I have found a paper on this theme
https://reader.elsevier.com/reader/sd/pii/S0370269318303721?token=34ECEDF0773E63690703BBAEC3492D69034DDBB3101F1A8F68C11E2A63F92F11B7222BCA2EA154DD90FD55773D62F1B0
It would be interesting to know you opinion about it.
I am not right, ##D_i\sqrt{\gamma}\ne\partial_i \sqrt{\gamma}##, because ##\sqrt{\gamma}## is not a scalar, but density of a scalar. See https://en.wikipedia.org/wiki/Covariant_derivative#Coordinate_description. Thus, all the expressions for momentum constraint are equivalent.
Ravi, thank you.
Let me ask, why we could not write ##D_i\sqrt {\gamma}=\partial_i \sqrt {\gamma}\sim\gamma^{ab}\partial_i\gamma_{ab}\ne0##? I ask this because it is well known that ##d\gamma\sim\gamma^{ab}d\gamma_{ab}##, where ##d## is usual differencial. From the other hand it seems that...
Momentum constraint in GR in ADM formalism is written in the form
$$\mathcal M_i=\gamma_{ij}D_k\pi^{kj},~~~~~~~~~~(1a)$$ or equivalently
$$\mathcal M_i=D_k\pi^{k}_i,~~~~~~~~~~(1b)$$ where
##\pi^{ij}=-\gamma^{1/2}\left(K^{ij}-\gamma^{ij}K\right)~##, ##K=\gamma^{ij}K_{ij}~##, ##\gamma=\det...
After suggestion to search for black holes at LHC one can ask how much
black hole is similar to the elementary particle?
Can we apply second quantization to the field of black holes?
Can we talk, for instance, about cosmological black holes production in analogy with
cosmological...