From de Sitter to anti-de Sitter singularity regularization: Theory and phenomenology

Abstract

Recent investigations of vacuum polarization in extremely compact stars suggest that, in such regimes, the effective matter content of spacetime may acquire a vacuum-energy equation of state with negative energy density, mimicking a negative cosmological constant. Motivated by this observation, we introduce a general algorithm to modify well-known spherically symmetric regular black hole metrics by replacing their usual de Sitter cores (dSC) with Anti-de Sitter cores (AdSC). Like their dSC counterparts, these AdSC solutions may exhibit two, one, or no horizons depending on the value of a regularization parameter l. We present explicit examples of AdSC-Bardeen and AdSC-Dymnikova metrics, analyze their main properties, and investigate some of their phenomenological signatures using test fields. In particular, we compare their fundamental quasinormal modes and echo signals with those of the dSC cases, highlighting potential avenues for distinguishing them observationally.

Figures (13)

• Figure 1: Top panel: Sequence of constant-density stars approaching a gravastar in the black hole limit. As the star is compressed, a spherical shell of infinite curvature moves towards the surface, inside of which lies a region of negative effective pressure (in blue). Bottom panel: Sequence of constant-density stars approaching the black hole limit together with their vacuum polarization effects. The star is regular and displays a core of negative effective energy that expands to fill the whole interior in the black hole limit, where they can be approximated by the AdS counterparts of gravastars Arrechea:2024vxp.
• Figure 2: Plot of the metric function $f_{ \text{B--AdS}}$ for different values of the regularization parameter $\ell$. Depending on its value, the metric can exhibit two, one, or no horizons. The Anti-de Sitter core causes $f$ to take values greater than $1$ at small radii.
• Figure 3: Comparison of the $f$ and $m$ functions for the dSC and AdSC-Bardeen metrics. The regularization parameters have been fixed to $\ell_{ \text{B--dS}}\approx 0.77$ and $\ell_{ \text{B--AdS}}\approx 0.46$ so that both solutions exhibit a single, extremal horizon, even though this horizon is at different radial positions for both models. While their geometries are similar at large $r$, discrepancies appear near the origin. In particular, the Misner--Sharp--Hernandez mass takes negative values in some region for the AdSC-Bardeen metric.
• Figure 4: Stress-energy tensor components of the AdSC-Bardeen solution for $\ell=0.62$, which corresponds to a solution of the horizonless kind. The negative energy interior must be surrounded by an exterior region of positive energy density to ensure positivity of the mass at infinity. For this particular solution, the strong energy condition is violated inside a sphere of radius $r\approx 0.854$, indicated by the thin vertical line.
• Figure 5: Metric function $f_{ \text{D--AdS}}$ for different values of the regularization parameter $\ell$. Depending on its value, the metric can exhibit two, one, or no horizons. At large radii this metric quickly approaches the Schwarzschild solution.