- #Regular expression not space only in angular 5 full
- #Regular expression not space only in angular 5 free
#Regular expression not space only in angular 5 free
by energy-momentum: Only a general expression containing arbitrary functions, or rather a definite one free of any ambiguities, even of additive constants), or on the list of the criteria of reasonableness of such expressions.
Nowadays, the state of the art is typically postmodern: Although there are several promising and useful suggestions, we have not only no ultimate, generally accepted expression for the energy-momentum and especially for the angular momentum, but there is no consensus in the relativity community even on general questions (for example, what should we mean e.g. However, contrary to the high expectations of the eighties, finding an appropriate quasi-local notion of energy-momentum has proven to be surprisingly difficult. Therefore, a solid theoretical foundation of the quasi-local conserved quantities is needed. However, in such calculations all the domains are finite, i.e. In numerical calculations conserved quantities (or at least those for which balance equations can be derived) are used to control the errors. The correct, ultimate formulation of black hole thermodynamics should probably be based on quasi-locally defined internal energy, entropy, angular momentum etc.
#Regular expression not space only in angular 5 full
For example, they may play a central role in the proof of the full Penrose inequality (as they have already played in the proof of the Riemannian version of this inequality). Moreover, finding an appropriate notion of energy-momentum and angular momentum would be important from the point of view of applications as well. Obviously, the quasi-local quantities could provide a more detailed characterization of the states of the gravitational ‘field’ than the global ones, so they (together with more general quasi-local observables) would be interesting in their own right. This success inspired the more ambitious claim to associate energy (or rather energy-momentum and, ultimately, angular momentum too) to extended but finite spacetime domains, i.e. It is precisely its positivity that makes this notion not only important (because of its theoretical significance), but a useful tool as well in the everyday practice of working relativists. During the last 25 years one of the greatest achievements in classical general relativity is certainly the proof of the positivity of the total gravitational energy, both at spatial and null infinity.