Gravitational Instanton Solutions Research Articles

Self-dual gravitational instantons in conformal gravity: Conserved charges and thermodynamics

We study non-Einstein Bach-flat gravitational instanton solutions that can be regarded as the generalization of the Taub-NUT/Bolt and Eguchi-Hanson solutions of Einstein gravity to conformal gravity. These solutions include non-Einstein spaces which are either asymptotically locally flat spacetimes (ALF) or asymptotically locally Anti-de Sitter (AlAdS). Nevertheless, solutions with different asymptotic conditions exist: we find geometries that present a weakened AlAdS asymptotia, exhibiting the typical low decaying mode of conformal gravity. This permits to identify the simple Neumann boundary condition that, as it happens in the asymptotically AdS sector, selects the Einstein solution out of the solutions of conformal gravity. All the geometries present non-vanishing Hirzebruch signature and Euler characteristic, being single-centered instantons. We compute the topological charges as well as the Noether charges of the Taub-NUT/Bolt and Eguchi-Hanson spacetimes, which happen to be finite. This enables us to study the thermodynamic properties of these geometries.

Sharpening the weak gravity conjecture with dimensional reduction

We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a "Lattice Weak Gravity Conjecture" that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.

Spontaneous Creation of Inflationary Universes and the Cosmic Landscape

We study some gravitational instanton solutions that offer a natural realization of the spontaneous creation of inflationary universes in the brane world context in string theory. Decoherence due to couplings of higher (perturbative) modes of the metric as well as matter fields modifies the Hartle-Hawking wavefunction for de Sitter space. Generalizing this new wavefunction to be used in string theory, we propose a principle in string theory that hopefully will lead us to the particular vacuum we live in, thus avoiding the anthropic principle. As an illustration of this idea, we give a phenomenological analysis of the probability of quantum tunneling to various stringy vacua. We find that the preferred tunneling is to an inflationary universe (like our early universe), not to a universe with a very small cosmological constant (i.e., like today's universe) and not to a 10-dimensional uncompactified de Sitter universe. Such preferred solutions are interesting as they offer a cosmological mechanism for the stabilization of extra dimensions during the inflationary epoch.

ERRATA: DUALITY AND SELF-DUAL TRIPLET SOLUTIONS IN EUCLIDEAN GRAVITY

Starting from the self-dual "triplet" of gravitational instanton solutions in Euclidean gravity, we obtain the corresponding instanton solutions in string theory by making use of the target space duality symmetry. These dual triplet solutions can be obtained from the general dual Taub-NUT de Sitter solution through some limiting procedure as in the pure gravity case. The dual gravitational instanton solutions obtained here are self-dual for some cases, with respect to certain isometries, but not always.

DUALITY AND SELF-DUAL TRIPLET SOLUTIONS IN EUCLIDEAN GRAVITY

Starting from the self-dual “triplet” of gravitational instanton solutions in Euclidean gravity, we obtain the corresponding instanton solutions in string theory by making use of the target space duality symmetry. We show that these dual triplet solutions can be obtained from the general dual Taub-NUT de Sitter solution through some limiting procedure as in the Euclidean gravity case. The dual gravitational instanton solutions obtained here are self-dual for some cases, with respect to certain isometries, but not always.

Symmetries of four-dimensional string effective action with cosmological constant

Classical solutions for a four-dimensional Minkowskian string effective action and an Euclidean one with cosmological constant term are derived. The former corresponds to electrovac solutions whereas the later solutions are identified as gravitational instanton solutions for Fubini-Study metric. The symmetries of the effective actions are identified and new classical solutions are generated by implementing appropriate noncompact transformations. The S-duality transformations on the equations of motion are discussed and it is found that they are S-duality noninvariant due to the presence of cosmological constant term.

Gravitational instantons with a scalar field.

Analytic gravitational instanton solutions in a theory which includes a self-interacting scalar field are obtained. The relevant potential for the scalar field satisfying equations of motion is determined by developing a general technique. The corresponding actions are calculated exactly and the qualitative features of the solutions discussed.

Instanton solutions in gravitational theories with nonlinear lagrangian

We obtain gravitational instanton solutions in the Einstein theory coupled with a scalar matter field that is conformally equivalent to gravitational theories with nonlinear lagrangian which are polynomial in the scalar curvature and contain a cosmological constant both for the quadratic and the large curvature limit cases. We also argue that the necessary condition for the existence of these solutions may be satisfied for nonlinear theories whose lagrangian depends on the full Ricci tensor. The implications of these solutions to the mechanism for vanishing of the low-energy cosmological constant are considered.

Axionic instantons and the creation of expanding universes

Abstract In a class of models of scalar matter coupled to N = 1 supergravity, we investigate the existence of gravitational instantons that correspond to the creation of expanding universes. Expressing the derivatively coupled pseudoscalar field in terms of a second rank antisymmetric tensor field (axion), we show that, under mild assumptions about the scalar potential, the theory possesses axion-induced gravitational instanton solutions with the desired interpretation. The assumptions made can be met in the effective four-dimensional theory obtained in a particular compactification of the zero-slope limit of the ten-dimensional superstring theory. Such a system offers an appealing framework for the natural realization of the recent idea that coupling constants, including the cosmological constant, are determined by universal dynamics.