## Abstract

In previous works we suggested to consider a (3 + 1)D quantum

gravitational field as an “evolution” of a (2 + 1)D renormalized quan-

tum gravitational field along the direction of the gravitational force.

The starting point of the suggestion is derivation of a unique hyper-

surface which looks effectively like (2 + 1)D from the point of view of

Einstein equations in (3 + 1)D. In this paper we derive such unique

hypersurfaces for different kinds of stationary spherical metrics. We

find that these hypersurfaces exist whenever all the components of the

gravitational force field vanish on the hypersurface. We discuss the

implication of this result and the necessary further work.

gravitational field as an “evolution” of a (2 + 1)D renormalized quan-

tum gravitational field along the direction of the gravitational force.

The starting point of the suggestion is derivation of a unique hyper-

surface which looks effectively like (2 + 1)D from the point of view of

Einstein equations in (3 + 1)D. In this paper we derive such unique

hypersurfaces for different kinds of stationary spherical metrics. We

find that these hypersurfaces exist whenever all the components of the

gravitational force field vanish on the hypersurface. We discuss the

implication of this result and the necessary further work.

Original language | American English |
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Article number | 1910.13522 |

Number of pages | 26 |

Journal | arXiv preprint |

State | Published - Feb 2021 |