Higher Curvature Terms Research Articles

Entanglement entropy for singular surfaces in hyperscaling violating theories

We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.

Radiating cylindrical gravitational collapse with structure scalars in f(R) gravity

In this paper, we discuss dynamical properties of dissipative collapsing cylindrical self-gravitating systems with account of f(R)=R+γR2+β1R3 gravity model. In this perspective, we see effects of higher curvature terms in the formulations of structure scalars already obtained from the orthogonal decomposition of Weyl curvature scalar in general relativity. We compute mass function by generalizing Misner-Sharp formalism and discuss the contribution of relaxation time in the radiating collapsing process. The contribution of scalar functions in the modeling of static anisotropic as well as isotropic fluid configurations are explored. We conclude that all static anisotropic cylindrical solutions of f(R) field equations can be written explicitly by means of triplet of these scalar functions.

N = 2 $$ \mathcal{N}=2 $$ dilaton-Weyl multiplets in 5D and Nishino-Rajpoot supergravity off-shell

We describe in detail the derivation of a superconformal off-shell formulation of the alternative $$ \mathcal{N}=2 $$ , d = 5 ungauged supergravity of Nishino and Rajpoot, coupled to n Abelian vector multiplets, using a general dilaton-Weyl multiplet. We generalize the vector multiplet coupling available in the literature and show under which assumptions that the scalar manifold reduces to the known case of SO(1, 1) × SO(1, n)/SO(n). As an application of the formalism we propose generalized vector multiplet coupled higher curvature terms, whose construction we sketch briefly.

Dynamics of relativistic fluids with structure scalars and $$\epsilon R^2$$ ϵ R 2 cosmology

This work is devoted to analyze the effects of $$f(R)$$ model on the dynamics of dissipative shearing viscous and anisotropic spherical matter configuration. In this framework, we develop scalar functions and link their expressions with various physical parameters and inflationary $$f(R)$$ dark source terms. We also relate the Weyl tensor as well as other matter variables with $$R+{\epsilon }R^2$$ background and obtain evolution equations for shear and expansion scalars. We conclude that structure scalars and $$f(R)$$ higher curvature terms have significant importance in the dynamics of self-gravitating systems.

Equilibrium configuration of perfect fluid orbiting around black holes in some classes of alternative gravity theories

The hydrodynamic behavior of perfect fluid orbiting around black holes in spherically symmetric spacetime for various alternative gravity theories has been investigated. For this purpose we have assumed a uniform distribution for the angular momentum density of the rotating perfect fluid. The contours of equipotential surfaces are illustrated in order to obtain the nature of inflow and outflow of matter. It has been noticed that the marginally stable circular orbits originating from decreasing angular momentum density lead to closed equipotential surfaces along with cusps, allowing the existence of accretion disks. On the other hand, the growing part of the angular momentum density exhibits central rings for which stable configurations are possible. However, inflow of matter is prohibited. Among the solutions discussed in this work, the charged F(R) gravity and Einstein–Maxwell–Gauss–Bonnet solutions exhibit inflow and outflow of matter with central rings present. These varied accretion disk structures of perfect fluid attribute astrophysical importance to these spacetimes. The effect of higher curvature terms predominantly arises from the region near the black hole horizon. Hence the structural difference of the accretion disk in modified gravity theories in comparison to general relativity may act as an experimental probe for these alternative gravity theories.

On M-theory fourfold vacua with higher curvature terms

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kähler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions.

A worldsheet theory for supergravity

We present a worldsheet theory that describes maps into a curved target space equipped with a B-field and dilaton. The conditions for the theory to be consistent at the quantum level can be computed exactly, and are that the target space fields obey the nonlinear d = 10 supergravity equations of motion, with no higher curvature terms. The path integral is constrained to obey a generalization of the scattering equations to curved space. Remarkably, the supergravity field equations emerge as quantum corrections to these curved space scattering equations.

Spherically symmetric brane spacetime with bulk $$f(\mathcal {R})$$ f ( R ) gravity

Introducing $f(\mathcal{R})$ term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with $f(\mathcal{R})$ gravity in the bulk.

Anisotropic scale invariant spacetimes and black holes in Zwei-Dreibein Gravity

We show that Zwei-Dreibein Gravity (ZDG), a bigravity theory recently proposed by Bergshoeff, de Haan, Hohm, Merbis, and Townsend in Phys.Rev.Lett. 111 (2013) 111102, admits exact solutions with anisotropic scale invariance. These type of geometries are the three-dimensional analogues of the spacetimes which were proposed as gravity duals for condensed matter systems. In particular, we find Schr\"odinger invariant spaces as well as Lifshitz spaces with arbitrary dynamical exponent $z$. We also find black holes that are asymptotically Lifshitz with $z=3$, showing that these (non-constant curvature) solutions of New Massive Gravity (NMG) are persistent after the introduction of the infinite tower of higher-curvature terms of ZDG, provided a renormalization of the parameters. Black holes in asymptotically warped Anti-de Sitter spaces are also found. Interestingly, in almost all the geometries studied in this work, the metric associated with the second dreibein turns out to be equivalent, up to a constant global factor, to the first one. This phenomenon has been previously observed in other bigravity theories in asymptotically flat and asymptotically Anti-de Sitter backgrounds. However, for the particular case of the $z=3$ Lifshitz black hole, here we found that the second metric corresponds to a different black hole that coincides with the former only in the asymptotic region. In fact, we find a new family of $z=3$ black holes that corresponds to a one-parameter deformation of the NMG solution.

Lovelock black holes with nonmaximally symmetric horizons

We present a new class of black hole solutions in third-order Lovelock gravity whose horizons are Einstein space with two supplementary conditions on their Weyl tensors. These solutions are obtained with the advantage of higher curvature terms appearing in Lovelock gravity. We find that while the solution of third-order Lovelock gravity with constant-curvature horizon in the absence of a mass parameter is the anti de Sitter (AdS) metric, this kind of solution with nonconstant- curvature horizon is only asymptotically AdS and may have horizon. We also find that one may have an extreme black hole with non-constant curvature horizon whose Ricci scalar is zero or a positive constant, while there is no such black hole with constant-curvature horizon. Furthermore, the thermodynamics of the black holes in the two cases of constant- and nonconstant-curvature horizons are different drastically. Specially, we consider the thermodynamics of black holes with vanishing Ricci scalar and find that in contrast to the case of black holes of Lovelock gravity with constant-curvature horizon, the area law of entropy is not satisfied. Finally, we investigate the stability of these black holes both locally and globally and find that while the black holes with constant curvature horizons are stable both locally and globally, those with nonconstant-curvature horizons have unstable phases.

Stability of a class of non-static axial self-gravitating systems in f(R) gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, $\Gamma_1$, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the $f(R)$ model affect the instability ranges.

Electromagnetic field and dynamical instability of collapse with CDTT model

This work investigates the dynamical instability of the relativistic self-gravitating collapsing fluids with electromagnetic field in Carrol–Duvvuri–Trodden–Turner (CDTT) f(R) model for spherical symmetric spacetime. In this scenario, we provide dynamical equations from the contracted Bianchi identities for the usual, effective dark source and electromagnetic energy–momentum tensor. The perturbation technique is used on the metric variables which ultimately induce perturbation on the selected f(R) model and on the physical variables. We conclude that higher curvature terms of CDTT model, density profile, electromagnetism and pressure anisotropy affect the range of instability at the Newtonian and post Newtonian regimes. It is worthwhile to mention here that our results approach asymptotically to general relativity solutions when δ→0.

Massive Gravity in Extra Dimensions

We discuss a Brane World scenario where we live on a 3-brane with massive gravity in infinite-volume bulk. The bulk graviton can be much heavier than the inverse Hubble size, as heavy as the bulk Planck scale, whose lower bound is roughly the inverse of 0.1 mm. The 4D Einstein-Hilbert term on the brane shields the brane matter from both strong bulk gravity and large bulk graviton mass. Gravity on the brane does not become higher-dimensional at large distances. Instead, at distance scales above the bulk Planck length, gravity on the brane behaves as 4D gravity with small graviton mass roughly of order or below the inverse Hubble size. Unlike the massless case, with massive gravity in the bulk one can have: i) 4D tensor structure on a codimension-1 brane; and ii) no infrared tachyon for smoothed-out higher codimension branes. The effects of the brane dynamics on the bulk are exponentially suppressed away from the brane. One consequence is that there are no "self-accelerated" solutions. In codimension-2 cases there exist nonsingular solutions with a flat 3-brane for a continuous positive range of the brane tension. In higher codimension cases, as in the massless case, higher curvature terms are required to obtain such solutions.

Planar AdS black holes in Lovelock gravity with a nonminimal scalar field

In arbitrary dimension D, we consider a self-interacting scalar field nonminimally coupled with a gravity theory given by a particular Lovelock action indexed by an integer k. To be more precise, the coefficients appearing in the Lovelock expansion are fixed by requiring the theory to have a unique AdS vacuum with a fixed value of the cosmological constant. This yields to k = 1, 2,⋯, $ \left[ {\frac{D-1 }{2}} \right] $ inequivalent possible gravity theories; here the case k = 1 corresponds to the standard Einstein-Hilbert Lagrangian. For each par (D, k), we derive two classes of AdS black hole solutions with planar event horizon topology for particular values of the nonminimal coupling parameter. The first family of solutions depends on a unique constant and is valid only for k ≥ 2. In fact, its GR counterpart k = 1 reduces to the pure AdS metric with a vanishing scalar field. The second family of solutions involves two independent constants and corresponds to a stealth black hole configuration; that is a nontrivial scalar field together with a black hole metric such that both side of the Einstein equations (gravity and matter parts) vanishes identically. In this case, the standard GR case k = 1 reduces to the Schwarzschild-AdS-Tangherlini black hole metric with a trivial scalar field. We show that the two-parametric stealth solution defined in D dimension can be promoted to the uniparametric black hole solution in (D + 1) dimension by fixing one of the two constants in term of the other and by adding a transversal coordinate. In both cases, the existence of these solutions is strongly inherent of the presence of the higher order curvature terms k ≥ 2 of the Lovelock gravity. We also establish that these solutions emerge from a stealth configuration defined on the pure AdS metric through a Kerr-Schild transformation. Finally, in the last part, we include multiple exact (D − 1) − forms homogenously distributed and coupled to the scalar field. For a specific coupling, we obtain black hole solutions for arbitrary value of the nonminimal coupling parameter generalizing those obtained in the pure scalar field case.

Euclidian 4d quantum gravity with a non-trivial measure term

Abstract We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations. We add a measure term which can also serve as a generalized higher curvature term and determine the phase diagram and the geometries dominating in the various regions. A first order phase transition line is observed, but no second order transition point is located. As a consequence we cannot attribute any continuum physics interpretation to the so-called crinkled phase of 4d dynamical triangulations.

Inside the degenerate horizons of regular black holes

The regularized stress-energy tensor of the quantized massive scalar, spinor and vector fields inside the degenerate horizon of the regular charged black hole in the (anti-)de Sitter universe is constructed and examined. It is shown that although the components of the stress-energy tensor are small in the vicinity of the black hole degenerate horizon and near the regular center, they are quite big in the intermediate region. The oscillatory character of the stress-energy tensor can be ascribed to various responses of the higher curvature terms to the changes of the metric inside the (degenerate) event horizon, especially in the region adjacent to the region described by the nearly flat metric potentials. Special emphasis is put on the stress-energy tensor in the geometries being the product of the constant curvature two-dimensional subspaces.

Chaotic dynamics of the Bianchi IX universe in Gauss-Bonnet gravity

We investigate the dynamics of closed FRW universe and anisotropic Bianchi type-IX universe characterized by two scale factors in a gravity theory including a higher curvature (Gauss-Bonnet) term. The presence of the cosmological constant creates a critical point of saddle type in the phase space of the system. An orbit starting from a neighborhood of the separatrix will evolve toward the critical point, and it eventually either expands to the de Sitter space or collapses to the big crunch. In the closed FRW model, the dynamics is reduced to hyperbolic motions in the two-dimensional center manifold, and the system is not chaotic. In the anisotropic model, anisotropy introduces the rotational mode, which interacts with the hyperbolic mode to present a cylindrical structure of unstable periodic orbits in the neighborhood of the critical point. Due to the non-integrability of the system, the interaction of rotational and hyperbolic modes makes the system chaotic, making it impossible for us to predict the final fate of the universe. We find that the chaotic dynamics arises from the fact that orbits with even small perturbations around the separatrix oscillate in the neighborhood of the critical point before finally expanding or collapsing. The chaotic character is also evidenced by the fractal structures in the basins of attraction.

Hoop Conjecture, Minimal Length and Black Hole Formation in the Asymptotically Safe Scenario of Quantum Gravity

Black hole dominance, assumed to be a fairly ubiquitous feature of any theory of quantum gravity, amounts to that any observer trying to perform a localized experiment on ever smaller length scales will ultimately be thwarted by the formation of a trapped surface within the spatial domain of the experiment. The argument based on Thorne's hoop conjecture, conjointly leads to a fundamental length scale in physics. Black hole dominance also suggests that ordinary field theory cannot be used to describe quantum gravity in the extreme UV, contrary to implications of asymptotic safety. We re-examine black hole dominance in an asymptotically safe scenario, in the presence of higher curvature terms an with running couplings, by modifying a proof of Thorne's hoop conjecture. We find that the proof falls apart, and along with it, so does the argument for a mandatory formation of a trapped surface inside the domain of the experiment. However, neither is there a contrary proof that local trapped surfaces do not form. Instead in this approach whether an observer can perform local measurements in arbitrary small regions of spacetime depends on the specific values of the couplings near the UV fixed point. In this sense there is no all pervasive local version of the minimal length argument. However, we argue that one trapped surface must still form outside an experiment, when the domain of this experiment is localized to scales much smaller than the Planck length. This enshrouding horizon then prevents any information from reaching observers at infinity, thus retaining a vestige of "asymptotic darkness" for them.

Horizon entropy and higher curvature equations of state

The Clausius relation between entropy change and heat flux has previously been used to derive Einstein's field equations as an equation of state. We examine here whether a similar derivation can be given for extensions beyond Einstein gravity to include higher derivative and higher curvature terms.

Birkhoff’s theorem in higher derivative theories of gravity II

As a continuation of a previous work, here we examine the admittance of Birkhoff's theorem in a class of higher derivative theories of gravity. This class is contained in a larger class of theories which are characterized by the property that the trace of the field equations are of second order in the metric. The action representing these theories are given by a sum of higher curvature terms. Moreover the terms of a fixed order k in the curvature are constructed by taking a complete contraction of k conformal tensors. The general spherically (hyperbolic or plane) symmetric solution is then given by a static asymptotically Lifshitz black hole with the dynamical exponent equal to the spacetime dimensions. However, theories which are homogeneous in the curvature (i.e., of fixed order k) possess additional symmetry which manifests as an arbitrary conformal factor in the general solution. So, these theories are analyzed separately and have been further divided into two classes depending on the order and the spacetime dimensions.