Fake Schwarzschild and Kerr black holes

We present exact solutions describing a fake Schwarzschild black hole that cannot be distinguished from the Schwarzschild black hole by observations. They are constructed by attaching a spherically symmetric dynamical interior solution with a matter field to the Schwarzschild exterior solution at the event horizon without a lightlike thin shell. The dynamical region inside a Killing horizon of a static spherically symmetric perfect-fluid solution obeying an equation of state $p=χρ$ for $χ\in[-1/3,0)$ can be the interior of a fake Schwarzschild black hole. The matter field inside such a black hole is an anisotropic fluid that violates at least the weak energy condition and can be interpreted as a spacelike (tachyonic) perfect fluid. While the author constructed the first model of fake Schwarzschild black holes using Semiz’s solution for $χ=-1/5$, we present another one using Whittaker’s solution for $χ=-1/3$ in this paper. We also present a model of fake Kerr black holes whose interior is filled with a different matter field violating only the dominant energy condition near the event horizon. Because it contradicts the conservation theorem, this configuration of black holes is, in fact, precluded by the dominant energy condition.

💡 Research Summary

The paper introduces exact spacetime solutions that mimic the exterior of a Schwarzschild or Kerr black hole while possessing a non‑vacuum interior that cannot be distinguished from the standard black hole by any external observation. The construction hinges on attaching a spherically symmetric, dynamical interior solution to the Schwarzschild exterior at the event horizon without invoking a light‑like thin shell. The key requirement for a regular matching is that the interior be a static, spherically symmetric perfect‑fluid solution with a linear equation of state p = χ ρ where χ lies in the interval