It is well known that general relativity does not admit gravitational geons that are stationary, asymptotically flat, singularity free and topologically trivial. However, it is likely that general relativity will receive corrections at large curvatures and the modified field equations may admit solutions corresponding to this type of geon. If geons are produced in the early universe and survive until today they could account for some of the dark matter that has been "observed" in galaxies and galactic clusters.
In this paper I consider gravitational geons in 1+1 dimensional theories of gravity. I show that the Jackiw-Teitelboim theory with corrections proportional to $R^2$ and $\Box R$ admits gravitational geons. I also show that gravitational geons exist in a class of theories that includes Lagrangians proportional to $R^{2/3}$.
The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high frequency gravitational waves is reviewed and critically analyzed. The Regge-Wheeler formalism is used to represent gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a non-singular solution to meet the requirements of a gravitational geon. High-frequency waves are seen to be a necessary condition for the geon and the field equations are decomposed accordingly. It is shown that this leads to the impossibility of f…
In a recent paper [arXiv:0807.0611] I found gravitational geons in two classes of 1+1 dimensional theories of gravity. In this paper I examine these theories, with the possibility of a cosmological constant, and find strong field gravitational geons. In the spacetimes in [arXiv:0807.0611] a test particle that is reflected from the origin suffers a discontinuity in $d^2t/dτ^2$. The geons found in this paper do not suffer from this problem.
In this paper, we examine the possibility of static, spherically symmetric gravitational geons on a 3 dimensional brane embedded in a 4+1 dimensional space-time. We choose a specific g_tt for the brane-world space-time metric. We then calculate g_rr analytically in the weak field limit and numerically for stronger fields. We show that the induced field equations on the brane do admit gravitational geon solutions.
Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the …
A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equa…
Geons are particle-like electrovacua. The concept is well-defined, but it still lacks a proper first example. Emerging as such is a self-confined exact 2-parameter pp-wave non-Dirac monopole {\cal G} with primordial Q/r^2 (r\geq r_o) field plus higher moments. {\cal G} has effective mass, independently-scaled NUT-like charge κ|Q|=2r_o as diameter, and spin. {\cal G} {\em cannot} have actual {\sc em} charge $Q$ (by \partial{\cal G}=0), Ricci-flat limits, nor spacetime or Dirac-string singularities, but Dirac's quantization condition holds. {\cal G}/2, as an upgraded `Kerr-Newman' alternative or…
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3+1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order $\sim 1/2$ of the AdS length, and with deviations of the order of 50\% compared to third order perturbative approaches. The consistency of our results with numerical r…
Effective geometries arising from a hypothetical discrete structure of space-time can play an important role in the understanding of the gravitational physics beyond General Relativity. To discuss this question, we make use of lessons from crystalline systems within solid state physics, where the presence of defects in the discrete microstructure of the crystal determine the kind of effective geometry needed to properly describe the system in the macroscopic continuum limit. In this work we study metric-affine theories with non-metricity and torsion, which are the gravitational analog of cryst…
We present a theoretical analysis of an electron confined by a Penning trap, also known as geonium, that is affected by gravity. In particular, we investigate the gravitational influence on the electron dynamics and the electromagnetic field of the trap. We consider the special case of a homogeneous gravitational field, which is represented by Rindler spacetime. In this spacetime the Hamiltonian of an electron with anomalous magnetic moment is constructed. Based on this Hamiltonian and the exact solution to Maxwell equations for the field of a Penning trap in Rindler spacetime, we derived the …
Being a key ingredient of the AdS/CFT correspondence, AdS space-time is suspected to be non-linearly unstable since 2011. Even with arbitrarily small initial data, a singularity almost invariably emerges. However, some configurations allow for perfectly regular and quasi-periodic solutions. These are the so-called islands of stability. Among them, geons play the role of purely gravitational excitations of AdS space-time. In this manuscript, we tackle the problem of the numerical construction of several families of asymptotically AdS geons. We are able to definitely demonstrate the existence of…
We discuss the possibility that gravitational fluctuations ("gravitational-waves") are trapped in space by gravitational interactions in two dimensional Jackiw-Teitelboim gravity. In the standard geon (gravitational electromagnetic entity) approach, the effective energy is entirely deposited in a thin layer, the active region, that achieves spatial self-confinement and raises doubts about the geon's stability. In this paper we relinquish the "active region" approach and obtain self-confinement of "gravitational waves" that are trapped by the vacuum geometry and can be stable against the backre…
We construct new geon-type black holes in D>3 dimensions for Einstein's theory coupled to gauge fields. A static nondegenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D-2 with a pure F^2 action can be included by an appropriate (and in most cases nontrivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers-Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuousl…
Boson stars are descendants of the so-called geons of Wheeler, except that they are built from scalar particles instead of electromagnetic fields. If scalar fields exist in nature, such localized configurations kept together by their self-generated gravitational field can form within Einstein's general relativity. In the case of complex scalar fields, an absolutely stable branch of such non-topological solitons with conserved particle number exists. Our present surge stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part…
We investigate $D$-dimensional gravitational model with curvature-quadratic and curvature-quartic correction terms: $R+R^2+R^4$. It is assumed that the corresponding higher dimensional spacetime manifold undergos a spontaneous compactification to a manifold with warped product structure. Special attention is paid to the stability of the extra-dimensional factor space for a model with critical dimension D=8. It is shown that for certain parameter regions the model allows for a freezing stabilization of this space. The effective four-dimensional cosmological constant is negative and the external…
Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.
We define gravitational mass in asymptotically de Sitter space-times with compactified dimension. It was shown that the mass can be negative for space-time with matter spreading beyond the cosmological horizon scale or large outward `momentum' in four dimension. We give simple examples with negative energy in higher dimensions even if the matter is not beyond horizon or system does not have large `momentum'. They do not have the lower bound on the mass. We also give a positive energy argument in higher dimensions and realise that elementary fermion cannot exist in our examples.
We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity. Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions. After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories. It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational wave…
In this manuscript a different perspective on gravitational field has been proposed, suggesting different features of gravity depending on spacetime dimension, which can explain preventing the formation of singularity inside blackholes and also suggest interpreting spin-1 fields emerged in theories with dimensional reduction mechanism, as different aspects of gravitational field.
We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for an arbitrary cosmological constant.
It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution;i.e. Riemann vanishes whenever Ricci does so) in $3$ dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one $N$th order term in action) gravity for which $N$th order Lovelock Riemann tensor is indeed given in terms of corresponding Ricci for all odd $d=2N+1$ dimensions. This feature of gravity is realized only in higher dimensions a…
We discuss observational constraints coming from CMB and type Ia supernovae, for the model of accelerated universe produced by gravitational leakage into extra dimensions. Our fits indicate that the model is currently in agreement with the data. We also give the equations governing the evolution of cosmological perturbations. Future observations will be able to severely constrain the model.
It is pointed out that the action recently proposed by Bañados et al. for gravitation in odd dimensions higher (and lower) than four, provides a natural quantization for the gravitational constant. These theories possess no dimensionful parameters and hence they may be power counting renormalizable.
We investigate whether enhanced gravitational scattering on small scales (< 0.1mm), which becomes possible in models with large extra dimensions, can establish statistical equilibrium between different particle species in the early Universe. We calculate the classical relativistic energy transfer rate for two species with a large ratio between their masses for a general elastic scattering cross section. Although the classical calculation suggests that ultra-light WIMPs (e.g., axions) can be thermalized by gravitational scattering, such interactions are considerably less efficient once quantum …
It is shown that there is a universal gravitational memory effect measurable by inertial detectors in even spacetime dimensions $d\geq 4$. The effect falls off at large radius $r$ as $r^{3-d}$. Moreover this memory effect sits at one corner of an infrared triangle with the other two corners occupied by Weinberg's soft graviton theorem and infinite-dimensional asymptotic symmetries.
In this paper, we derive the master equations for gravitational perturbations of vector and scalar type for static vacuum Lovelock black holes. Together with our previous work on the tensor type perturbation, we now provide the full set of master equations that governs all types of gravitational perturbations of static vacuum Lovelock black holes in any dimensions.
It has been recently claimed [arXiv:1102.3434] that quantum gravity models where the number of dimensions reduces at the ultraviolet exhibit a potentially observable cutoff in the primordial gravitational wave spectrum, and that this is a "generic" and "robust" test for such models, since "(2+1)-dimensional spacetimes have no gravitational degrees of freedom". We argue that such a claim is misleading.
We study the contribution to entropy of Black Holes in D=2+1 dimensions from an extension of the Chern Simons theory including higher derivative in a curved space-time.
We summarize the fall-off of electromagnetic and gravitational fields in n>5 dimensional Ricci-flat spacetimes along an asympotically expanding non-singular geodesic null congruence.
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.
We use effective field theory tools to study non-conservative effects in systems of gravitating objects in general spacetime dimension. Using the classical version of the Closed Time Path formalism, we treat both the radiative gravitational field and its dynamical sources within a single action principle. New results include the radiation-reaction effective action in arbitrary dimensions to leading and +1PN orders, as well as the generalized Quadrupole formula to order +1PN.
We introduce a 'quasi-topological` term [1] in D=1+1 dimensions and the entropy for black holes is calculated [2]. The source of entropy in this case is justified by a non-null stress-energy tensor.
Chern-Simons gravities and gravitational Chern-Simons densities are constructed using the non-Abelian Yang-Mills Chern-Simons densities. As such, they are defined only in odd dimensions. We propose instead an analogous construction employing what we term Higgs--Chern-Simons (HCS) densities, which are defined in $all\ dimensions$. This enables the definition of extended versions of Chern-Simons gravities in all dimensions. Employing the same prescription, the definition of gravitational Chern-Simons densities is extended to all even dimensions, but only to $4p-1$ $odd$ dimensions. All our consi…
We study the gravitational field of a spinning radiation beam-pulse in a higher dimensional spacetime. We derive first the stress-energy tensor for such a beam in a flat spacetime and find the gravitational field generated by it in the linear approximation. We demonstrate that this gravitational field can also be obtained by boosting the Lense-Thirring metric in the limit when the velocity of the boosted source is close to the velocity of light. We then find an exact solution of the Einstein equations describing the gravitational field of a polarized radiation beam-pulse in a space-time with a…
The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a natural way, to reduce to two (the cosmological and Newton's constant) these several arbitrary coefficients, yielding a restricted Lovelock gravity. In this process one separates theories in even dimensio…
We study inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold under dimensional reduction. Stability due to different types of effective potentials is analyzed for specific configurations of internal spaces. Necessary restrictions on the parameters of the models are found and masses of gravitational excitons (small inhomogeneous excitations of the scale factors of the internal spaces near minima of effective potentials) are calculated.
Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric. The requirement of general covariance for the resulting non-local effective field equations puts severe restrictions on the nature of the solutions that can be obtained. In general the existence of vacuum solutions to the effective field equations restricts the value of the gravitational scaling exponent $ν^{-1}$ to be a positive integer greater than one. We give further arguments suggesting that in fact only for $ν^{-1}=3$ consiste…
We discuss in detail how string-inspired lineal gravity can be formulated as a gauge theory based on the centrally extended Poincaré group in $(1+1)$ dimensions. Matter couplings are constructed in a gauge invariant fashion, both for point particles and Fermi fields. A covariant tensor notation is developed in which gauge invariance of the formalism is manifest.
In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We study the local gravitational energy in higher dimensions through the lens of the small sphere limits of various quasilocal mass proposals which can be appropriately generalised beyond four dimensions, and report a new quantity $\Q$ which potentially characterises the local gravi…
The solution of Einsteins equations for 4-brane embedded in 5-dimensional Anti-de-Sitter space-time is found. It is shown that the cosmological constant can provide the existence of ordinary 4-dimensional Newton's low and trapping of a matter on the brane.
We investigate in detail the gravitational wave signal from kinks on cosmic (super)strings, including the kinematical effects from the internal extra dimensions. We find that the signal is suppressed, however, the effect is less significant that that for cusps. Combined with the greater incidence of kinks on (super)strings, it is likely that the kink signal offers the better chance for detection of cosmic (super)strings.
Lower-dimensionality at higher energies has manifold theoretical advantages as recently pointed out. Moreover, it appears that experimental evidence may already exists for it - a statistically significant planar alignment of events with energies higher than TeV has been observed in some earlier cosmic ray experiments. We propose a robust and independent test for this new paradigm. Since (2+1)-dimensional spacetimes have no gravitational degrees of freedom, gravity waves cannot be produced in that epoch. This places a universal maximum frequency at which primordial waves can propagate, marked b…
We consider non-linear gravitational models with a multidimensional warped product geometry. Particular attention is payed to models with quadratic scalar curvature terms. It is shown that for certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. In this case, the 4-dimensional effective cosmological constant as well as the bulk cosmological constant become negative. As a consequence, the homogeneous and isotropic external space is asymptotically AdS. The connection between the D-dimensional and the 4-dimensional fundamental mass…
When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat space kinks, governed by identical potentials.
In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder how the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study the threshold of black-hole formation in 4+1 dimensions, where we add a massless minimally coupled scalar matter field to the gravitational wave ansatz of Bizón, Chmaj and Schmidt (in…
There are several fundamental differences between four-dimensional and higher-dimensional gravitational waves, namely in the so called braneworld set-up. One of them is their asymptotic behavior within the Cauchy problem. This study is connected with the so called Hadamard problem, which aims at the question of Huygens principle validity. We investigate the effect of braneworld scenarios on the character of propagation of gravitational waves on FRW background.
We develop a general formalism for treating radiative degrees of freedom near $\mathscr{I}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the BMS group to include angle-dependent isometries of the internal space. We apply this formalism to study…
We examine the problem of the gravitational collapse using higher dimensional Husain spacetime for the null fluid. The equations of state chosen to solve the field equations contain linear, quadratic and arbitrary powers of the radial parameter. The resulting mass evolution is discussed for each case.
We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar Type II critical behavior at the threshold of black hole formation.
We study inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold under dimensional reduction and show that small inhomogeneous excitations of the scale factors of the internal spaces near minima of effective potentials should be observable as massive scalar particles (gravitational excitons) in the external space-time.
The Lovelock gravity extends the theory of general relativity to higher dimensions in such a way that the field equations remain of second order. The theory has many constant coefficients with no a priori meaning. Nevertheless it is possible to reduce them to two, the cosmological constant and Newton's constant. In this process one separates theories in even dimensions from theories in odd dimensions. In a previous work gravitational collapse in even dimensions was analysed. In this work attention is given to odd dimensions. It is found that black holes also emerge as the final state of gravit…
We derive formulae for the time variation of the gravitational ``constant'' and of the fine structure ``constant'' in various models with extra dimensions and analyze their consistency with the observational data.
Two non-static solutions for three dimensional gravity coupled to matter fields are given. One describes the collapse of radiation that results in a black hole. This is the three dimensional analog of the Vaidya metric, and is used to construct a model for mass inflation. The other describes plane gravitational waves for coupling to a massless scalar field.
The main issue of the present letter is to fix specific features (which turn out being independent of extradimension size) of gravitational waves generated before a dimensional compactification process. Valuable is the possibility to detect our prediction from gravitational wave experiment without high energy laboratory investigation. In particular we show how gravitational waves can bring information on the number of Universe dimensions. Within the framework of Kaluza-Klein hypotheses, a different morphology arises between waves generated before than the compactification process settled down …
The Einstein equation in D dimensions, if restricted to the class of space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions with n scalar fields. For n = 2, this results reduces to the known reduction of certain 4-dimensional metrics which include gravitational waves. Here, we give such a representation which leads to a new proof of the Birkhoff theorem for plane-symmetric space--times, and which leads to an explanation, in which sense two (spin zero-) scalar fields in 2 dimensions may incorporat…
The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.
We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We discuss the nature of the singularity formed by analyzing the outgoing radial null geodesics. We examine the formation of trapped surfaces during the collapse.
We study a solution of the Einstein-Gauus-Bonnet theory in 5 dimensions coupled to a Maxwell field, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.
In the present paper, we analyze the well-known 2+1 dimensional black holes (assuming a non-vanishing cosmological constant) in light of the gravitational decoupling by the minimal geometric deformation approach. To illustrate our results, we consider the BTZ geometry as the seed solution to generate new anisotropic ones. To complement the study, the curvature scalars and the energy conditions are analyzed.
