A New Taub-NUT black hole in multiple coordinate systems is solved and analyzed. This black-hole is found to be an extension of the Clifton-Barrow metric for the specific case that $δ=-1/2$. We look at physical properties such as test particle orbits, thermodynamics, and various space-time limits. In addition, we show an Eguchi-Hanson type-II $f(R)$ solution related to the found Taub-NUT framework.
Eguchi-Hanson solitons are odd-dimensional generalizations of the four-dimensional Eguchi-Hanson metric and are asymptotic to AdS$_5$\mathbb{Z}_p$ when the cosmological constant is either positive or negative. We find soliton solutions to Lovelock gravity in 5 dimensions that are generalizations of these objects.
Using the numerical method, we study dynamics of coalescing black holes on the Eguchi-Hanson base space. Effects of a difference in spacetime topology on the black hole dynamics is discussed. We analyze appearance and disappearance process of marginal surfaces. In our calculation, the area of a coverall black hole horizon at the creation time in the coalescing black holes solutions on Eguchi-Hanson space is larger than that in the five-dimensional Kastor-Traschen solutions. This fact suggests that the black hole production on the Eguchi-Hanson space is easier than that on the flat space.
We consider a model of $F(R)$ gravity in which exponential and power corrections to Einstein-$Λ$ gravity are included. We show that this model has 4-dimensional Eguchi-Hanson type instanton solutions in Euclidean space. We then seek solutions to the five dimensional equations for which space-time contains a hypersurface corresponding to the Eguchi-Hanson space. We obtain analytic solutions of the $F(R)$ gravitational field equations, and by assuming certain relationships between the model parameters and integration constants, find several classes of exact solutions. Finally, we investigate the…
We construct higher-dimensional generalizations of the Eguchi-Hanson gravitational instanton in the presence of higher-curvature deformations of general relativity. These spaces are solutions to Einstein gravity supplemented with the dimensional extension of the quadratic Chern-Gauss-Bonnet invariant in arbitrary even dimension $D=2m\geq 4$, and they are constructed out of non-trivial fibrations over $(2m-2)$-dimensional Kähler-Einstein manifolds. Different aspects of these solutions are analyzed; among them, the regularization of the on-shell Euclidean action by means of the addition of topol…
We obtain new charged rotating multi-black hole solutions on the Eguchi-Hanson space in the five-dimensional Einstein-Maxwell system with a Chern-Simons term and a positive cosmological constant. In the two-black holes case, these solutions describe the coalescence of two rotating black holes with the spatial topologies of S^3 into a single rotating black hole with the spatial topology of the lens space S^3/Z_2. We discuss the differences in the horizon areas between our solutions and the two-centered Klemm-Sabra solutions which describe the coalescence of two rotating black holes with the spa…
We construct two types of Eguchi-Hanson metrics with the negative constant scalar curvature. The type I metrics are Kähler. The type II metrics are ALH whose total energy can be negative.
We numerically study the event horizons of two kinds of five-dimensional coalescing black hole solutions with different asymptotic structures: the five-dimensional Kastor-Traschen solution (5DKT) and the coalescing black hole solution on Eguchi-Hanson space (CBEH). Topologies of the spatial infinity are ${\rm S}^3$ and $L(2;1)={\rm S}^3/{\mathbb Z}_2$, respectively. We show that the crease sets of event horizons are topologically ${\rm R}^1$ in 5DKT and ${\rm R}^1\times {\rm S}^1$ in CBEH, respectively. If we choose the time slices which respect space-time symmetry, the first contact points of…
In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely determined in terms of known analytical functions. Moreover, we find the solutions can be extended to non-stationary exact solutions to Einstein-Maxwell theory with cosmological constant. We show that the solutions are asymptotically expanding patches of de-Sitter spacetime.
The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gau…
We construct new solutions of the vacuum Einstein field equations in four dimensions via a solution generating method utilizing the SL(2,R) symmetry of the reduced Lagrangian. We apply the method to an accelerating version of the Zipoy-Voorhees solution and generate new solutions which we interpret to be the accelerating versions of the Zipoy-Voorhees generalisation of the Taub-NUT solution (with Lorentzian signature) and the Zipoy-Voorhees generalisation of the Eguchi-Hanson solitons (with Euclidean signature). As an intermediary in the solution-generating process we obtain charged versions o…
The Einstein vacuum equations in five dimensions with negative cosmological constant are studied in biaxial Bianchi IX symmetry. We show that if initial data of Eguchi-Hanson type, modelled after the four-dimensional Riemannian Eguchi-Hanson space, have negative mass, the future maximal development does not contain horizons, i.e. the complement of the causal past of null infinity is empty. In particular, perturbations of Eguchi-Hanson-AdS spacetimes within the biaxial Bianchi IX symmetry class cannot form horizons, suggesting that such spacetimes are potential candidates for a naked singularit…
We present novel regular Euclidean solutions to General Relativity in presence of Maxwell and conformally coupled scalar fields. In particular, we consider metrics of the Eguchi-Hanson and Taub-NUT families to solve the field equations analytically. The solutions have nontrivial topology labeled by the Hirzebruch signature and Euler characteristic that we compute explicitly. We find that, although the solutions are locally inequivalent with the original (anti-)self-dual Eguchi-Hanson metric, their asymptotically locally Euclidean limit leads to the same global properties. We revisit the Taub-N…
The Dirichlet boundary-value problem and isoperimetric inequalities for positive definite regular solutions of the vacuum Einstein equations are studied in arbitrary dimensions for the class of metrics with boundaries admitting a U(1) action. We show that in the case of non-trivial bundles Taub-Bolt infillings are double-valued whereas Taub-Nut and Eguchi-Hanson infillings are unique. In the case of trivial bundles, there are two Schwarzschild infillings in arbitrary dimensions. The condition of whether a particular type of filling in is possible can be expressed as a limitation on squashing t…
We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. We also find the the multiple nut parameter extension of the inhomogeneous Einstein metrics on complex line bundles found recently by Lu, Page and Pope. We also provide a more general form of the Eguchi-Hanson solitons found by Clarkson and Mann. We discuss the global structure of such solutions and possible applications in string theory.
In this paper, we classify and construct five-dimensional black holes on gravitational instantons in vacuum Einstein gravity, with RxU(1)xU(1) isometry. These black holes have spatial backgrounds which are Ricci-flat gravitational instantons with U(1)xU(1) isometry, and are completely regular space-times outside the event horizon. Most of the known exact five-dimensional vacuum black-hole solutions can be classified within this scheme. Amongst the new space-times presented are static black holes on the Euclidean Kerr and Taub-bolt instantons. We also present a rotating black hole on the Eguchi…
Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）
In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L^2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the Levi-Civita connection onto the positive su(2) subalgebra of the Lie algebra so(4). Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R^4. That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a…
We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special Kähler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the STU model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the STU black hole solution, in the neighbourhood…
We study here the phase-transitional evolution between the Eguchi-Hanson soliton, the orbifolded Schwarzschild Anti de-Sitter black hole, and orbifolded thermal Anti de-Sitter space in Gauss-Bonnet gravity for a small Gauss-Bonnet coefficient $α$. Novel phase structure is uncovered for both negative and positive $α$ with spacetime configurations that are stable in Gauss-Bonnet gravity without being so in Einsteinian gravity. The evolutionary tracks taken towards such stable configurations are guided by quantum tunnelling and can be represented with a phase diagram constructed by comparing the …
