What do we mean by pure gravity

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what do we mean by "pure gravity"

1-what we mean by "pure gravity" and "gravity coupled to matter"?
2- why pure gravity characterized by c=0 (c: central charge), and what is the conceptual meaning of central charge
regards
 
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Central charges appear when one has normal ordering issues, or when Lagrangians transform to total derivatives under symmetry transformations. The first situation appears in e.g. string theory upon quantization. An example of the second situation is the Bargmann algebra, which is a centrally-extended Galilei algebra; the commutator between spatial translations and boosts is then centrally extended. This is related to the fact that the Lagrangian of a non-rel. point paricle transforms under boosts as a total time derivative.
 
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