Pure-connection gravity and anisotropic singularities

TL;DR

This paper explores a class of chiral modified gravity theories described by a connection field, demonstrating how specific modifications can resolve black-hole and anisotropic singularities by maintaining regularity of the fundamental connection.

Contribution

It reviews how simple modifications in chiral gravity theories can eliminate singularities in black-hole and Kasner solutions, emphasizing the role of the connection field.

Findings

Modified theories resolve Schwarzschild singularity with a regular connection

Kasner anisotropic singularities are smoothed out in these models

The fundamental connection remains regular in the modified solutions

Abstract

In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. They are most properly described by a connection field, with space-time metric being a secondary and derived concept. All these theories have the same number of degrees of freedom as general relativity, which is the only parity-invariant member of this family. Modifications of general relativity can be arranged so as to become important in regions with large curvature. In this paper we review how a certain simple modification of this sort can resolve the Schwarzschild black-hole and Kasner anisotropic singularities of general relativity. In the corresponding solutions, the fundamental connection field is regular in space-time.