space-time
by the relation
d
s
2
=
∑
μ
,
ν
g
μ
ν
d
x
μ
d
x
ν
, where
d
s
2
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaciizaiaadohadaahaa Wcbeqaaiaaikdaaaaaaa@3671@
is a
squared interval
and
d
x
μ
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaciizaiaadIhadaahaa WcbeqaaiaajY7aaaaaaa@3667@
,
d
x
ν
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaiizaiaadIhadaahaa Wcbeqaaiaaj27aaaaaaa@3666@
are components of a quasi-infinitesimal
displacement four-vector