Pure Gauss-Bonnet Research Articles

Pure Gauss–Bonnet NUT black hole solution: I

We obtain an exact Lambda -vacuum solution in the pure Gauss–Bonnet gravity with NUT charge in six dimension, with horizon having the product topology of S^{(2)} times S^{(2)}. We discuss its horizon and singularity structure, and consequently arrive at parameter windows for its physical viability. It turns out that for the curvatures to remain function of r alone for NUT black hole spacetime, horizon topology has to be product of S^{(2)} spheres. This is true for Einstein as well as for pure Gauss–Bonnet gravity, and perhaps would hold good for higher order pure Lovelock as well.

Circular orbits around higher dimensional Einstein and pure Gauss–Bonnet rotating black holes

In this paper we study circular orbits around higher dimensional rotating Myers–Perry and pure Gauss–Bonnet (GB) black holes. It turns out that for the former there occurs no potential well to harbour bound and thereby stable circular orbits. The only circular orbits that could occur are all unstable and their radius is bounded from the below by that of the photon circular orbit. On the other hand bound and stable circular orbits do exist for pure GB/Lovelock rotating black holes (the metric is though not an exact solution of pure Lovelock vacuum equation but it satisfies the equation in the leading order and has all the desired properties) in dimensions, 2 N + 2 ≤ D ≤ 4 N (for N = 2 pure GB in D = 6 , 7 , 8 ) where N is the degree of Lovelock polynomial. Thus bound and stable circular orbits could exist around higher dimensional rotating black holes only for pure GB/Lovelock gravity. This property is a nice discriminator between Myers–Perry and pure GB/Lovelock rotating black holes.

New exact even-dimensional pure Lovelock interior metrics

While it is well known that Nth-order pure Lovelock spacetimes of dimension $$d = 2N + 1$$ do not admit bounded compact objects, this is not the case for the $$d = 2N + 2$$ case. In the $$N = 2$$ , pure Gauss–Bonnet gravity exact models for the Vaidya–Tikekar superdense star ansatz are investigated and new classes of metrics are discovered in terms of elementary functions. An astrophysical model of a stellar distribution that is consistent with the physical expectations extrapolated from four-dimensional gravity is exhibited. The isothermal sphere is re-considered and found to be inconsistent in pure Lovelock theory. Finally, we briefly consider the case of the third-order Lovelock polynomial term and several classes of exact solutions emerge.

Thin-shell wormholes with ordinary matter in pure Gauss-Bonnet gravity

In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by N⩾5-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.

Perfect fluid filled universe in odd dimensional pure Lovelock gravity

It is well known that d = 2 N + 1 dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that 2 N + 1 pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with d = 2 N + 1 that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ( N = 2 ) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all N and d = 2 N + 1 . In particular the special case N = 3 , d = 7 has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.

Pure Lovelock black holes in dimensions d=3N+1 are stable

In this paper we show that pure Lovelock static Schwarzschild's analogue black hole in dimensions $d>3N+1$, where $N$ is the degree of Lovelock polynomial action, is stable even though pure Gauss-Bonnet $N=2$ black hole is unstable in dimension $d<7$. We also discuss and compare quasinormal modes for pure Lovelock and the corresponding Einstein black hole in the same dimension. We find that perturbations decay with characteristic time which is weakly dimensional dependent as it depends only on the gravitational potential of the background solution, while frequency of oscillations however depend on the dimension. Also we show that spectrum of perturbations is not isospectral except in $d=4$.

Topological black holes in pure Gauss-Bonnet gravity and phase transitions

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordstr\"{o}m AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the St\"{u}ckelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.

Pure Lovelock Kasner metrics

We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single Nth order Lovelock term in the action in dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in the critical odd dimension, , is kinematic, i.e. we may define an analogue Lovelock–Riemann tensor that vanishes in vacuum for , yet the Riemann curvature is non-zero. We completely classify isotropic and vacuum Kasner metrics for this class of theories in several isotropy types. The different families can be characterized by means of certain higher order 4th rank tensors. We also analyze in detail the space of vacuum solutions for five- and six dimensional pure Gauss–Bonnet theory. It possesses an interesting and illuminating geometric structure and symmetries that carry over to the general case. We also comment on a closely related family of exponential solutions and on the possibility of solutions with complex Kasner exponents. We show that the latter imply the existence of closed timelike curves in the geometry.

Energetics and optical properties of 6-dimensional rotating black hole in pure Gauss–Bonnet gravity

We study physical processes around a rotating black hole in pure Gauss-Bonnet (GB) gravity. In pure GB gravity, gravitational potential has slower fall off as compared to the corresponding Einstein potential in the same dimension. It is therefore expected that the energetics of pure GB black hole would be weaker, and our analysis bears out that the efficiency of energy extraction by Penrose process is increased to $25.8\%$ and particle acceleration is increased to $55.28\%$, and optical shadow of the black hole is decreased. These are the distinguishing in principle observable features of pure GB black hole.

New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term

A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to $ {{\mathcal{R}}_{uv}}^2-\frac{1}{3}{{\mathcal{R}}^2} $ , which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

R2corrections to asymptotically Lifshitz spacetimes

We study $R^{2}$ corrections to five-dimensional asymptotically Lifshitz spacetimes by adding Gauss-Bonnet terms in the effective action. For the zero-temperature backgrounds we obtain exact solutions in both pure Gauss-Bonnet gravity and Gauss-Bonnet gravity with non-trivial matter. The dynamical exponent undergoes finite renormalization in the latter case. For the finite-temperature backgrounds we obtain black brane solutions perturbatively and calculate the ratio of shear viscosity to entropy density $\eta/s$. The KSS bound is still violated but unlike the relativistic counterparts, the causality of the boundary field theory cannot be taken as a constraint.

Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter black hole with higher derivative gauge corrections

The local and global thermal phase structure for asymptotically anti-de Sitter black holes charged under an abelian gauge group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all three possible horizon topologies — spherical, flat or hyperbolic. For spherical horizons, new metastable configurations are exhibited both for the pure Gauss-Bonnet theory as well as the pure higher derivative gauge theory and combinations thereof. In the pure Gauss-Bonnet theory with negative coefficient and five or more spatial dimensions, two locally thermally stable black hole solutions are found for a given temperature. Either one or both of them may be thermally favored over the anti-de Sitter vacuum — corresponding to a single or a double decay channel for the metastable black hole. Similar metastable configurations are uncovered for the theory with pure quartic field strength corrections, as well combinations of the two types of corrections, in three or more spatial dimensions. Finally, a secondary Hawking-Page transition between the smaller thermally favored black hole and thermal anti-de Sitter space is observed when both corrections are turned on and their couplings are both positive.

Shear viscosity from Gauss-Bonnet gravity with a dilaton coupling

We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a nontrivial dilaton using anti-de Sitter/conformal field theory. We find that the dilaton field has a nontrivial contribution to the ratio of shear viscosity over entropy density, and, after imposing a causal constraint for the boundary field theory, the new lower bound $4/25\ensuremath{\pi}$, obtained from pure Gauss-Bonnet gravity, may have a small violation.

“Mass without mass” from thin shells in Gauss-Bonnet gravity

Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well-known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the nonsingular components of the bulk stress tensor on the sides of the thin shell. The equations are applied to spherically symmetric thin shells in the vacuum. The shells are part of the vacuum; they carry no energy tensor. We classify these solutions of ``thin shells of nothingness'' in the pure Gauss-Bonnet theory. There are three types of solutions, with one, zero, or two asymptotic regions, respectively. The third kind of solutions are wormholes. Although vacuum solutions, they have the appearance of mass in the asymptotic regions. It is striking that in this theory, exotic matter is not needed in order for wormholes to exist---they can exist even with no matter.

Lie-algebra expansions, Chern–Simons theories and the Einstein–Hilbert Lagrangian

Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus nonminimally coupled matter. The deformed system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like General Relativity plus corrections due to matter sources, it is shown that the nonminimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions.