6 Conclusions, Open Issues and Future Problems

As we have seen, the quantization of midisuperspace models has been – and still is – a very useful test bed to understand many different methods and techniques proposed for the quantization of GR. In this respect the models described in this Living Review will certainly be of use in the near future, in particular to explore new avenues to the quantization of gravity both in the geometrodynamical approach and in LQG. These models have also been used with some success to extract qualitative physical results that are expected to be present in full quantum gravity (black hole mass quantization, Hawking radiation, unitarity of quantum evolution, microcausality, singularity resolution, semiclassical limit, …). Certainly a complete full quantization of the symmetry reductions described here will shed light on many methods and approaches and may be useful to arrive at a fully functioning theory of quantum gravity.

Among the open problems that we think should be considered we provide the following list:

We expect that a lot of progress on these issues will happen in the near future. We will report on them in future updates of this Living Review.

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