Tidal Stretching and Compression in Black Bounce Backgrounds

TL;DR

This work investigates how tidal forces behave for radially infalling observers in four black-bounce spacetimes (SV, Bardeen-type BB, holonomy-corrected BH, and polymerized BH) by solving the geodesic deviation equation in an orthonormal tetrad. The authors derive general expressions for the tidal components $k_1$ and $k_2$ in terms of the metric functions $f(r)$ and $h(r)$ and analyze their behavior across models, finding that all tidal components remain finite throughout the manifold, including at wormhole throats; notably, the Bardeen-type BB exhibits a rich tidal structure with possible radial compression in inner regions. SV and holonomy-corrected spacetimes generally resemble Schwarzschild in that sign changes of tidal components may lie behind horizons, while the polymerized BH shows distinct, model-specific trends and lacks simple analytical displacement-vector solutions. Overall, tidal signatures provide a diagnostic to distinguish BB geometries and motivate extensions to rotating cases and tidal-disruption scenarios to assess observational implications.

Abstract

Black bounces are compact objects that combine the structures of regular black holes with those of wormholes. These spacetimes exhibit a rich causal structure and can differ fundamentally from usual black holes. In this work, we study the behavior of the tidal forces by considering different black bounce models. To this end, we start with the geodesic deviation equation and the tidal tensor, from which we compute the radial and angular components of the tidal forces. We find that these components are finite throughout the entire spacetime, including at the wormhole throats. Through the components of the displacement vector, we observe that, unlike the Schwarzschild case, a compression effect on bodies may occur in certain regions.

Figures (16)

• Figure 1: Behavior of the horizon radii and the wormhole throat radius for the Bardeen-type solution as a function of the regularization parameter. We choose $m=1$.
• Figure 2: A schematic representation of the tetrad basis attached to the particle at $P$ is shown. The infinitesimal displacement vector $\xi^\mu$ between two nearby geodesics $x^\mu(\tau)$ and $\tilde{x}^\mu(\tau)$ is also depicted.
• Figure 3: Radial tidal force as function of coordinate $r$ for different values of $a$, fixing $m = 1$. The vertical line is located at $r = 2m$.
• Figure 4: Angular tidal force as function of coordinate $r$ for different values of $a$, fixing $m = 1$ and $b = 30m$. The vertical line is located at $r = 2m$.
• Figure 5: Radial (top) and tangential (bottom) components of the displacement vector for radial geodesics in the SV spacetime as a function of the radial coordinate for different values of $a$. In this case, the boundary conditions \ref{['ICI']} were used with $b=100$ and $m=1$.