Gauss-Bonnet Black Holes Research Articles

ENTROPY QUANTIZATION OF D-DIMENSIONAL GAUSS–BONNET BLACK HOLES

The entropy and area spectra for D-dimensional Gauss–Bonnet black holes are investigated from two different approaches, which are the quasinormal modes approach developed by Hod, Kunstatter and Maggiore, and the very recent method proposed by Ropotenko. The two methods give the same results, which show that the entropy spectrum of Gauss–Bonnet black holes is equidistantly quantized with spacing ΔS = 2πℏ, while the area spectrum is not equally spaced.

Hamilton–Jacobi counterterms for Einstein–Gauss–Bonnet gravity

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton–Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein–Gauss–Bonnet black holes.

Study on internal structure of Maxwell-Gauss-Bonnet black hole

The influence of the Maxwell field on a static, asymptotically flat and spherically-symmetric Gauss-Bonnet black hole is considered. Numerical computations suggest that if the charge increases beyond a critical value, the inner determinant singularity is replaced by an inner singular horizon.

Transport coefficients from extremal Gauss-Bonnet black holes

We calculate the shear viscosity of strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature with nonzero chemical potential. We find that the ratio of the shear viscosity over the entropy density is $1/4\pi$, which is in accordance with the zero temperature limit of the ratio at nonzero temperatures. We also calculate the DC conductivity for this system at zero temperature and find that the real part of the DC conductivity vanishes up to a delta function, which is similar to the result in Einstein gravity. We show that at zero temperature, we can still have the conclusion that the shear viscosity is fully determined by the effective coupling of transverse gravitons in a kind of theories that the effective action of transverse gravitons can be written into a form of minimally coupled scalars with a deformed effective coupling.

BOUNCING BRANEWORLD WITH BORN–INFELD AND GAUSS–BONNET

We show the existence of some bouncing cosmological solutions in the braneworld scenario. More specifically, we consider a dynamical three-brane in the background of Born–Infeld and electrically charged Gauss–Bonnet black hole. We find that, in certain range of parameter space, the brane universe, at least classically, never shrinks to a zero size, resulting in a singularity-free cosmology within the classical domain.

Einstein–Gauss–Bonnet black holes in de Sitter spacetime and the quasilocal formalism

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein–Gauss–Bonnet theory by using the counterterm method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d⩽7. We apply this technique for several different solutions in Einstein–Gauss–Bonnet theory with a positive cosmological constant. Apart from known solutions, we consider also d=5 vacuum rotating black holes with equal magnitude angular momenta. These solutions are constructed numerically within a nonperturbative approach, by directly solving the Einstein–Gauss–Bonnet equations with suitable boundary conditions.

Internal structure of a Maxwell-Gauss-Bonnet black hole

The influence of the Maxwell field on a static, asymptotically flat, and spherically-symmetric Gauss-Bonnet black hole is considered. Numerical computations suggest that if the charge increases beyond a critical value, the inner determinant singularity is replaced by an inner singular horizon.

Logarithmic corrections to entropy for black holes with a hyperbolic horizon

We compute logarithmic corrections to entropy for black holes with a hyperbolic horizon. For this purpose, we introduce the topological black hole and Martinez–Troncoso–Zanelli (MTZ) black holes in four dimensions, while in five dimensions, the topological black holes and Gauss–Bonnet black hole with negative coupling are considered. As they stand, logarithmic corrections are problematic because small black holes with positive heat capacity have negative energies. However, introducing the background state of an extremal black hole, the logarithmic corrections are performed for a black hole with a hyperbolic horizon.

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norström-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.

Kerr-Gauss-Bonnet black holes: Exact analytical solution

Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.

Slowly rotating charged Gauss-Bonnet black holes in AdS spaces

Rotating charged Gauss-Bonnet black hole solutions in higher dimensional ($d&gt;4$), asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit. The angular momentum, magnetic dipole moment, and the gyromagnetic ratio of the black holes are calculated and it turns out that the Gauss-Bonnet term does not affect the gyromagnetic ratio.

The mystery of the asymptotic quasinormal modes of Gauss–Bonnet black holes with small Gauss–Bonnet coupling

We analyse the quasinormal modes of D-dimensional Schwarzschild black holes with the Gauss–Bonnet correction in the large damping limit and show that standard analytic techniques cannot be applied in a straightforward manner to the case of infinite damping. However, by using a combination of analytic and numeric techniques, which can only be applied to vector perturbations, we are able to calculate the quasinormal mode frequencies of vector perturbations for a range where the damping is large but finite. We show that in this ‘intermediate’ damping region, the famous ln(3) appears in the real part of the quasinormal mode frequency. In our calculations, the Gauss–Bonnet coupling, α, is taken to be much smaller than the parameter μ, which is related to the black hole mass. Even though our calculations are done for the simplest case of five spacetime dimensions, it is shown that the results hold in every dimension greater than four by substituting an approximate expression for the metric in the calculations, which is valid in the intermediate damping region for small α.

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.

Global properties of charged dilatonic Gauss-Bonnet black holes

We study the phase space of the spherically symmetric solutions of Einstein-Maxwell-Gauss-Bonnet system nonminimally coupled to a scalar field and prove the existence of solutions with unusual asymptotics in addition to asymptotically flat ones. We also find new dyonic solutions of dilatonic Einstein-Maxwell theory.

Scalar field evolution in Gauss-Bonnet black holes

It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $\ensuremath{\Lambda}$ and the Gauss-Bonnet coupling $\ensuremath{\alpha}$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on $\ensuremath{\alpha}$, even though the black hole metric contains $\ensuremath{\alpha}$ as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.

Global properties of dilatonic Gauss–Bonnet black holes

We study the phase space of the spherically symmetric solutions of the Einstein–Gauss–Bonnet system nonminimally coupled to a scalar field and show that in four dimensions the only regular black-hole solutions are asymptotically flat.

Holography in Einstein Gauss-Bonnet Gravity

We investigate a holographic relation between Einstein Gauss-Bonnet gravity in $n$ dimensions and its dual field theory in ($n-1$) dimensions. We briefly review the AdS/CFT correspondence for the entropy in the $n$-dimensional Einstein gravity and consider its extension to the case of the $n$-dimensional Einstein Gauss-Bonnet gravity. We show that there is a holographic relation between entropies of an Einstein Gauss-Bonnet black hole in the bulk and the corresponding radiation on the brane in the high temperature limit. In particular, we find that the Hubble entropy evaluated when the brane crosses the horizon also coincides with the black hole entropy in the high temperature limit.

Gauss-Bonnet black holes in dS spaces

We study the thermodynamic properties associated with the black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension $d=5,$ the stable small black hole disappears, and the Gauss-Bonnet black hole is always unstable quantum mechanically when $d&gt;~6.$ On the other hand, the cosmological horizon is found to be always locally stable independent of the spacetime dimension. But the solution is not globally preferred; instead, the pure de Sitter space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on the value of the coefficient, beyond which the gravity theory is not well defined. As a result, there is not only an upper bound on the size of black hole horizon radius at which the black hole horizon and cosmological horizon coincide with each other, but also a lower bound depending on the Gauss-Bonnet coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable and the cosmological horizon is always stable; furthermore, as in the case of the positive coefficient, the pure de Sitter space is still globally preferred. This result is consistent with the argument that the pure de Sitter space corresponds to an UV fixed point of dual field theory.

Conserved charges in Einstein Gauss–Bonnet theory

Using Noether's identities, we define a superpotential with respect to a background for the Einstein Gauss–Bonnet theory of gravity. As an example, we show that its associated conserved charge yields the mass-energy of a D-dimensional Gauss–Bonnet black hole in an anti-de Sitter spacetime.

Gauss–Bonnet black holes at the LHC: beyond the dimensionality of space

The Gauss–Bonnet invariant is one of the most promising candidates for a quadratic curvature correction to the Einstein action in expansions of supersymmetric string theory. We study the evaporation of such Schwarzschild–Gauss–Bonnet black holes which could be formed at future colliders if the Planck scale is of order of TeV, as predicted by some modern brane world models. We show that, beyond the dimensionality of space, the corresponding coupling constant could be measured by the LHC. This opens new windows for physics investigation in spite of the possible screening of microphysics due to the event horizon.