Higher Curvature Corrections Research Articles

Spinning black strings in five-dimensional Einstein–Gauss–Bonnet gravity

We construct generalizations of the D=5 Kerr black string by including higher curvature corrections to the gravity action in the form of the Gauss–Bonnet density. These uniform black strings satisfy a generalized Smarr relation and share the basic properties of the Einstein gravity solutions. However, they exist only up to a maximal value of the Gauss–Bonnet coupling constant, which depends on the solutionsʼ mass and angular momentum.

Choptuik’s critical phenomenon in Einstein-Gauss-Bonnet gravity

We investigate the effects of higher order curvature corrections to Einstein's Gravity on the critical phenomenon near the black hole threshold, namely the Choptuik phenomenon. We simulate numerically a five dimensional spherically symmetric gravitational collapse of massless scalar field in Einstein-Gauss-Bonnet gravity towards a black hole formation threshold. When the curvature is sufficiently large the additional higher order terms, affect the evolution of the whole system. Since high curvature characterizes the region when the critical behavior takes place this critical behavior is destroyed. Both the self similarity and the mass scaling relation disappear. Instead we find a different behavior near the black hole threshold, which depends on the coupling constant of the higher order terms. The new features include a change of the sign of the Ricci scalar on the origin which indicates changes in the local geometry of space-time, and never occurs in classical general relativity collapse, and oscillations with a constant rather than with a diminishing length scale.

Mass inflation in f(R) gravity — A conjecture on the resolution of the mass inflation singularity

We study gravitational collapse of a charged black hole in f(R) gravity using double-null formalism. We require cosmological stability to f(R) models; we used the Starobinsky model and the R+(1/2)cR2 model. Charged black holes in f(R) gravity can have a new type of singularity due to higher curvature corrections, the so-called f(R)-induced singularity, although it is highly model-dependent. As the advanced time increases, the internal structure will approach the Cauchy horizon, which may not be an inner apparent horizon.There is mass inflation as one approaches the Cauchy horizon and hence the Cauchy horizon may be a curvature singularity with nonzero area. However, the Ricci scalar is finite for an out-going null observer. This can be integrated as follows: Cosmologically stable higher curvature corrections of the Ricci scalar made it bounded even in the presence of mass inflation.Finally, we conjecture that if there is a general action including general higher curvature corrections with cosmological stability, then the corrections can make all curvature components finite even in the presence of mass inflation. This might help us to resolve the problem of inner horizon instability of regular black hole models.

Holographic Screens and Transport Coefficients in the Fluid-Gravity Correspondence

We consider in the framework of the fluid-gravity correspondence the dynamics of hypersurfaces located in the holographic radial direction at r = r(0). We prove that these hypersurfaces evolve, to all orders in the derivative expansion and including all higher curvature corrections, according to the same hydrodynamics equations with identical transport coefficients. The analysis is carried out for normal fluids as well as for superfluids. Consequently, this proves the exactness of the bulk viscosity formula derived by us [J. High Energy Phys. 06 (2011) 007] via the null horizon dynamics.

Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory

We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.

Gravity localization in non-minimally coupled scalar thick braneworlds with a Gauss-Bonnet term

We consider a warped five-dimensional thick braneworld with a four-dimensional Poincaré invariant space-time in the framework of scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term in the bulk. Scalar field and higher curvature corrections to the background equations as well as the perturbed equations are shown. A relationship between 4-dimensional and 5-dimensional Planck masses is studied in general terms. By imposing finiteness of the 4-dimensional Planck mass and regularity of the geometry, the localization properties of the tensor modes of the first order perturbed geometry are analized for an important class of solutions motivated by models with scalar fields which are minimally coupled to gravity. In order to study the gravity localization properties for this model, the normalizability condition for the lowest level of the tensor fluctuations is analized. We see that for the class of solutions examined, gravity in 4 dimensions is recovered if the curvature invariants are regular and Planck masses are finite.

Holographic superconductors and higher curvature corrections

We study a fully backreacted holographic model of a four-dimensional superconductor by including a higher curvature interaction in the bulk action. We study how the critical temperature and the field theory condensate vary in this model and conclude that positive higher curvature couplings make the condensation harder. We also compute the conductivity, finding significant deviations from the conjectured universal frequency gap to critical temperature ratio.

Long life of Gauss-Bonnet corrected black holes

Dictated by the string theory and various higher dimensional scenarios, black holes in $D>4$-dimensional space-times must have higher curvature corrections. The first and dominant term is quadratic in curvature, and called the Gauss-Bonnet (GB) term. We shall show that although the Gauss-Bonnet correction changes black hole's geometry only softly, the emission of gravitons is suppressed by many orders even at quite small values of the GB coupling. The huge suppression of the graviton emission is due to the multiplication of the two effects: the quick cooling of the black hole when one turns on the GB coupling and the exponential decreasing of the grey-body factor of the tensor type of gravitons at small and moderate energies. At higher $D$ the tensor gravitons emission is dominant, so that the overall lifetime of black holes with Gauss-Bonnet corrections is many orders larger than was expected. This effect should be relevant for the future experiments at the Large Hadron Collider (LHC). Keywords: Hawking radiation, black hole evaporation.

Causality in AdS/CFT and Lovelock theory

We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS space-time. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.

Global solutions for higher-dimensional stretched small black holes

Small black holes in heterotic string theory have vanishing horizon area at the supergravity level, but the horizon is stretched to the finite radius $AdS_2 \times S^{D-2}$ geometry once higher curvature corrections are turned on. This has been demonstrated to give good agreement with microscopic entropy counting. Previous considerations, however, were based on the classical local solutions valid only in the vicinity of the event horizon. Here we address the question of global existence of extremal black holes in the $D$-dimensional Einstein-Maxwell-Dilaton theory with the Gauss-Bonnet term introducing a variable dilaton coupling $a$ as a parameter. We show that asymptotically flat black holes exist only in a bounded region of the dilaton couplings $0 < a < a_{\rm cr}$ where $a_{\rm cr}$ depends on $D$. For $D \geq 5$ (but not for $D = 4$) the allowed range of $a$ includes the heterotic string values. For $a > a_{\rm cr}$ numerical solutions meet weak naked singularities at finite radii $r = r_{\rm cusp}$ (spherical cusps), where the scalar curvature diverges as $|r - r_{\rm cusp}|^{-1/2}$. For $D \geq 7$ cusps are met in pairs, so that solutions can be formally extended to asymptotically flat infinity choosing a suitable integration variable. We show, however, that radial geodesics cannot be continued through the cusp singularities, so such a continuation is unphysical.

Holographic superconductors with higher curvature corrections

We study (3+1)-dimensional holographic superconductors in Einstein-Gauss-Bonnet gravity both numerically and analytically. It is found that higher curvature corrections make condensation harder. We give an analytic proof of this result, and directly demonstrate an analytic approximation method that explains the qualitative features of superconductors as well as giving quantitatively good numerical results. We also calculate conductivity and ωg/Tc, for ωg and Tc the gap in the frequency dependent conductivity and the critical temperature respectively. It turns out that the `universal' behaviour of conductivity, ωg/Tc ≃ 8, is not stable to the higher curvature corrections. In the appendix, for completeness, we show our analytic method can also explain (2+1)-dimensional superconductors.

On the trail of dark energy

I present some recent results on efforts to constraint the variation of dark energy as a function of redshift. In particular I concentrate on observational determinations of the expansion history H ( z ) . I review a formalism that makes use of quantities similar to the Horizon-flow parameters in inflation and is general enough that can deal with multiscalar quintessence scenarios, exotic matter components, and higher order curvature corrections to General Relativity. I show how the shape of the dark energy potential can be recovered non parametrically using this formalism and I present approximations analogous to the ones relevant to slow-roll inflation. Since presently available data do not allow a non-parametric and exact reconstruction of the potential, I consider a general parametric description. This reconstruction can also be used in other approaches followed in the literature (e.g., the reconstruction of the redshift evolution of the dark energy equation of state w ( z ) ). Using observations of passively evolving galaxies and supernova data I derive constraints on the dark energy potential shape in the redshift range 0.1 z 1.8 . Our findings show that at the 1σ level the potential is consistent with being constant, although at the same level of confidence variations cannot be excluded with current data.

Viable Singularity-Freef(R)Gravity without a Cosmological Constant

Several authors have argued that self-consistent f(R) gravity models distinct from the cold dark matter model with a cosmological constant (LambdaCDM) are almost ruled out. Confronting such claims, we present a particular two-parameter f(R) model that (a) is cosmologically viable and distinguishable from LambdaCDM, (b) is compatible with the existence of relativistic stars, (c) is free of singularities of the Ricci scalar during the cosmological evolution, and (d) allows the addition of high-curvature corrections that could be relevant for inflation.

Can higher curvature corrections cure the singularity problem inf(R)gravity?

Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $\ensuremath{\mu}\ensuremath{\lesssim}{10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{GeV}$, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.

Extremal dyonic black holes inD=4Gauss-Bonnet gravity

We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant $a$. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of $a$ to continuous domains in the plane $(a,{q}_{m})$ where ${q}_{m}$ is the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordstr\"om solution but not to the extremal dyons of the Einstein-Maxwell-dilaton theory. Both solutions have the same dependence of the horizon radius in terms of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature-corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.

Higher curvature corrections to primordial fluctuations in slow-roll inflation

We study higher curvature corrections to the scalar spectral index, the tensor spectralindex, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find thatthere are cases where the higher curvature corrections cannot be negligible in the dynamicsof the scalar field, although they are always negligible energetically. Indeed, it turns outthat the tensor-to-scalar ratio could be enhanced and the tensor spectral indexcould be blue due to the Gauss–Bonnet term. We estimate the degree of circularpolarization of gravitational waves generated during the slow-roll inflation. Weargue that the circular polarization could be observable with the help of both theGauss–Bonnet and the parity violating terms. We also present several examples to revealobservational implications of higher curvature corrections for chaotic inflationarymodels.

Hydrogen atom in Palatini theories of gravity

We study the effects that the gravitational interaction of $f(R)$ theories of gravity in Palatini formalism has on the stationary states of the hydrogen atom. We show that the role of gravity in this system is very important for Lagrangians $f(R)$ with terms that grow at low curvatures, which have been proposed to explain the accelerated expansion rate of the universe. In fact, new gravitationally induced terms in the atomic Hamiltonian generate a strong backreaction that is incompatible with the very existence of bound states. In fact, in the $1/R$ model, hydrogen disintegrates in less than two hours. The universe that we observe is, therefore, incompatible with that kind of gravitational interaction. Lagrangians with high curvature corrections do not lead to such instabilities.

Entropy function and universality of entropy-area relation for small black holes

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy ${S}_{BH}$ of the small black hole is proportional to its horizon area $A$. In particular, we find a universal result that ${S}_{BH}=A/2G$, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

Dark energy generated from a (super-) string effective action with higher-order curvature corrections and a dynamical dilaton

We investigate the possibility of a dark energy universe emerging from an action with higher-order string loop corrections to Einstein gravity in the presence of a massless dilaton. These curvature corrections (up to $R^4$ order) are different depending upon the type of (super)string model which is considered. We find in fact that Type II, heterotic, and bosonic strings respond differently to dark energy. A dark energy solution is shown to exist in the case of the bosonic string, while the other two theories do not lead to realistic dark energy universes. Detailed analysis of the dynamical stability of the de-Sitter solution is presented for the case of a bosonic string. A general prescription for the construction of a de-Sitter solution for the low-energy (super)string effective action is also indicated. Beyond the low-energy (super)string effective action, when the higher-curvature correction coefficients depend on the dilaton, the reconstruction of the theory from the universe expansion history is done with a corresponding prescription for the scalar potentials.

A note on causality constraining higher curvature corrections to gravity

We show that causality constrains the sign of quartic Riemann corrections to the Einstein–Hilbert action. Our constraint constitutes a restriction on candidate theories of quantum gravity.