Weyl Card Diagrams

TL;DR

This paper introduces 'card diagrams' as a new way to visualize and analyze the global structure of Weyl spacetimes across various dimensions, capturing horizons, singularities, and causal features more clearly than traditional Penrose diagrams.

Contribution

It develops the concept of card diagrams for generalized Weyl spacetimes, illustrating their use in understanding horizons, singularities, and analytic continuations, with applications to diverse solutions including black holes and branes.

Findings

Card diagrams effectively depict spacetime features and causal structures.

They can be continuously deformed with geometric parameters.

Applications include analysis of Kerr-Newman black holes, black rings, and brane solutions.

Abstract

To capture important physical properties of a spacetime we construct a new diagram, the card diagram, which accurately draws generalized Weyl spacetimes in arbitrary dimensions by encoding their global spacetime structure, singularities, horizons, and some aspects of causal structure including null infinity. Card diagrams draw only non-trivial directions providing a clearer picture of the geometric features of spacetimes as compared to Penrose diagrams, and can change continuously as a function of the geometric parameters. One of our main results is to describe how Weyl rods are traversable horizons and the entirety of the spacetime can be mapped out. We review Weyl techniques and as examples we systematically discuss properties of a variety of solutions including Kerr-Newman black holes, black rings, expanding bubbles, and recent spacelike-brane solutions. Families of solutions will share qualitatively similar cards. In addition we show how card diagrams not only capture information about a geometry but also its analytic continuations by providing a geometric picture of analytic continuation. Weyl techniques are generalized to higher dimensional charged solutions and applied to generate perturbations of bubble and S-brane solutions by Israel-Khan rods. This paper is a condensed and simplified presentation of the card diagrams in hep-th/0409070.