# From Static to Cosmological Solutions of N=2 Supergravity

## TL;DR

This paper constructs cosmological solutions with Kasner-like behavior in N=2 supergravity by analytically continuing black hole solutions, revealing dynamic patches and connections to higher-dimensional brane configurations.

## Contribution

It introduces a method to derive cosmological solutions from static black hole solutions in N=2 supergravity through analytic continuation, including explicit higher-dimensional lifts.

## Key findings

- Existence of Kasner-like cosmological patches derived from black hole solutions.
- Explicit higher-dimensional lifts to 5, 6, 10, and 11 dimensions.
- In the extremal limit, solutions correspond to BPS brane configurations.

## Abstract

We obtain cosmological solutions with Kasner-like asymptotics in N=2 gauged and ungauged supergravity by maximal analytic continuation of planar versions of non-extremal black hole solutions. Initially, we construct static solutions with planar symmetry by solving the time-reduced field equations. Upon lifting back to four dimensions, the resulting static regions are incomplete and bounded by a curvature singularity on one side and a Killing horizon on the other. Analytic continuation reveals the existence of dynamic patches in the past and future, with Kasner-like asymptotics. For the ungauged STU-model, our solutions contain previously known solutions with the same conformal diagram as a subset. We find explicit lifts to five, six, ten and eleven dimensions which show that in the extremal limit, the underlying brane configuration is the same as for STU black holes. The extremal limit of the six-dimensional lift is shown to be BPS for special choices of the integration constants. We argue that there is a universal correspondence between spherically symmetric black hole solutions and planar cosmological solutions which can be illustrated using the Reissner-Nordstr\"om solution of Einstein-Maxwell theory.