Planar black holes and wormholes with a flat exterior

TL;DR

This paper constructs planar black holes and wormholes in $n\ge4$ dimensions whose exterior is Minkowski, by leveraging the extended dynamical region inside a nondegenerate Killing horizon of Gamboa's static plane-symmetric solution with a fluid obeying $p=\chi\rho$ for $\chi\in[-1/3,0)$. The interior matter becomes an anisotropic spacelike (tachyonic) fluid, and the exterior remains flat; the horizon is shown to be regular ($C^{1,1}$) in single-null coordinates, avoiding lightlike thin shells. The authors provide an explicit solvable case $\chi=-(n-4)/(3n-4)$ (with $n\ge5$) where the interior-to-exterior matching yields either a planar black hole with a Minkowski exterior or a traversable wormhole, and they extend the construction to general $\chi$ in $[-1/3,0)$. They analyze energy conditions: inside the horizon NEC and SEC can hold while WEC/DEC are violated for BHs, and all standard energy conditions are violated inside wormholes, highlighting interesting implications for horizon regularity and the role of tachyonic matter. The work opens questions on the thermodynamics and physical viability of these planar configurations within GR.

Abstract

We present $n(\ge 4)$-dimensional planar black holes and wormholes with a flat exterior, which are originated by an exact solution in general relativity. The nonvacuum regions of these objects are described by the extended dynamical region inside a nondegenerate Killing horizon of Gamboa's static plane symmetric solution with a perfect fluid obeying a linear equation of state $p=χρ$ for $χ\in[-1/3,0)$. The matter field inside the horizon is not a perfect fluid but an anisotropic fluid that may be interpreted as a {\it spacelike} (tachyonic) perfect fluid. While it satisfies the null and strong energy conditions in the black hole case, it violates all the standard energy conditions in the wormhole case. The metric on the horizon is not analytic but at least $C^{1,1}$ in the single-null coordinates in both cases, so it is regular and there is no lightlike massive thin shell on the horizon.

Figures (3)

• Figure 1: The Penrose diagram of the Minkowski spacetime in the quasiglobal coordinates (\ref{['metric-Buchdahl']}). $\Im^{+(-)}$ stands for a future (past) null infinity and its subscript is to distinguish different null infinities.
• Figure 2: The Penrose diagram of a planar black hole with the Minkowski exterior (a) in the regions I and III and (b) in the regions I, III, and IV. The shaded regions are described by the Gamboa solution (\ref{['ansatz00-2']}). A zigzag line corresponds to a curvature singularity located at $r=0$.
• Figure 3: The Penrose diagram of a planar wormhole with the Minkowski exterior (a) in the regions I and III and (b) in the regions I, III, and IV. The shaded regions are described by the Gamboa solution (\ref{['ansatz00-2']}). The Killing horizon $x=x_{\rm h}$ is not an event horizon in these cases.