de Sitter versus Anti de Sitter flows and the (super)gravity landscape: Part II

TL;DR

This work systematically maps the space of regular gravitational solutions in Einstein-scalar theory that interpolate between AdS and dS regimes. Using a robust first-order (superpotential) formalism and a spherical-sliced black-hole-like ansatz, it classifies flow endpoints, derives global rules governing horizons and endpoint types, and constructs a rich set of explicit flows including AdS/dS boundaries, Minkowski boundaries, shrinking endpoints, and Gubser-regular endpoints. A key result is a no-go theorem ruling out regular flows connecting AdS boundaries to dS shrinking endpoints for $d>2$, with the no-go extending to multi-scalar setups. The paper also generalizes Gubser-regularity criteria to radial, non-Lorentz-invariant contexts, explores multiscalar extensions, thin-wall brane junctions, and the hyperbolic-slicing variant, thereby broadening the holographic landscape of cosmological and black-hole solutions and their dual field theories.

Abstract

Generic solutions are studied in Einstein-scalar gravity in an ansatz that can interpolate between de Sitter and Anti-de Sitter regimes. The scalar potential is arbitrary. All solutions are determined by their end-points in the scalar field space. All such end-points are classified. This provides a complete classification and characterization of the full space of regular solutions. It is shown that there are no regular (Centaur) solutions that interpolate between an AdS boundary and a dS interior, within our ansatz, when $d>2$. This no-go theorem persists in the presence of multiple scalar fields with a non-trivial field space metric. The Gubser classification of regular solutions is also upgraded to include cases that are not Lorentz invariant and do not contain AdS boundaries.

Figures (33)

• Figure 1: Depiction of the structure of possible flows in the spherically sliced ansatz. All horizons included are regular. The finite endpoints in the upper row are minima (maxima) of a positive (negative) superpotential. The finite endpoints in the lower correspond to maxima (minima) of the positive (negative) superpotential. We have excluded flows with naked singularities, i.e. flows running to a bad singularity that is not covered by a black-hole event horizon. Gubser-reg. stands for Gubser-regular endpoint, extensively discussed in Appendix \ref{['asymp']}.
• Figure 2: Flow from a boundary of dS$_5$ at $\varphi=1$, to the center of AdS$_5$ at $\varphi=0$. The solution has a horizon in the dS regime. $T$ and $f$ diverge at $\varphi=0$ in a correlated manner so that the curvature invariants are finite. We added zoom-in plots for $f$ and $V$ to emphasize the presence of a horizon and of the extremum respectively. In the bottom-left panel, we display the functions that appear in the curvature invariants, defined in Appendix \ref{['sect:inv_sphere']}. They are regular everywhere along the flow.
• Figure 3: Flow from a boundary of dS$_5$ at $\varphi=1$ to the center of dS$_5$ at $\varphi=0$. The flow develops a horizon in the dS regime. $T$ and $f$ diverge at $\varphi=0$ in a correlated manner so that the curvature invariants are finite. We display the combinations that appear in the curvature invariants \ref{['sect:inv_sphere']}.
• Figure 4: Flow from a boundary of M$_5$ at $\varphi=1$ to the center of AdS$_5$ at $\varphi=0$. $T$ and $f$ diverge at $\varphi=0$ in a correlated manner so that the curvature invariants are finite. We display the combinations that appear in the curvature invariants \ref{['sect:inv_sphere']}.
• Figure 5: Flow from a $d+1$ boundary endpoint at $\varphi=0$ to a black hole. The sign of the potential at the boundary, $V(0)$, determines whether this is an AdS, dS or Minkowski boundary. The vanishing of $f$ signals the presence of a horizon. All three solutions have a black-hole event horizon, with a singularity in the interior.