Black holes inside cosmic voids

TL;DR

This work derives a new analytic metric for a static, spherically symmetric black hole embedded in a cosmic void by sourcing the spacetime with the universal void density profile. The solution reveals two horizons: an inner black-hole horizon and an outer de Sitter-like horizon, with the inner horizon growing and the outer horizon shrinking as the void becomes emptier (larger $|\delta_c|$). Thermodynamic analysis shows a modified Hawking temperature $T_H$ compared to the Schwarzschild case, an area-law entropy $S=\pi r_h^2$, and a specific-heat minimum signaling a thermal transition influenced by the void; evaporation times decrease as the void empties. The study also sketches a potential thermodynamic interaction between horizons and suggests that voids can stabilize black-hole evolution, offering a link between local gravitational collapse and large-scale cosmic structure with possible implications for cosmological dynamics. These findings open avenues for more detailed investigations of black holes in underdense environments and their role in cosmic evolution, including horizon interactions and the timescape-like behavior of voids.

Abstract

This study examines the gravitational and thermodynamic properties of static, spherically symmetric black holes within cosmic voids -- vast underdense regions of the universe. By deriving a novel solution based on a universal density profile for voids, we analyze its spacetime structure, which reveals two horizons: One of the black hole and the other related to the de Sitter-like behavior. As the void approaches a perfect vacuum, the black hole horizon diminishes, tending to that of the Schwarzschild solution, while the outer horizon increases. We also study the solution stability via sound speed of the fluid, as well as the thermodynamic properties, including Hawking temperature, evaporation time, entropy, and specific heat. Our results show that as the void empties, the Hawking temperature rises, shortening evaporation times. The entropy follows the area's law and specific heat exhibits a minimum for a given black hole size, indicating a thermal transition and highlighting the role of voids in the black hole evolution. These findings offer new insights into the relationship between local gravitational collapse and large-scale cosmic structure, enhancing our understanding of the black hole behavior in underdense environments. We also provide a glimpse of a potential thermodynamic interaction between the event horizon and the cosmological horizon.

Figures (9)

• Figure 1: Universal density profile $\rho(r)$ as a function of $r$, for some values of $\delta_c$, namely, $\delta_c=-0.90$ (solid blue), $\delta_c=-0.95$ (dashed orange), $\delta_c=-0.99$ (dotdashed green), considering the parameters $\rho_0=0.00003$, $\alpha=2.4$, $\beta=7.5$, $r_v=100$, and $r_s=80$.
• Figure 2: Metric coefficient as a function of $r$, for some values of $\delta_c$, from bottom to top, namely, $\delta_c=-0.90$ (blue), $\delta_c=-0.95$ (orange), $\delta_c=-0.99$ (green), and Schwarzschild ($\rho_0=0$, red), considering the parameters $\rho_0=0.00003$, $\alpha=2.4$, $\beta=7.5$, $r_v=100$, $r_s=80$, $M=10$.
• Figure 3: On the horizontal axis $r$ such that $f(r) = 0$. On the vertical axis the Mass parameter $M$ for $r_s=80,r_v=100, \delta_c=-0.9,\rho_0=0.00003$
• Figure 4: Metric coefficient $f(r)$ as a function of r for $M<M_{crit}$ (upper blue curve), $M=M_{crit}$ (orange curve below), and $M>M_{crit}$ (lower green curve). We are using $r_s=80,r_v=100, \delta_c=-0.90$, and $\rho_0=0.00003$.
• Figure 5: Plot of $v_s^2$ (orange) and $f(r)$ (blue) as functions of $r$, considering the parameters $\rho_0=0.00003$, $\alpha=2.4$, $\beta=7.5$, $r_v=100$, $r_s=80$, $M=10.0$, and $\delta_c=-0.90$.