Disformal map and Petrov classification in modified gravity

被引：9

作者：

Ben Achour, Jibril ^{[1
]}

De Felice, Antonio ^{[2
]}

Gorji, Mohammad Ali ^{[2
]}

Mukohyama, Shinji ^{[2
,3
]}

Pookkillath, Masroor C. ^{[2
]}

机构：

[1] Arnold Sommerfeld Ctr Theoret Phys, Munich, Germany

[2] Kyoto Univ, Ctr Gravitat Phys, Yukawa Inst Theoret Phys, Kyoto 6068502, Japan

[3] Univ Tokyo, Kavli Inst Phys & Math Universe WPI, Kashiwa, Chiba 2778583, Japan

来源：

JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS | 2021年 / 10期

基金：

日本学术振兴会;

关键词：

modified gravity; GR black holes; GENERAL-RELATIVITY; MULTIPOLE MOMENTS;

D O I：

10.1088/1475-7516/2021/10/067

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

Disformal transformation provides a map relating different scalar-tensor and vector-tensor theories and gives access to a powerful solution-generating method in modified gravity. In view of the vast family of new solutions one can achieve, it is crucial to design suitable tools to guide their construction. In this work, we address this question by revisiting the Petrov classification of disformally constructed solutions in modified gravity theories. We provide close formulas which relate the principal nulls directions as well as the Weyl scalars before and after the disformal transformation. These formulas allow one to capture if and how the Petrov type of a given seed geometry changes under a disformal transformation. Finally, we apply our general setup to three relevant disformally constructed solutions for which the seeds are respectively homogeneous and isotropic, static spherically symmetric and stationary axisymmetric. For the first two cases, we show that the Petrov type O and Petrov type D remain unchanged after a disformal transformation while we show that disformed Kerr black hole is no longer of type D but of general Petrov type I. The results presented in this work should serve as a new toolkit when constructing and comparing new disformal solutions in modified gravity.

引用

页数：32

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