Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form

Autor: Nguyen, Hoang Ky
Rok vydání: 2022
Předmět:
Zdroj: Phys. Rev. D 106, 104004 (2022) (set to be online for November 03, 2022)
Druh dokumentu: Working Paper
DOI: 10.1103/PhysRevD.106.104004
Popis: Some sixty years ago Buchdahl pioneered a program in search of static spherically symmetric vacua for pure $R^{2}$ gravity (Nuovo Cimento, Vol 23, No 1, pp 141-157 (1962); [https://link.springer.com/article/10.1007/BF02733549]). Surpassing several obstacles, his work culminated in a non-linear second-order ordinary differential equation (ODE) which required being solved. However Buchdahl deemed the ODE intractable and prematurely abandoned his pursuit for an analytical solution. We have finally managed to break this six-decades-old impasse and accomplish his goal. Reformulating the Buchdahl ODE, we obtain a novel exhaustive class of metrics (which we shall call the Buchdahl-inspired metrics hereafter) in a compact form. We are able to verify ex post, via direct inspection, that the metric obtained herein satisfies the $R^{2}$ vacuo field equation, hence establishing its validity. We show why the Buchdahl-inspired metrics, which exhibit non-constant scalar curvature, defeat a Lichnerowicz-type no-go theorem, previously proved for quadratic gravity, by evading the overly strong restriction on the asymptotic falloff of the metric at spatial infinity. Our novel solution thereby completes Buchdahl's six-decades-old program. We also explore the mathematical properties of the Buchdahl-inspired metrics in the limit of small k and in the region around the coordinate origin.
Comment: This recently accepted paper is the first installment of a three-paper "Beyond SdS spacetimes" series, being under review at Phys. Rev. D. Link to PRD: https://journals.aps.org/prd/accepted/e907dQ06D1310133219288223264bd8b133a125f1
Databáze: arXiv
Externí odkaz: