On a Class of Exact Arbitrarily Differentiable de Sitter Cores with Kerr Exteriors: Possible gravastar or regular black hole mimickers

TL;DR

This work constructs rotating gravastar-like objects with exact de Sitter interiors and Kerr exteriors by gluing them with a finite, highly differentiable transition shell, controlled by radial functions $\mu(r)$ and $\lambda(r)$ to achieve $C^{n}$ continuity. The outer atmospheric layer is analyzed for energy conditions (WEC, DEC, SEC), with a concrete example showing that appropriate parameter choices yield a physically acceptable atmosphere and a Lorentzian, non-singular spacetime. The model predicts a topological change of the ergoregion to $S^{1}\times S^{1}$ and identifies observational signatures in null geodesics that could distinguish these mimickers from true Kerr black holes. Overall, the paper provides a nonperturbative framework for exact, differentiable Kerr exterior solutions with de Sitter cores suitable as gravastar-like black hole mimickers, with potential astrophysical implications and tests via lensing and dynamics near the horizon.

Abstract

Within the paradigm of non-perturbative Einstein gravity we study continuous curvature manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds could represent the spacetime of rotating gravastars or other similar black hole mimickers. The scheme presented here allows for a $C^{n}$ metric transition from the exactly de Sitter interior to the exactly Kerr exterior, with $n$ arbitrarily large. Generic properties that such models must possess are discussed, such as the changing of the topology of the ergosphere from $S^{2}$ to $S^{1}\times S^{1}$. It is shown how in the outer layers of the transition region (the ``atmosphere'' as it is often called in astrophysics) the dominant/weak and strong energy conditions can be respected. However, much like in the case of its static spherically symmetric gravastar counterpart, there must be some assumptions imposed in the atmosphere for the energy conditions to hold. These assumptions turn out to not be severe. The class of manifolds presented here are expected to possess all the salient features of the fully generic case. Strictly speaking, a number of the results are also applicable to the locally anti-de Sitter core scenario, although we focus on the case of a positive cosmological constant.

Figures (16)

• Figure 1: Domains of the pure Kerr spacetime. The outer orange line represents the outer limit of the ergoregion. The solid red line represents the event horizon. The dashed red line represents the inner Cauchy horizon, and the dashed orange line the inner limit of the ergoregion. Here the Boyer-Lindquist $r$ coordinate directly measures distance from the center of the plot, hence the peculiar shape of the inner ergosurface. (i.e. In this plot, and those that follow, the BL $r$ and $\theta$ coordinates are being utilized as "polar" coordinates.)
• Figure 2: This simplest continuous and differentiable gravastar model with physical atmosphere, taken from ref:ourgrava and inspired by ref:grava1. The radial pressure ($p_{r}$) is plotted as a function of radius. The de Sitter negative pressure exists at the center ($p_{c}$), removing the Schwarzschild singularity. In order to respect energy conditions in the atmosphere the radial pressure must transition through a crust region to become positive before falling to zero at the boundary $R$.
• Figure 3: A superposition of the interesting surfaces of de Sitter spacetime, Kerr spacetime, and the shell. The solid and dashed red and orange lines represent the same Kerr surfaces as in figure \ref{['fig:kerrdomains']}. The thick blue circle represents the transition shell, and the dashed blue line represent the pure de Sitter horizon. The outer layer of the shell should be located just outside the Kerr horizon, but inside the de Sitter horizon, for a black hole mimicker such as a gravastar.
• Figure 4: A representative model of the black hole mimicker generated using actual parameters of the models in the paper, which will be discussed below in subsection \ref{['sec:toy']}. The transition shell is represented as the thick blue region, and the ergosurface is indicated by the dashed orange line. Notice that now the ergosurface has $S^{1}\times S^{1}$ topology. Inset: A close up of where the ergosurface penetrates the transition shell.
• Figure 5: A (partial) possible Penrose-Carter diagram for the spacetime under study. The blue region represents the shell which is bounded by de Sitter on the left and Kerr on the right. The exact structure inside the shell is quite complex and therefore that region may not be accurately depicted. The full structure is not depicted as the spacetime for $r < r_{1}$ is not considered in our domain. (See (\ref{['eq:coorddomain']}) and the comments that follow it.)