相关论文: Einstein Metrics on Spheres
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
The Neumann system on the 2-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian point of view on separation of variables. It is shown that, from this standpoint, its separation coordinates and its integrals of…
Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage…
We introduce a convolution on a 2-sphere and use it to show that the linearised Becchi-Rouet-Stora-Tyutin transformations and gauge fixing conditions of Einstein-Hilbert gravity coupled to a two-form and a scalar field, follow from the…
We obtain new invariant Einstein metrics on the compact Lie group $\SU(N)$ which are not naturally reductive. This is achieved by using the generalized flag manifold $G/K=\SU(k_1+\cdots +k_p)/\s(\U(k_1)\times\cdots\times\U(k_p))$ and by…
We construct solutions of an Einstein-Yang-Mills system including a cosmological constant in 4+n space-time dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and…
A theorem of Anderson and Bando-Kasue-Nakajima from 1989 states that to compactify the set of normalized Einstein metrics with a lower bound on the volume and an upper bound on the diameter in the Gromov-Hausdorff sense, one has to add…
We study a class of two-dimensional compact extra spaces isomorphic to the sphere $S^2$ in the framework of multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary)…
In this paper we introduce the "interpolation-degneration" strategy to study Kahler-Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By…
In this paper, we construct Poincar\'e-Einstein 4-manifolds with various kinds of cusps. In particular, we construct: (1) Infinite families of Einstein metrics on $(0,\infty)\times \mathscr{N}$, where $\mathscr{N}\to T^2$ is a principal…
We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of General Relativity in four and higher dimensions, building on recent work in hep-th/0408141. We write the Einstein equations in a new…
In this paper we define the magnitude of metric spaces using measures rather than finite subsets as had been done previously and show that this agrees with earlier work with Leinster in arXiv:0908.1582. An explicit formula for the magnitude…
In the present work, we attempt to find a new class of solutions for the spherically symmetric perfect fluid sphere by employing the Homotopy Perturbation Method (HPM), a new tool via which the mass polynomial function facilitates to tackle…
This paper derives a sufficient condition for the existence of cohomogeneity one Einstein metrics on double disk bundles of two summands type. The condition is an inequality that involves geometric data from the principal orbits.
The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we…
We calculate a wall crossing formula for 4-dimensional Poincare-Einstein metrics, through a wall made of orbifold Poincare-Einstein metrics with A1 singularities. This is based on a formalism which enables to deal with higher order terms of…
We study spherical quadrilaterals whose angles are odd multiples of pi/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
The requirement that a (non-Einstein) K\"ahler metric in any given complex dimension $m>2$ be almost-everywhere conformally Einstein turns out to be much more restrictive, even locally, than in the case of complex surfaces. The local…
The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…