## Generalized uncertainty principle, extra dimensions and holography.(English)Zbl 1048.83009

Summary: We consider uncertainty principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such generalized uncertainty principles in $$4+n$$ dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.

### MSC:

 83C45 Quantization of the gravitational field 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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