Linear perturbations of Einstein-Gauss-Bonnet black holes
Résumé
We study linear perturbations about non rotating black hole solutions in scalar-tensor theories, more specifically Horndeski theories. We consider two particular theories that admit known hairy black hole solutions. The first one, Einstein-scalar-Gauss-Bonnet theory, contains a Gauss-Bonnet term coupled to a scalar field, and its black hole solution is given as a perturbative expansion in a small parameter that measures the deviation from general relativity. The second one, known as 4-dimensional-Einstein-Gauss-Bonnet theory, can be seen as a compactification of higher-dimensional Lovelock theories and admits an exact black hole solution. We study both axial and polar perturbations about these solutions and write their equations of motion as a first-order (radial) system of differential equations, which enables us to study the asymptotic behaviours of the perturbations at infinity and at the horizon following an algorithm we developed recently. For the axial perturbations, we also obtain effective Schrödinger-like equations with explicit expressions for the potentials and the propagation speeds. We see that while the Einstein-scalar-Gauss-Bonnet solution has well-behaved perturbations, the solution of the 4-dimensional-Einstein-Gauss-Bonnet theory exhibits unusual asymptotic behaviour of its perturbations near its horizon and at infinity, which makes the definition of ingoing and outgoing modes impossible. This indicates that the dynamics of these perturbations strongly differs from the general relativity case and seems pathological.
Mots clés
Gauss-Bonnet-Lovelock-Horndeski-Palatini etc gravity theories
Gravitational waves in GR and beyond: theory
modified gravity
perturbation: linear
perturbation: axial
field theory: scalar
perturbation: asymptotic behavior
black hole: hair
Gauss-Bonnet term
general relativity
horizon
differential equations
gravitation: scalar tensor
Lovelock
compactification
field equations
higher-dimensional
propagation
Einstein
gravitation: model
coupling: scalar
dimension: 4
higher-order: 1
Schroedinger equation
velocity
Exact solutions
black holes and black hole thermodynamics in GR and beyond
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