Note on the strong hyperbolicity of f(R) gravity with dynamical shifts

被引：3

作者：

Cao, Li-Ming ^{[1
,2
,3
]}

Wu, Liang-Bi ^{[2
,3
]}

机构：

[1] Peng Huanwu Ctr Fundamental Theory, Hefei 230026, Anhui, Peoples R China

[2] Univ Sci & Technol China, Interdisciplinary Ctr Theoret Study, Hefei 230026, Anhui, Peoples R China

[3] Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China

来源：

PHYSICAL REVIEW D | 2022年 / 105卷 / 12期

基金：

中国国家自然科学基金;

关键词：

GRAVITATIONAL-WAVES; GENERAL-RELATIVITY; FORMULATION; EVOLUTION;

D O I：

10.1103/PhysRevD.105.124062

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

The well-posedness of the gravitational equations of f(R) gravity is studied in this paper. Three formulations of the f(R) gravity with dynamical shifts [which are all based on the Arnowitt-Deser-Misner (ADM) formalism of the equations] are investigated. These three formulations arc all proved to be strongly hyperbolic by pseudodifferential reduction. The first one is the Baumagarte-Shapiro-Shibata-Nakamura formulation with the so-called "hyperbolic K-driver" condition and the "hyperbolic Gamma driver" condition. The second one is the ADM formulation with modified harmonic gauge conditions. We find that the equations arc not strong hyperbolic in traditional Z4 formulation for f(R) gravity. So, in the third formulation, we improve the Z4 formulation, and show these equations are strong hyperbolic with modified harmonic gauge conditions.

引用

页数：12

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