Fake Schwarzschild and Kerr black holes

TL;DR

This paper constructs exact solutions for fake Schwarzschild and Kerr black holes that are observationally indistinguishable from real ones, using interior matter fields that violate certain energy conditions, challenging their physical plausibility.

Contribution

It introduces new models of fake black holes with specific interior matter configurations, expanding the theoretical landscape of such solutions.

Findings

Fake Schwarzschild black holes can have interior solutions with anisotropic fluids violating energy conditions.

A new model of fake Kerr black holes with matter violating the dominant energy condition is proposed.

Some configurations are physically inconsistent due to violation of conservation laws and energy conditions.

Abstract

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 $p=\chi\rho$ for $\chi\in[-1/3,0)$ 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 $\chi=-1/5$, we present another one using Whittaker's solution for $\chi=-1/3$ 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.