Lovelock Coefficients Research Articles

Dynamical wormholes in Lovelock gravity

In this study we present evolving wormhole configurations in third-order Lovelock gravity and investigate the possibility that these solutions satisfy the energy conditions. Using a generalized Friedmann-Robertson-Walker spacetime, we derive evolving wormhole geometries by considering a constraint on the Ricci scalar. In standard cosmological models, the Ricci scalar is independent of the radial coordinate $r$ and is only a function of time. We use this property to introduce dynamic wormhole solutions expanding in an inflationary cosmological background and explore the effects of higher-order Lovelock terms on the dynamics of such wormholes. Our analysis shows that for suitable third-order Lovelock coefficients, there are wormhole solutions that respect the weak energy condition (WEC). In addition to this, we also present other wormhole solutions that satisfy the WEC throughout their respective evolution.

Criticality and extended phase space thermodynamics of AdS black holes in higher curvature massive gravity

Considering de Rham–Gabadadze–Tolley theory of massive gravity coupled with (ghost free) higher curvature terms arisen from the Lovelock Lagrangian, we obtain charged-AdS black hole solutions in diverse dimensions. We compute thermodynamic quantities in the extended phase space by considering the variations of the negative cosmological constant, Lovelock coefficients (alpha _{i}) and massive couplings (c_{i}). We also prove that such variations are necessary in order to satisfy the extended first law of thermodynamics as well as associated Smarr formula. In addition, by performing a comprehensive thermal stability analysis for the topological black hole solutions, we show that in which regions thermally stable phases exist. Calculations show the results are radically different from those in the Einstein gravity. We find that the phase structure and critical behavior of topological AdS black holes are drastically restricted by the geometry of the event horizon. We also show that the phase structure of AdS black holes with non-compact (hyperbolic) horizon could give birth to three critical points corresponds to a reverse van der Waals behavior for phase transition which is accompanied with two distinct van der Waals phase transitions. For black holes with the spherical horizon, the van der Waals, reentrant and analogue of solid/liquid/gas phase transitions are observed.

Hawking radiation and entropy of a black hole in Lovelock-Born-Infeld gravity from the quantum tunneling approach**Supported by Guangdong Natural Science Foundation (2016A030307051, 2015A030313789)

The tunneling radiation of particles from black holes in Lovelock-Born-Infeld (LBI) gravity is studied by using the Parikh-Wilczek (PW) method, and the emission rate of a particle is calculated. It is shown that the emission spectrum deviates from the purely thermal spectrum but is consistent with an underlying unitary theory. Compared to the conventional tunneling rate related to the increment of black hole entropy, the entropy of the black hole in LBI gravity is obtained. The entropy does not obey the area law unless all the Lovelock coefficients equal zero, but it satisfies the first law of thermodynamics and is in accordance with earlier results. It is distinctly shown that the PW tunneling framework is related to the thermodynamic laws of the black hole.

Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

In this paper, we consider third order Lovelock gravity with a cosmological constant term in an n-dimensional spacetime $\mathcal{M}^{4}\times \mathcal{K}^{n-4}$, where $\mathcal{K}^{n-4} $ is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum $\mathcal{K}^{n-4} $ space. Applying the latter constraint, we determine the second and third order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and $\Lambda$, we obtain the 4-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by $\rho =(\gamma p-\tau )/[\omega (1+\gamma )]$, we find the exact solution for the shape function which represents both asymptotically flat and non-flat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a 4-dimensional spacetime, implies a negative effective cosmological constant.

Extended phase space of black holes in Lovelock gravity with nonlinear electrodynamics

In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We also show how considering cosmological constant, nonlinearity and Lovelock parameters as thermodynamical variables will modify Smarr formula and first law of thermodynamics. In addition, we study the behavior of universal ratio of $\frac{P_{c}v_{c}}{T_{c}}$ for different values of nonlinearity power of electrodynamics as well as the Lovelock coefficients.

Higher-dimensional thin-shell wormholes in third-order Lovelock gravity

In this work, we explore asymptotically flat charged thin-shell wormholes of third order Lovelock gravity in higher dimensions, taking into account the cut-and-paste technique. Using the generalized junction conditions, we determine the energy-momentum tensor of these solutions on the shell, and explore the issue of the energy conditions and the amount of normal matter that supports these thin-shell wormholes. Our analysis shows that for negative second order and positive third-order Lovelock coefficients, there are thin-shell wormhole solutions that respect the weak energy condition. In this case, the amount of normal matter increases as the third-order Lovelock coefficient decreases. We also find novel solutions which possess specific regions where the energy conditions are satisfied for the case of a positive second order and negative third-order Lovelock coefficients. Finally, a linear stability analysis in higher dimensions around the static solutions is carried out. Considering a specific cold equation of state, we find a wide range of stability regions.

Lovelock black holes in a string cloud background

We present an exact static, spherically symmetric black hole solution to the third-order Lovelock gravity with a string cloud background in seven dimensions for the special case when the second- and third-order Lovelock coefficients are related via $$\tilde{\alpha }^2_2=3\tilde{\alpha }_3\;(\equiv \alpha ^2)$$ . Further, we examine thermodynamic properties of this black hole to obtain exact expressions for mass, temperature, heat capacity and entropy, and also perform the thermodynamic stability analysis. We see that a string cloud background has a profound influence on the horizon structure, thermodynamic properties, and the stability of black holes. Interestingly the entropy of the black hole is unaffected due to the string cloud background. However, the critical solution for thermodynamic stability is affected by the string cloud background.

Lovelock thin-shell wormholes

We construct the asymptotically flat charged thin-shell wormholes of Lovelock gravity in seven dimensions by cut-and-paste technique, and apply the generalized junction conditions in order to calculate the energy-momentum tensor of these wormholes on the shell. We find that for negative second order and positive third order Lovelock coefficients, there are thin-shell wormholes that respect the weak energy condition. In this case, the amount of normal matter decreases as the third order Lovelock coefficient increases. For positive second and third order Lovelock coefficients, the weak energy condition is violated and the amount of exotic matter decreases as the charge increases. Finally, we perform a linear stability analysis against a symmetry preserving perturbation, and find that the wormholes are stable provided the derivative of surface pressure density with respect to surface energy density is negative and the throat radius is chosen suitable.

Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss—Bonnet coefficient α2 < 0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k = −1, the third order Lovelock black holes are thermodynamically stable for the whole range r+. When k = 1, we found that the black hole has an intermediate unstable phase for D = 7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient is under a critical value. For D ≥ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient is under a critical value for D = 8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon do not depend on the Lovelock coefficients and are the same as those of black holes in general gravity.

Thermodynamics of Lovelock-Lifshitz black branes

We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients.

Thermodynamic instability of black holes of third order Lovelock gravity

In this paper, we compute the mass and the temperature of the uncharged black holes of third order Lovelock gravity and compute the entropy through the use of first law of thermodynamics. We perform a stability analysis by studying the curves of temperature versus the mass parameter, and find that there exists an intermediate thermodynamically unstable phase for black holes with hyperbolic horizon. The existence of this unstable phase for the uncharged topological black holes of third order Lovelock gravity does not occur in the lower order Lovelock gravity. We also perform a stability analysis for a spherical, 7-dimensional black hole of Lovelock gravity and find that while these kinds of black holes for small values of Lovelock coefficients have an intermediate unstable phase, they are stable for large values of Lovelock coefficients. We also find that there exists an intermediate unstable phase for these black holes in higher dimensions. This stability analysis shows that the thermodynamic stability of black holes with curved horizons is not a robust feature of all the generalized theories of gravity.

Lorentzian wormholes in Lovelock gravity

In this paper, we introduce the $n$-dimensional Lorentzian wormhole solutions of third order Lovelock gravity. In contrast to Einstein gravity and as in the case of Gauss-Bonnet gravity, we find that the wormhole throat radius, $r_0$, has a lower limit that depends on the Lovelock coefficients, the dimensionality of the spacetime and the shape function. We study the conditions of having normal matter near the throat, and find that the matter near the throat can be normal for the region $r_0 \leq r \leq r_{\max}$, where $r_{\max}$ depends on the Lovelock coefficients and the shape function. We also find that the third order Lovelock term with negative coupling constant enlarges the radius of the region of normal matter, and conclude that the higher order Lovelock terms with negative coupling constants enlarge the region of normal matter near the throat.

Magnetic branes in third order Lovelock-Born-Infeld gravity

Considering both the nonlinear invariant terms constructed by the electromagnetic field and the Riemann tensor in gravity action, we obtain a new class of $(n+1)$-dimensional magnetic brane solutions in third order Lovelock-Born-Infeld gravity. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\ensuremath{\delta}$. We find that, as the Born-Infeld parameter decreases, which is a measure of the increase of the nonlinearity of the electromagnetic field, the deficit angle increases. We generalize this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the Born-Infeld parameter, which is evident from the fact that the effects of the nonlinearity of the electromagnetic fields on the boundary at infinity are wiped away. We also find that the properties of our solution, such as deficit angle, are independent of Lovelock coefficients.

Topological black holes in the dimensionally continued gravity

We investigate topological black holes in a special class of Lovelock gravity. In odd dimensions, the action is the Chern-Simons form for the anti--de Sitter group. In even dimensions, it is the Euler density constructed with the Lorentz part of the anti--de Sitter curvature tensor. The Lovelock coefficients are reduced to two independent parameters: the cosmological constant and gravitational constant. The event horizons of these topological black holes may have constant positive, zero, or negative curvature. Their thermodynamics is analyzed and electrically charged topological black holes are also considered. We emphasize the differences due to the different curvatures of event horizons.

Dynamically generated four-dimensional models in Lovelock cosmology

We consider a class of $D$-dimensional Lovelock models provided with a positive cosmological constant whose induced metric is given by the product of the metrics of a three-dimensional (external) and a $D\ensuremath{-}4$-dimensional (internal) maximally symmetric space. When all the Lovelock coefficients are non-negative, we show that these models admit classical solutions with a constant internal scale factor, and that for these solutions the evolution of the external dimensions can be described by a four-dimensional Einstein theory with a positive effective Hilbert-Einstein coefficient and non-negative effective cosmological constant. In addition, we prove that the perturbative formalism for the treatment of the Lovelock model is always well defined in the region of the gravitational configuration space covered by the considered solutions with a constant internal scale factor. We also examine the dynamically generated four-dimensional theory that is obtained when the internal scale factor remains constant, and discuss the role played by the no-boundary condition in the corresponding process of reducing the degrees of freedom of the minisuperspace model.

Lovelock gravity and classical wormholes

The authors first considers Lovelock gravity as a perturbative theory and then apply the results to a D-dimensional homogeneous and isotropic minisuperspace model provided with matter fields for which there exist instanton solutions. He develops a general procedure to analyse these solutions, which may be interpreted as representing tunnelling. Adding some reasonable restrictions to the Lovelock coefficients, it is shown that the Lovelock corrections preserve the essential feature of Einstein gravity models, giving rise to an essentially unique instanton solution.