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Recently, motivated by certain loop quantum gravity inspired corrections, itwas shown that for spherically symmetric midisuperspace models infinitely manysecond derivative theories of gravity exist (as revealed by the presence ofthree arbitrary functions in the corresponding Lagrangian/Hamiltonian) and notjust those allowed by spherically symmetric general relativity. This freedomcan be interpreted as the freedom to accommodate certain quantum gravitycorrections in these models even in the absence of higher curvature terms (at asemi-classical level, at least). For a particular choice of the arbitraryfunctions it is shown that the new theories map to spherically symmetricgeneral relativity in arbitrary number of (integer) dimensions thus explicitlydemonstrating that when working with midisuperspace models, one loses theinformation about the dimensionality of the full spacetime. In addition, it isshown that these new theories can accommodate scenarios of fractional spacetimedimensions as well as those of emergent spacetime dimensions -- a possibilitysuggested by various approaches to quantum gravity.

Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions