We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in $D$ dimensions. In the limit that $D$ tends to $2$ with simultaneous singular rescaling of the scalar curvature coupling constant as $1/(D-2)$, we get the novel Einstein and higher-derivative gravity. Due to non-trivial contribution of scalar curvature which is topological invariant in exactly two dimensions to gravitational equations in the two-dimensional limit one gets novel cosmological and black hole solutions.In particular, the de Sitter and radiation-dominated universe and the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter black hole solutions are obtained and their properties are discussed.
This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a field redefinition containing an infinite number of higher derivatives. It is also shown that the current-current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved.
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
We construct a classical solution of an Einstein-Yang-Mills system with a fourth order term with respect to the field strength of the Yang-Mills field. The solution provides a spontaneous compactification proposed by Cremmer and Scherk; ten-dimensional space-time with a cosmological constant is compactified to the four-dimensional Minkowski space with a six-dimensional sphere S^6 on which an instanton solution exists. The radius of the sphere is not a modulus but is determined by the gauge coupling and the four-derivative coupling constants and the Newton's constant. We also construct a soluti…
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the …
We consider a gravitating system of vanishing cosmological constant consisting of an electromagnetic field and a scalar field coupled to the Einstein tensor. A Reissner-Nordström black hole undergoes a second-order phase transition to a hairy black hole of generally anisotropic hair at a certain critical temperature which we compute. The no-hair theorem is evaded due to the coupling between the scalar field and the Einstein tensor. Within a first order perturbative approach we calculate explicitly the properties of a hairy black hole configuration near the critical temperature and show that it…
We propose to compute the action and global charges of the asymptotically anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary counterterms to the gravitational action. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension $d\leq 9$. We apply this tehnique for several different types of black objects. Apart from static and rotating black holes, we consider also Einstein-Gauss-Bonnet black string solutions with negative cosmological constant.
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed…
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium solutions are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-Aether models.
A new approach to the cosmological constant problem is proposed by modifying Einstein's theory of general relativity, using instead a scalar-tensor theory of gravitation. This theory of gravity crucially incorporates the concept of quantum symmetry breaking. The role of the cosmological constant $λ$ as a graviton mass in the weak-field limit is necessarily utilized. Because $λ$ takes on two values as a broken symmetry, so does the graviton mass -- one of which cannot be zero. Gravity now exhibits both long- and short-range forces, by introducing hadron bags into strong interaction physics usin…
We find the membrane equations which describe the leading order in $1/D$ dynamics of black holes in the $D\rightarrow\infty$ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor f…
We construct non-stationary exact solutions to five dimensional Einstein-Maxwell-Chern-Simons theory with positive cosmological constant. The solutions are based on four-dimensional Atiyah-Hitchin space. In asymptotic regions, the solutions approach to Gibbons-Perry-Sorkin monopole solutions. On the other hand, near the four-dimensional bolt of Atiyah-Hitchin space, our solutions show a bolt structure in five dimensions. The c-function for the solutions shows monotonic increase in time, in agreement with the general expected behaviour of c-function in asymptotically dS spacetimes.
The Hamiltonian of any quantum cosmological model must obey some conditions in order to be self-adjoint, or to admit self-adjoint extensions. We will consider in this paper the self-adjoint character of the Hamiltonian resulting from the Brans-Dicke theory, both in Einstein and Jordan frames. In both cases we find the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe. We show that the specific cosmological scenarios obtained depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between Einstein and Jor…
We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions with generic initial conditions in the four dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.
We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.
Lovelock gravity is a class of higher-derivative gravitational theories whose linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity coupled to a p-form gauge field. This extends the known example of an f(R) theory of gravity, which can be described as Einstein gravity coupled to a scalar field.
In this paper, the dependence of the Einstein gravity with the cosmological constant as well as of this theory in the first-order formalism on the gauge and parametrization is been analyzed. The one-loop counterterms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed.
We present arguments for the existence of charged, rotating black holes with equal-magnitude angular momenta in an odd number of dimensions $D\geq 5$. These solutions posses a regular horizon of spherical topology and approach asymptotically the Anti-de Sitter spacetime background. We analyze their global charges, their gyromagnetic ratio and their horizon properties.
The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns out that even without fundamental Higgs fields and other physical matter, gravitational self-interactions can generate this mechanism if the cosmological constant is non-vanishing. This article identifies the order parameter, and clarifies how these Abelian instanton solutions are associated with a …
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory. The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.
By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the two vacua with the same scale factor $a$, but opposite $\dot a$. The tunneling from one vacuum to the other provides a robust mechanism for bounce universes; it always occurs for systems with positive energy density. For suitable matter energy-momentum tensor we also construct cyclic universes. Cosmological solutions that resemble the classical time crystals c…
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $Λ$. These solutions approach asymptotically the anti-de Sitter spacetime and possess a regular event horizon. A discussion of the main properties of the solutions and the differences with respect to the asymptotically flat case is presented. The mass of these configurations is computed by using a counterterm method. We note that the $Λ=-3$ configurations have an higher dimensional interpretation in context of $d=11$ supergravity. The existen…
We study black hole solutions in the Einstein gravity with Gauss-Bonnet term, the dilaton and a positive "cosmological constant" in various dimensions. Physically meaningful black holes with a positive cosmological term are obtained only for those in static spacetime with $(D-2)$-dimensional hyperbolic space of negative curvature and $D>4$. We construct such black hole solutions of various masses numerically in $D=5,6$ and 10 dimensional spacetime and discuss their properties. In spite of the positive cosmological constant the spacetime approach anti-de Sitter spacetime asymptotically. The bla…
We suggest an interpretation of Einstein Equations of General Relativity at large scales in which the Cosmological constant is exactly zero in the limit of zero spacetime variations of fundamental constants. We argue that in a quasiclassical Universe such variation should be tiny which leads to a tiny value for the Dark Energy. Next, we suggest that the are two sources of the Dark Energy. The first is the variation in Newton's constant $G_N$. It is a form of Dark Energy in that it has negative pressure, but it differs from the Cosmological Constant by a negative contribution to the energy. The…
We derive the wave equation obeyed by electromagnetic fields in curved spacetime. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in a local inertial frame is in general less than $c$. The effective photon mass in the Schwarzschild metric is $m_γ= ( 2GM/r^3 )^{1/2}$ and near the horizon it is larger than the Hawking temperature of the blackhole. Our result…
In this paper, we will show that the equations of motion of the quadratic in curvature, ghost free, infinite derivative theory of gravity will not permit an anisotropic collapse of a homogeneous Universe for a Kasner-type vacuum solution.
We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is equivalent to the Robertson-Walker metric of cosmology. This general solution shows interconnections among many 5D solutions, such as the solution in the braneworld scenario and the topological black hole with cosmological constant. If the 5D cosmological constant is positive, the metric periodically depends on the extra dimension. Thus we can compactify the e…
It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by…
In this paper, we will analyse the cosmological models in Einstein-aether gravity, which is a modified theory of gravity in which a time-like vector field breaks the Lorentz symmetry. We will use this formalism to analyse different cosmological models with different behavior of the scale factor. In this analysis, we will use a certain functional dependence of the dark energy on the Hubble parameter. It will be demonstrated that the aether vector field has a non-trivial effect on these cosmological models. We will also perform the \emph{Om} diagnostic in Einstein-aether gravity. Thus, we will f…
We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special nonlocal form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared terms.
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restrictions on the Lie derivative of fields.
Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. In the Bose-Einstein Condensation model, dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present work, we study the Bose-Einstein Condensation process in a cosmological context, by assuming that this process can be described (at least approxima…
We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.
Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. In this work we analyze in detail the physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe. The resulting Dirac-like and Maxwell-like equat…
We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solut…
We consider the global cosmological evolution and the evolution of the density contrast in the Bose-Einstein condensate dark matter model, in the framework of a Post-Newtonian cosmological approach. In the Bose-Einstein model, dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state. For a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. The basic equation describing the evolution of the perturbations of the Bose-Einstein condensate is obtained, an…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a space-time metric from the homogeneous isotropic Friedmann-Robertson-Walker (FRW) background are large while locally measurable quantities like Riemann tensor …
We construct black hole solutions to Einstein-Born-Infeld gravity with a cosmological constant. Since an elliptic function appears in the solutions for the metric, we construct horizons numerically. The causal structure of these solutions differ drastically from their counterparts in Einstein-Maxwell gravity with a cosmological constant. The charged de-Sitter black holes can have up to three horizons and the charged anti-de Sitter black hole can have one or two depending on the parameters chosen.
General types of Bose-Einstein condensates are considered. The formation of black-hole analogues is examined for both short- and long-range interactions for arbitrary spatial dimensions greater than two. The former case includes non-linear derivative terms plus an inevitable external potential, while the latter one consists solely of gravity-like self-interactions for which intrinsic formation of analogue Schwarzschild-type background space-times is possible. The corresponding geometries are studied, and it is shown how they can be made stable. Their Hawking temperature is estimated, and it is…
Proposing new solution problems of the hierarchy and smallness of the cosmological constant using the Tev scale of the Standard Model in new framework of the higher-order gravity.
We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tenors of the CFT ($t_2$ and $t_4$). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just $\frac{d}{2(d+1)}$. This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in $AdS…
We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.
One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation {\it geodesically comple…
We study static non-critical hairy black holes of four dimensional gravitational model with nonminimal derivative coupling and a scalar potential turned on. By taking an ansatz, namely, the first derivative of the scalar field is proportional to square root of a metric function, we reduce the Einstein field equation and the scalar field equation of motions into a single highly nonlinear differential equation. This setup implies that the hair is secondary-like since the scalar charge-like depends on the non-constant mass-like quantity in the asymptotic limit. Then, we show that near boundaries …
Motivated by applications to black hole physics and duality, we study the effect of higher derivative corrections on the dimensional reduction of four-dimensional Einstein, Einstein Liouville and Einstein-Maxwell gravity to one direction, as appropriate for stationary, spherically symmetric solutions. We construct a field redefinition scheme such that the one-dimensional Lagrangian is corrected only by powers of first derivatives of the fields, eliminating spurious modes and providing a suitable starting point for quantization. We show that the Ehlers symmetry, broken by the leading $R^2$ corr…
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describ…
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of p…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame…
We find a new homogeneous solution to the Einstein-Maxwell equations with a cosmological term. The spacetime manifold is $R \times S^3$. The spacetime metric admits a simply transitive isometry group $G = R \times SU(2)$ of isometries and is of Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non-null and non-inheriting: it is only invariant with respect to the $SU(2)$ subgroup and is time-dependent in a stationary reference frame.
The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction…
We probe the pure Einstein's gravity contributions to the second-order density power spectrum. In the small-scale, we discover that the Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is sufficient to handle the baryon acoustic oscillation scale. In the large scale, however, we discover that the Einstein's gravity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the solutions is shown to describe a formation of a black hole in a cosmological setting. Some properties of this solution are described. There are two kinds of event horizons: a black hole horizon and cosmological horizons. The cosmological horizons are not smooth. There is a mild curvature singularity, which affects extended bodies but allows geodesics to be ext…
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is re…
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(\infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.
All the causally regular geometries obtained from (2+1)-anti-de Sitter space by identifications by isometries of the form $P \rightarrow (\exp πξ) P$, where $ξ$ is a self-dual Killing vector of $so(2,2)$, are explicitely constructed. Their remarkable properties (Killing vectors, Killing spinors) are listed. These solutions of Einstein gravity with negative cosmological constant are also invariant under the string duality transformation applied to the angular translational symmetry $ϕ\rightarrow ϕ+a$ The analysis is made particularly convenient through the construction of {\em global} coordinat…
