TY - JOUR

T1 - Where and why does Einstein-scalar-Gauss-Bonnet theory break down

AU - Hegade K. R, Abhishek

AU - Ripley, Justin L.

AU - Yunes, Nicolás

N1 - Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/2/15

Y1 - 2023/2/15

N2 - We present a systematic exploration of the loss of predictivity in Einstein-scalar-Gauss-Bonnet (ESGB) gravity in spherical symmetry. We first formulate a gauge covariant method of characterizing the breakdown of the hyperbolicity of the equations of motion in the theory. With this formalism, we show that strong geodesic focusing leads to the breakdown of hyperbolicity, and the latter is unrelated to the violation of the null convergence condition. We then numerically study the hyperbolicity of the equations during gravitational collapse for two specific ESGB gravity theories: "shift symmetric Gauss-Bonnet gravity"and a version of the theory that admits "spontaneously scalarized"black holes. We devise a "phase space"model to describe the end states for a given class of initial data. Using our phase space picture, we demonstrate that the two theories we consider remain predictive (hyperbolic) for a range of GB couplings. The range of couplings, however, is small, and thus, the presence of spontaneously scalarized solutions requires fine-tuning of initial data. Our results, therefore, cast doubt as to whether scalarized black hole solutions can be realistically realized in nature even if ESGB gravity happened to be the correct gravitational description.

AB - We present a systematic exploration of the loss of predictivity in Einstein-scalar-Gauss-Bonnet (ESGB) gravity in spherical symmetry. We first formulate a gauge covariant method of characterizing the breakdown of the hyperbolicity of the equations of motion in the theory. With this formalism, we show that strong geodesic focusing leads to the breakdown of hyperbolicity, and the latter is unrelated to the violation of the null convergence condition. We then numerically study the hyperbolicity of the equations during gravitational collapse for two specific ESGB gravity theories: "shift symmetric Gauss-Bonnet gravity"and a version of the theory that admits "spontaneously scalarized"black holes. We devise a "phase space"model to describe the end states for a given class of initial data. Using our phase space picture, we demonstrate that the two theories we consider remain predictive (hyperbolic) for a range of GB couplings. The range of couplings, however, is small, and thus, the presence of spontaneously scalarized solutions requires fine-tuning of initial data. Our results, therefore, cast doubt as to whether scalarized black hole solutions can be realistically realized in nature even if ESGB gravity happened to be the correct gravitational description.

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U2 - 10.1103/PhysRevD.107.044044

DO - 10.1103/PhysRevD.107.044044

M3 - Article

AN - SCOPUS:85149547644

SN - 2470-0010

VL - 107

JO - Physical Review D

JF - Physical Review D

IS - 4

M1 - 044044

ER -