Quantum corrections to the Schwarzschild metric and reparametrization transformations

TL;DR

This paper investigates the reparametrization invariance of quantum corrections to the Schwarzschild metric, demonstrating that only the complete set of diagrams yields invariant results, highlighting the importance of reparametrization independence in quantum gravity calculations.

Contribution

The paper shows that quantum corrections to the Schwarzschild metric are reparametrization invariant only when all relevant diagrams are included, clarifying discrepancies in previous results.

Findings

Incomplete diagram sets lead to non-invariant corrections.

Complete diagram sets ensure reparametrization invariance.

Reparametrization invariance is crucial for consistent quantum gravity results.

Abstract

Quantum corrections to the Schwarzschild metric generated by loop diagrams have been considered by Bjerrum-Bohr, Donoghue, and Holstein (BHD) [Phys. Rev. D68, 084005 (2003)], and Khriplovich and Kirilin (KK) [J. Exp. Theor. Phys. 98, 1063 (2004)]. Though the same field variables in a covariant gauge are used, the results obtained differ from one another. The reason is that the different sets of diagrams have been used. Here we will argue that the quantum corrections to metric must be independent of the choice of field variables, i.e., must be reparametrization invariant. Using simple reparametrization transformation, we will show that the contribution considered by BDH, is not invariant under it. Meanwhile the contribution of the complete set of the diagrams, considered by KK, satisfies the requirement of the invariance.