In Einstein-Gauss-Bonnet gravity, for a group of warped product spacetimes, we get a generalized master equation for the perturbation of tensor type. We show that the "effective metric" or "acoustic metric" for the tensor perturbation equation can be defined even without a static condition. Since this master equation does not depend on the mode expansion, the hyperbolicity and causality of the tensor perturbation equation can be investigated for every mode of the perturbation. Based on the master equation, we study the hyperbolicity and causality for all relavent vacuum solutions of this theory. For each solution, we give the exact hyperbolic condition of the tensor perturbation equations. Our approach can also applied to dynamical spacetimes, and Vaidya spacetime have been investigated as an example.
We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coup…
We study the role of the Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action on the Kaluza-Klien modes and their interactions for different bulk fields which enable one to study various phenomenological implications of string loop corrected Gauss-Bonnet modified warped geometry model in one canvas. We have explicitly derived a phenomenological bound on the Gauss-Bonnet parameter so that the required Planck to TeV scale hierarchy can be achieved through the warp factor in the light of recently discovered Higgs like boson at 125 GeV. Moreover due to the presence…
We study the axial quasinormal modes of hairy black holes in Gauss-Bonnet gravity with massive self-interacting scalar field. Two coupling functions of the scalar field to the Gauss-Bonnet invariant are adopted with one of them leading to black hole scalarization. The axial perturbations are studied via time evolution of the perturbation equation, and the effect of the scalar field mass and the self-interaction constant on the oscillation frequency and damping time is examined. We study as well the effect of nonzero scalar field potential on the critical point at which the perturbation equatio…
We study the axial perturbations of spontaneously scalarized black holes in Einstein-Gauss-Bonnet (EGB) theories. We consider the nodeless solutions of the fundamental branch of the model studied in [1], which possesses a region of radially stable configurations, as shown in [2]. Here we show that almost all of the radially stable black holes are also stable under axial perturbations. When the axial potential is no longer strictly positive, we make use of the S-deformation method to show stability. As for the radial perturbations, hyperbolicity is lost below a certain critical horizon size for…
Spontaneous scalarization of black holes in scalar-Gauss-Bonnet (sGB) gravity is a very interesting phenomenon allowing black holes to circumvent the no-hair theorem and acquire scalar hair while leaving the weak field regime of the theory practically unaltered. It was recently shown that if we allow for a different form of the coupling between the scalar field and the Gauss-Bonnet invariant, a new type of scalarization is possible beyond the standard one that can be excited only nonlinearly. In this case the spectrum of black hole solutions can be more complicated, naturally opening the quest…
In this paper we study the hyperbolicity of the equations of motion for the most general Horndeski theory of gravity in a generic "weak field" background. We first show that a special case of this theory, namely Einstein-dilaton-Gauss-Bonnet gravity, fails to be strongly hyperbolic in any generalised harmonic gauge. We then complete the proof that the most general Horndeski theory which, for weak fields, is strongly hyperbolic in a generalised harmonic gauge is simply a "k-essence" theory coupled to Einstein gravity and that adding any more general Horndeski term will result in a weakly, but n…
We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases evolution of the system, treated as a hyperbolic initial boundary value problem, leads to the equations of motion becoming ill-posed when the elliptic region forms. No singularities or discontinuities are encountered on the corresponding effective "Cauchy horizon". Therefore it…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet coupling, the base manifold must be Einstein with an additional scalar restriction. The geometry of the boundary can be relaxed only when the Gauss-Bonnet coupling is related with the cosmological and Newton constants, so that the theory admits a unique maximally symmetric solution. This additional freedo…
Exact vacuum solutions with a nontrivial torsion for the Einstein-Gauss-Bonnet theory in five dimensions are constructed. We consider a class of static metrics whose spacelike section is a warped product of the real line with a nontrivial base manifold endowed with a fully antisymmetric torsion. It is shown requiring solutions of this sort to exist, fixes the Gauss-Bonnet coupling such that the Lagrangian can be written as a Chern-Simons form. The metric describes black holes with an arbitrary, but fixed, base manifold. It is shown that requiring its ground state to possess unbroken supersymme…
Quasi-Normal Mode Ringing of Binary Black Hole Mergers in Scalar-Gauss-Bonnet Gravity
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Eberhard Karls University of Tübingen（蒂宾根大学）；INRNE - Bulgarian Academy of Sciences（保加利亚科学院核研究与核能研究所）；Sofia University “St. Kliment Ohridski”（索菲亚大学）；Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon ge…
We derive field equations of Gauss-Bonnet gravity in 4 dimensions after dimensional reduction of the action and demonstrate that in this scenario Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein sphere the fifth force is negligibly small compared to the gravitational force. We also investigate stability of the spherically symmetric solution, clarify the vocabulary used in the literature about the hyperbolicity of the equation and the ghost-Laplacian stability conditions. We find superluminal behavior of the perturbation of the fiel…
We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of motion, without approximation, for general spacetimes. While we concentrate on the specific example of shift-symmetric ESGB, our methods, which make use of a recently proposed modification to the generalized harmonic formulation, should be generally applicable to all Horndeski theories of gravity (including general relativity). We demonstrate that these methods c…
In this paper we perform a systematic classification of the regimes of cosmological dynamics in Einstein-Gauss-Bonnet gravity with generic values of the coupling constants. We consider a manifold which is a warped product of a four dimensional Friedmann-Robertson-Walker space-time with a $D$-dimensional Euclidean compact constant curvature space with two independent scale factors. A numerical analysis of the time evolution as function of the coupling constants and of the curvatures of the spatial section and of the extra dimension is performed. We describe the distribution of the regimes over …
Binary neutron star mergers, which can lead to less massive black holes relative to other known astrophysical channels, have the potential to probe modifications to general relativity that arise at smaller curvature scales compared to more massive compact object binaries. As a representative example of this, here we study binary neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity using evolutions of the full, nonperturbative evolution equations. We find that the impact on the inspiral is small, even at large values of the modified gravity coupling (as expected, as neut…
An exhaustive classification of certain class of static solutions for the five-dimensional Einstein-Gauss-Bonnet theory in vacuum is presented. The class of metrics under consideration is such that the spacelike section is a warped product of the real line with a nontrivial base manifold. It is shown that for generic values of the coupling constants the base manifold must be necessarily of constant curvature, and the solution reduces to the topological extension of the Boulware-Deser metric. It is also shown that the base manifold admits a wider class of geometries for the special case when th…
We consider warped five-dimensional thick braneworlds with four-dimensional Poincaré invariance originated from bulk scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term. The background field equations as well as the perturbed equations are investigated. A relationship between 4D and 5D Planck masses is studied in general terms. By imposing finiteness of the 4D Planck mass and regularity of the geometry, the localization properties of the tensor modes of the perturbed geometry are analyzed to first order, for a wide class of solutions. In order to explore the gravity localiz…
We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n (\ge 5)$ dimensions. The spacetimes are given as a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-dimensional constant curvature space. We establish a generalized Birkhoff's theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on $K^{n-2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Cher…
Thick branes and fermion localization in five-dimensional $f(T,T_G)$ gravity
Huzhou Normal University（湖州师范学院）；Secretaria da Educação do Ceará (SEDUC), Coordenadoria Regional de Desenvolvimento da Educação (CREDE 9)（塞阿拉州教育厅（SEDUC），区域教育发展协调局（CREDE 9））；Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza（帕拉伊巴联邦大学，自然与精确科学中心）；Centro de Investigación en Computación, Instituto Politécnico Nacional（国家理工学院计算研究中心）；National Observatory of Athens（雅典国家天文台）；University of Science and Technology of China（中国科学技术大学）；Universidad Católica del Norte（北天主教大学）
In this article spacelike hypersurfaces immersed in twisted product spacetimes $I\times_f F$ with complete fiber are studied. Several conditions ensuring global hyperbolicity are presented, as well as a relation that needs to hold on each spacelike hypersurface in $I\times_f F$ for it to be a simple warped product. When the fiber is assumed to be closed (compact and without boundary) and the ambient spacetime has a suitable expanding behaviour, non-existence results for constant mean curvature hypersurfaces are obtained. Under the same hypothesis, a characterization of compact maximal hypersur…
