Dimensional Einstein Gauss Bonnet Research Articles

The role of dimension and electric charge on a collapsing geometry in Einstein–Gauss–Bonnet gravity

The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximum electric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnet gravity as well as general relativity. The charged gravitational collapse process is also similar for all dimensions N≥5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\\ge 5$$\\end{document} unlike in the neutral scenario where there is a marked difference between the N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} and N>5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N>5$$\\end{document} cases. In the case where N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, before succumbing to an event horizon. The similarity of charged collapse for all higher dimensions is a unique feature in the theory. The sufficient conditions for the formation of a naked singularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein–Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested and it is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible.

The mass gap in five dimensional Einstein–Gauss–Bonnet black holes: a geometrical explanation

It is well known that, unlike in higher dimensional general relativity (GR), we cannot have a black hole with an arbitrarily small mass in five dimensional Einstein–Gauss–Bonnet gravity. When we study the dynamical black hole formation via the radiation collapse in the radiating Boulware–Deser spacetime in five dimensions, the central zero mass singularity is weak, conical and naked, and the horizon forms only when a finite amount of matter, that depends on the coupling constant of the Gauss–Bonnet term, falls into the central singularity. To understand this phenomenon transparently and geometrically, we study the radiating Boulware–Deser spacetime in five dimensions using a 1+1+3 spacetime decomposition, for the first time. We find that the geometric and thermodynamic quantities can be expressed in terms of the gravitational mass and the Gauss–Bonnet (GB) parameter and separate each of them into their Gauss–Bonnet and matter parts. Drawing comparisons with five dimensional GR at every step, we explicitly show how the mass gap arises for a general mass function M(v) and what functions for M(v) make certain geometrical quantities well defined at the central singularity. We show in the case of self-similar radiation collapse in the modified theory, the central singularity is not a sink for timelike geodesics and is extendable. This clearly demonstrates how the GB invariant affects the nature of the final state of a continual collapse in this modified theory.

Bouncing behaviours in four dimensional Einstein Gauss-Bonnet gravity with cosmography and observational constraints

Bouncing behaviours in four dimensional Einstein Gauss-Bonnet gravity with cosmography and observational constraints

Charged radiation collapse in Einstein–Gauss–Bonnet gravity

We generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singularity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity separating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions Nge 5, charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post collapse for all Nge 6 and a weak conical singularity forms when N=5. A comparison with charged radiation collapse in general relativity is also given.

On stable exponential cosmological solutions with two factor spaces in (1+ m + 2)-dimensional Einstein-Gauss-Bonnet model with Λ-term.

A [Formula: see text]-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term [Formula: see text] is considered. Exact solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters [Formula: see text] and [Formula: see text], corresponding to factor spaces of dimensions [Formula: see text] and [Formula: see text], respectively, are found. Under certain restrictions on [Formula: see text], the stability of the solutions in a class of cosmological solutions with diagonal metrics is proved. A subclass of solutions with small enough variation of the effective gravitational constant [Formula: see text] is considered and the stability of all solutions from this subclass is shown. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

Gravitational lensing in 4-D Einstein–Gauss–Bonnet gravity in the presence of plasma

In this paper we have assumed a weak-field regime to explore the gravitational lensed photons in a 4 dimensional Einstein–Gauss–Bonnet gravity, which is very much in the limelight these days. The investigation is conducted in three distinct paradigms: uniform plasma, singular isothermal sphere and a non-singular isothermal sphere. The lensing angle associated with the distribution factor of the medium is individually derived for each case and further utilized to study the magnification of the image source brightness, selectively for the uniform plasma and singular isothermal sphere. The attained results are brought forth in contrast with the standard Schwarzschild geometry.

On Stability of Exponential Cosmological Type Solutions with Two Factor Spaces in the Einstein–Gauss–Bonnet Model with a $$\boldsymbol{\Lambda}$$-Term

We study a $$D$$-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss-Bonnet term and the cosmological constant $$\Lambda$$. We find a class of cosmological type solutions with exponential dependence of two scale factors on the variable $$u$$ (either cosmological time or a spatial coordinate), governed by two Hubble-like parameters $$H\neq 0$$ and $$h$$, corresponding to factor spaces of dimensions $$m>2$$ and $$l>2$$, respectively, and depending on the sign parameter $$\varepsilon=\pm 1$$ ($$\varepsilon=1$$ corresponds to cosmological solutions and $$\varepsilon=-1$$ to static ones). These solutions are governed by a certain master equation $$\Lambda\alpha=\lambda(x)$$ and the restriction $$\alpha\varepsilon(x-x_{+})(x-x_{-})<0$$ ($$x_{-}<x_{+}<0$$) for the ratio $$h/H=x$$, where $$\alpha=\alpha_{2}/\alpha_{1}$$ is the ratio of two constants of the model . The master equation is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. Imposing certain restrictions on $$x$$, and we prove the stability of the solutions for $$u\to\pm\infty$$ in a certain class of cosmological solutions with diagonal metrics.

Stable exponential cosmological solutions with three factor spaces of dimensions m = 3, k1 = k and k2 = k in the Einstein–Gauss–Bonnet model with a Λ-term

We consider a [Formula: see text]-dimensional Einstein–Gauss–Bonnet model with the cosmological [Formula: see text]-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional “our” world and internal subspaces with dimensions [Formula: see text] and [Formula: see text].

Stable exponential cosmological solutions with three factor spaces in (1 + 3 + 3 + k)-dimensional Einstein–Gauss–Bonnet model with a Λ-term

We consider a (7 + k)-dimensional Einstein–Gauss–Bonnet (EGB) model with the cosmological [Formula: see text]-term. A cosmological model with three factor spaces of dimensions 3, 3 and k, k[Formula: see text]2 is considered. Exact stable solutions with three (non-coinciding) Hubble-like parameters in these models are obtained. Some examples of solutions (e.g. with zero variation of the effective gravitational constant G) are considered in selected dimensions (for k = 5, 6).

Exact exponential cosmological solutions with two factor spaces of dimension m in EGB model with a Λ-term

A [Formula: see text]-dimensional Einstein–Gauss–Bonnet (EGB) model with the cosmological term [Formula: see text] is considered. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters [Formula: see text] and [Formula: see text], corresponding to two factor spaces of dimension [Formula: see text] and obeying [Formula: see text]. We prove that the solutions, obeying [Formula: see text], are stable (in a class of cosmological solutions with diagonal metrics) for [Formula: see text] and they are unstable for [Formula: see text]. A subclass of solutions with small enough variation of the effective gravitational constant [Formula: see text] is considered. It is shown that all solutions from this subclass are stable.

On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein–Gauss–Bonnet model with a Λ-term

We consider a [Formula: see text]-dimensional Einstein–Gauss–Bonnet (EGB) model with the cosmological [Formula: see text]-term. We restrict the metrics to be diagonal ones and find for certain [Formula: see text] class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions [Formula: see text] and 1. Any solution from this class describes an accelerated expansion of [Formula: see text]-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

Competing s-wave orders from Einstein–Gauss–Bonnet gravity

In this paper, the holographic superconductor model with two s-wave orders from 4+1 dimensional Einstein–Gauss–Bonnet gravity is explored in the probe limit. At different values of the Gauss–Bonnet coefficient α, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s + s coexistent phase, including the reentrant phase transition near the Chern–Simons limit α=0.25, can be found. We also give an explanation to the nontrivial behavior of the Tc–α curves near the Chern–Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern–Simons limit.

ON COSMOLOGICAL-TYPE SOLUTIONS IN MULTI-DIMENSIONAL MODEL WITH GAUSS–BONNET TERM

A (n + 1)-dimensional Einstein–Gauss–Bonnet (EGB) model is considered. For diagonal cosmological-type metrics, the equations of motion are reduced to a set of Lagrange equations. The effective Lagrangian contains two "minisuperspace" metrics on ℝn. The first one is the well-known 2-metric of pseudo-Euclidean signature and the second one is the Finslerian 4-metric that is proportional to n-dimensional Berwald–Moor 4-metric. When a "synchronous-like" time gauge is considered, the equations of motion are reduced to an autonomous system of first-order differential equations. For the case of the "pure" Gauss–Bonnet model, two exact solutions with power-law and exponential dependence of scale factors (with respect to "synchronous-like" variable) are obtained. (In the cosmological case, the power-law solution was considered earlier in papers of N. Deruelle, A. Toporensky, P. Tretyakov and S. Pavluchenko.) A generalization of the effective Lagrangian to the Lowelock case is conjectured. This hypothesis implies existence of exact solutions with power-law and exponential dependence of scale factors for the "pure" Lowelock model of mth order.

Dynamical black holes with symmetry in Einstein–Gauss–Bonnet gravity

We explore various aspects of dynamical black holes defined by a future outer trapping horizon in n(⩾5)-dimensional Einstein–Gauss–Bonnet gravity. In the present paper, we assume that the spacetime has symmetries corresponding to the isometries of an (n − 2)-dimensional maximally symmetric space and the Gauss–Bonnet coupling constant is non-negative. Depending on the existence or absence of the general relativistic limit, solutions are classified into GR and non-GR branches, respectively. Assuming the null energy condition on matter fields, we show that a future outer trapping horizon in the GR branch possesses the same properties as that in general relativity. In contrast, that in the non-GR branch is shown to be non-spacelike with its area non-increasing into the future. We can recognize that this peculiar behavior arises from the fact that the null energy condition necessarily leads to the null convergence condition for radial null vectors in the GR branch, but not in the non-GR branch. The energy balance law yields the first law of a trapping horizon, from which we can read off the entropy of a trapping horizon reproducing Iyer–Wald's expression. The entropy of a future outer trapping horizon is shown to be non-decreasing in both branches along its generator.

Isolated horizons in higher dimensional Einstein–Gauss–Bonnet gravity

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang–Mills etc) in D = 4 dimensions and cosmological constant in D ⩾ 3 dimensions. In this paper, we present a further extension of the framework that includes black holes in higher dimensional Einstein–Gauss–Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by In this expression SD−2 is the (D − 2)-dimensional cross section of the horizon with an area form and the Ricci scalar is the D-dimensional Newton constant and α is the Gauss–Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.

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.