We give analytical arguments and demonstrate numerically the existence of black hole solutions of the 4D Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of "secondary type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the "nohair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function fðϕÞ. We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for fðϕÞ. We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions fðϕÞ. DOI: 10.1103/PhysRevLett.120.131102 Introduction.-The existence or not of black holes associated with a nontrivial scalar field in the exterior region has attracted the attention of researchers over a period of many decades. Early on, a no-hair theorem [1] appeared that excluded static black holes with a scalar field, but this was soon outdated by the discovery of black holes with Yang-Mills [2] or Skyrme fields [3]. The emergence of additional solutions where the scalar field had a conformal coupling to gravity [4] led to the formulation of a novel nohair theorem [5] (for a review, see [6]). Recently, this argument was extended to the case of standard scalar-tensor theories [7], and a new form was proposed that covers the case of Galileon fields [8].However, both novel forms of the no-hair theorem [5,8] were shown to be evaded: the former in the context of the Einstein-dilaton-Gauss-Bonnet theory [9] and the latter in a special case of shift-symmetric Galileon theories [10][11][12]. A common feature of the above theories was the presence of the quadratic Gauss-Bonnet (GB) term defined as R 2 GB ¼ R μνρσ R μνρσ − 4R μν R μν þ R 2 , in terms of the Riemann tensor R μνρσ , the Ricci tensor R μν , and the Ricci scalar R. In both cases, basic requirements of the no-hair theorems were invalidated, and this paved the way for the construction of the counterexamples.Here, we consider a general class of scalar-GB theories, of which the cases [9,11] constitute particular examples. We demonstrate that black-hole solutions, with a regular horizon and an asymptotically flat limit, may in fact be constructed for a large class of such theories under mild only constraints on the coupling function fðϕÞ between the scalar field and the GB term. We address the requirements of both the old and novel no-hair theorems, and we show

We start by reviewing the existing literature on the creation of black holes during highenergy particle collisions, both in the absence and in the presence of extra, compact, spacelike dimensions. Then, we discuss in detail the properties of the produced higherdimensional black holes, namely the horizon radius, temperature and life-time, as well as the physics that governs the evaporation of these objects, through the emission of Hawking radiation. We first study the emission of visible Hawking radiation on the brane: we derive a master equation for the propagation of fields with arbitrary spin in the induced-on-thebrane black hole background, and we review all existing results in the literature for the emission of scalars, fermions and gauge bosons during the spin-down and Schwarzschild phases of the life of the black hole. Both analytical and numerical results for the greybody factors and radiation spectra are reviewed and exact results for the number and type of fields emitted on the brane as a function of the dimensionality of spacetime are discussed. We finally study the emission of Hawking radiation in the bulk: greybody factors and radiation spectra are presented for the emission of scalar modes, and the ratio of the missing energy over the visible one is calculated for different values of the number of extra dimensions.

We start our analysis by deriving a master equation that describes the motion of a field with arbitrary spin s on a 3-brane embedded in a non-rotating, uncharged (4 + n)-dimensional black hole background. By numerical analysis, we derive exact results for the greybody factors and emission rates for scalars, fermions and gauge bosons emitted directly on the brane, for all energy regimes and for an arbitrary number n of extra dimensions. The relative emissivities on the brane for different types of particles are computed and their dependence on the dimensionality of spacetime is demonstrated -we therefore conclude that both the amount and the type of radiation emitted can be used for the determination of n if the Hawking radiation from these black holes is observed. The emission of scalar modes in the bulk from the same black holes is also studied and the relative bulk-to-brane energy emissivity is accurately computed. We demonstrate that this quantity varies considerably with n but always remains smaller than unity -this provides firm support to earlier arguments made by Emparan, Horowitz and Myers.The above relation involves the volume of the extra dimensions, V ∼ R n , under the assumption that R is the common size of all n extra compact dimensions. Therefore, if the volume of the internal space is large (i.e. if R ≫ ℓ P l , where ℓ P l = 10 −33 cm is the Planck length) then M * can be substantially lower than M P l .In the regime r ≪ R, the extra dimensions 'open up' and gravity becomes strong. Hence, Newton's law for the gravitational interactions in this regime is modified, with the gravitational potential assuming a 1/r n+1 dependence on the radial separation between two massive particles. Experiments which measure the gravitational inversesquare law at short scales can provide limits on the size of the extra dimensions, or equivalently on the value of the fundamental scale M * ; for n = 2 such measurements give M * > 3.5 TeV [4] (the n = 1 case has already been excluded by astronomical data). Since gravitons can propagate both in the bulk and on the brane, massive Kaluza-Klein (KK) graviton states can modify both the cross sections of Standard Model particle interactions and astrophysical or cosmological processes. The absence of signatures of production of either real or virtual KK gravitons at colliders puts a relatively weak lower limit on M * -from 1.45 TeV (for n = 2) to 0.6 TeV (n = 6) [5]. Much more stringent constraints arise if one considers astrophysical or cosmological processes; ignoring the systematic errors, these constraints exclude by far even the n = 3 case, while allowing models with M *

We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalized Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.