TY - JOUR

T1 - Could the black hole singularity be a field singularity?

AU - Domènech, Guillem

AU - Naruko, Atsushi

AU - Sasaki, Misao

AU - Wetterich, Christof

N1 - Publisher Copyright: © 2020 World Scientific Publishing Company.

PY - 2020/2

Y1 - 2020/2

N2 - In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

AB - In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

KW - General relativity

KW - black hole singularity

KW - scalar hair

KW - scalar-tensor theory

UR - http://www.scopus.com/inward/record.url?scp=85081546674&partnerID=8YFLogxK

U2 - 10.1142/S0218271820500261

DO - 10.1142/S0218271820500261

M3 - Article

VL - 29

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

SN - 0218-2718

IS - 3

M1 - 2050026

ER -