Corners of gravity: the case of gravity as a constrained BF theory

TL;DR

This paper examines the boundary structure and charges in gravity formulated as a constrained BF theory, highlighting effects of the cosmological constant and topological terms, with applications to AdS--Schwarzschild solutions.

Contribution

It introduces the cosmological constant and topological terms into the constrained BF formulation of gravity and analyzes their effects on boundary charges.

Findings

Charges are affected by the cosmological constant and topological terms.

Established charge formulas are consistent with known results.

Application to AdS--Schwarzschild solution yields correct charge values.

Abstract

Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the influence of the topological terms present in the action of this theory. Established formulas for charges resemble previously obtained ones, but we show that they are affected by the presence of the cosmological constant and topological terms. As an example we discuss the charges in the case of the AdS--Schwarzschild solution and we find that the charges give correct values.