Solutions In Gauss-Bonnet Gravity Research Articles

AdS black holes with higher derivative corrections in presence of string cloud

We consider asymptotically AdS black hole solutions in Einstein Gauss Bonnet gravity in presence of string clouds. As in the case of black hole solutions in Gauss Bonnet gravity, it admits three black hole solutions in presence of string clouds as well within a region of the parameter space. Using holography, we have studied the quark–antiquark distance and binding energy in the dual gauge theory.

Extending the scope of holographic mutual information and chaotic behavior

We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black $Dp$ branes, (ii) asymptotically Lifshitz black holes, and (iii) black $AdS$ solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.

“Cusp” solutions in Gauss-Bonnet gravity

Einstein-dilaton-Gauss-Bonnet gravity is investigated for the existence of solutions with mild singularities, not shielded by the event horizons. These still may have sense since presumably such singularities will be smoothed by corrections to the Einstein theory from quantum gravity/string theory. We show that gravity with a first-order correction, the Gauss-Bonnet term, gives rise to special types of singularities, which we call cusps, with powers 1/2 and 1/3 in a series expansion. The full space then can be split into several regions with classically impenetrable borders, and/or a flat asymptotic.

Thermodynamics of rotating solutions in Gauss-Bonnet-Maxwell gravity and the counterterm method

By a suitable transformation, we present the $(n+1)$-dimensional charged rotating solutions of Gauss-Bonnet gravity with a complete set of allowed rotation parameters which are real in the whole spacetime. We show that these charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. Using the surface terms that make the action well defined for Gauss-Bonnet gravity and the counterterm method for eliminating the divergences in action, we compute finite action of the solutions. We compute the conserved and thermodynamical quantities through the use of free energy and the counterterm method, and find that the two methods give the same results. We also find that these quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.

NUT-charged black holes in Gauss-Bonnet gravity

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in $d$ dimensions. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity having a curvature singularity at $r=N$ in the limit $% \alpha \to 0$. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial fibration only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.

Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case

We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\ensuremath{\Lambda}$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\ensuremath{\alpha}$ is non-negative and $4\stackrel{\texttildelow{}}{\ensuremath{\alpha}}/{\ensuremath{\ell}}^{2}\ensuremath{\le}1$ in order to define the relevant vacuum state. Solutions have the $(n\ensuremath{-}2)$-dimensional Euclidean submanifold whose curvature is $k=1$, 0, or $\ensuremath{-}1$. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of a spacetime. A branch singularity appears at the finite radius $r={r}_{b}>0$ for any mass parameter. There the Kretschmann invariant behaves as $O((r\ensuremath{-}{r}_{b}{)}^{\ensuremath{-}3})$, which is much milder than the divergent behavior of the central singularity in general relativity $O({r}^{\ensuremath{-}4(n\ensuremath{-}2)})$. In the $k=1$ and 0 cases plus-branch solutions have no horizon. In the $k=\ensuremath{-}1$ case, the radius of a horizon is restricted as ${r}_{h}<\sqrt{2\stackrel{\texttildelow{}}{\ensuremath{\alpha}}}$ (${r}_{h}>\sqrt{2\stackrel{\texttildelow{}}{\ensuremath{\alpha}}}$) in the plus (minus) branch. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. There are topological black hole solutions with zero and negative mass in the plus branch regardless of the sign of the cosmological constant. Although there is a maximum mass for black hole solutions in the plus branch for $k=\ensuremath{-}1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k=\ensuremath{-}1$ and $n\ensuremath{\ge}6$ have an inner black hole and inner and outer black hole horizons. In the $4\stackrel{\texttildelow{}}{\ensuremath{\alpha}}/{\ensuremath{\ell}}^{2}=1$ case, only a positive mass solution is allowed, otherwise the metric function takes a complex value. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.

Spacetime structure of static solutions in Gauss-Bonnet gravity: Neutral case

We study the spacetime structures of the static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-$\ensuremath{\Lambda}$ system systematically. We assume the Gauss-Bonnet coefficient $\ensuremath{\alpha}$ is non-negative and a cosmological constant is either positive, zero, or negative. The solutions have the $(n\ensuremath{-}2)$-dimensional Euclidean submanifold, which is the Einstein manifold with the curvature $k=1$, 0, and $\ensuremath{-}1$. We also assume $4\stackrel{\texttildelow{}}{\ensuremath{\alpha}}/{\ensuremath{\ell}}^{2}\ensuremath{\le}1$, where $\ensuremath{\ell}$ is the curvature radius, in order for the sourceless solution ($M=0$) to be defined. The general solutions are classified into plus and minus branches. The structures of the center, horizons, infinity, and the singular point depend on the parameters $\ensuremath{\alpha}$, ${\ensuremath{\ell}}^{2}$, $k$, $M$, and branches complicatedly so that a variety of global structures for the solutions are found. In our analysis, the $\stackrel{\texttildelow{}}{M}\mathrm{\text{\ensuremath{-}}}r$ diagram is used, which makes our consideration clear and enables easy understanding by visual effects. In the plus branch, all the solutions have the same asymptotic structure at infinity as that in general relativity with a negative cosmological constant. For the negative-mass parameter, a new type of singularity called the branch singularity appears at nonzero finite radius $r={r}_{b}>0$. The divergent behavior around the singularity in Gauss-Bonnet gravity is milder than that around the central singularity in general relativity. There are three types of horizons: inner, black hole, and cosmological. In the $k=1,0$ cases, the plus-branch solutions do not have any horizon. In the $k=\ensuremath{-}1$ case, the radius of the horizon is restricted as ${r}_{h}<\sqrt{2\stackrel{\texttildelow{}}{\ensuremath{\alpha}}}$ (${r}_{h}>\sqrt{2\stackrel{\texttildelow{}}{\ensuremath{\alpha}}}$) in the plus (minus) branch. The black hole solution with zero or negative mass exists in the plus branch even for the zero or positive cosmological constant. There is also the extreme black hole solution with positive mass. We briefly discuss the effect of the Gauss-Bonnet corrections on black hole formation in a collider and the possibility of the violation of the third law of the black hole thermodynamics.

Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant

In this paper I show that one can have asymptotically de Sitter, anti-de Sitter (AdS), and flat solutions in Gauss-Bonnet gravity without a cosmological constant term in field equations. First, I introduce static solutions whose three surfaces at fixed $r$ and $t$ have constant positive ($k=1$), negative ($k=\ensuremath{-}1$), or zero ($k=0$) curvature. I show that for $k=\ifmmode\pm\else\textpm\fi{}1$ one can have asymptotically de Sitter, AdS, and flat spacetimes, while for the case of $k=0$, one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. I also find that the geometrical mass of these five-dimensional spacetimes is $m+2\ensuremath{\alpha}|k|$, which is different from the geometrical mass $m$ of the solutions of Einstein gravity. This feature occurs only for the five-dimensional solutions, and is not repeated for the solutions of Gauss-Bonnet gravity in higher dimensions. Second, I add angular momentum to the static solutions with $k=0$, and introduce the asymptotically AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, I introduce a class of solutions which yields an asymptotically AdS spacetime with a longitudinal magnetic field, which presents a naked singularity, and generalize it to the case of magnetic rotating solutions with two rotation parameters.