In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar field potential $V(ϕ)$, and provide full global geometric estimates when the solutions exist. Our main results are summarised as follows. For the Klein-Gordon field, namely when $V(ϕ)=m^{2}|ϕ|^{2}$, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is $ϕ$ is constant and equal to zero if $m\neq 0$). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When $V(ϕ)=m^{2}|ϕ|^{2}+2Λ$, that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when $Λ>0$, whereas when $Λ<0$ it is proved that no non-vacuum geodesically complete solution exists unless $m^{2}<-2Λ/(n-1)$, ($n$ is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on techniques in comparison geometry á la Backry-Emery.
In this paper we study the static Einstein-Maxwell space when it is conformal to an $n$-dimensional pseudo-Euclidean space, which is invariant under the action of an $(n-1)$-dimensional translation group. We also provide a complete classification of such space.
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
We prove that given any smooth metric $γ$ and smooth positive function $H$ on $S^{2}$, there is a constant $λ> 0$, depending on $(γ, H)$, and an asymptotically flat solution $(M, g, u)$ of the static vacuum Einstein equations on $M = {\mathbb R}^{3} \setminus B^{3}$, such that the induced metric and mean curvature of $(M, g, u)$ at $\partial M$ are given by $(γ, λH)$. This gives a partial resolution of a conjecture of Bartnik.
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally-invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter $λ$ between the energy-momentum tensor and the gradient of Ricci scalar. Thus, …
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, $δω_{g}(t)=-Cδa(t)$. We obtain neu…
Mass Formulas for Stationary Einstein-Yang-Mills Black Holes and a Simple Proof of Two Staticity Theorems
在Einstein-Yang-Mills理论中，导出了两个新的稳态黑洞的积分质量公式.由此我们导出了一个$ \J Ω-Q V $的公式，由此可以立即得出任何静止的、不旋转的、不带电的黑洞都是静止的，并且在静止的切片上具有消失的电场。在爱因斯坦-麦克斯韦的情况下，我们有，此外，“广义Smarr质量公式”，我们提供了一个新的，简单的推导。结合另外两个公式，我们得到了一个简单的证明：非旋转Einstein-Maxwell黑洞必定是静态的，并且在静态切片上有消失的磁场。我们的质量公式也可以推广到其他类型的物质场的情况下，我们描述这些推广的性质。
We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein-Maxwell theory.
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy tensor, respectively). The static and perturbed field equations are constructed for perfect fluid parameterized by linear equation of state parameter. We obtain solutions manifesting the Einstein static state by considering peculiar $f(R,T)$ forms for vanishing and non-vanishing conservation of the stress-energy tensor. It is observed that stable static Einstei…
The exact interior static solution of Einstein-Maxwell equations in Bondi's coordinates for the electrically charged fluid ball is obtained as a source of the Reissner-Nordström solution.
We study the stability of Einstein static Universe, with FLRW metric, by considering linear homogeneous perturbations in the kinetic coupled gravity. By taking linear homogeneous perturbations, we find that the stability of Einstein static Universe, in the kinetic coupled gravity with quadratic scalar field potential, for closed ($K=1$) isotropic and homogeneous FLRW Universe depends on the coupling parameters $κ$ and $\varepsilon$. Specifically, for $κ=L_P^2$ and $\varepsilon=1$ we find that the stability condition imposes the inequality $a_0>\sqrt{3}L_P$ on the initial size $a_0$ of the clos…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the Reissner-Nordström-de Sitter solution. The conformal factors for static space-time structure with an elastic matter are obtained. Further, we analyze the viability of energy conditions. And also discuss the matching problem with the exterior space-time.
In the present paper we prove a uniqueness theorem for the regular static, traversable wormhole solutions to the Einstein-phantom scalar field theory with two asymptotically flat regions (ends). We show that when a certain condition on the asymptotic values of the scalar field is imposed such solutions are uniquely specified by their mass $M$ and the scalar charge $D$.The main arguments in the proof are based on the positive energy theorem.
We study the cosmological models in which an extended Chaplygin gas universe is merged with the braneworld scenario. In particular, we examine the realization of Einstein static universe on the brane embedded in a non-constant curvature bulk space and perform a detailed perturbation analysis. We extract the stability conditions and find their impacts on the geometric equation of state parameter and the spatial curvature of the universe.
