Escaping from the black hole?

Abstract

We show that if there exists a special kind of Born-Infeld type scalar field, then one can send information from inside a black hole. This information is encoded in perturbations of the field propagating in non-trivial scalar field backgrounds, which serves as a "new ether". Although the theory is Lorentz-invariant it allows, nevertheless, the superluminal propagation of perturbations with respect to the "new ether". We found the stationary solution for background, which describes the accretion of the scalar field onto a black hole. Examining the propagation of small perturbations around this solution we show the signals emitted inside the horizon can reach an observer located outside the black hole. We discuss possible physical consequences of this result.

Figures (2)

• Figure 1: For the background solution in the case $c_{\infty }^{2}=5/4$ the squared sound speed (red) and the normalized energy density, $(\varepsilon -\Lambda )/\alpha ^{2}$, (blue) are shown as functions of radial coordinate $x\equiv r/r_{g}$. The sound horizon $r_{\ast }/r_{g}=4/5$ is located inside the Schwarzschild horizon.
• Figure 2: In the Eddington-Finkelstein coordinates the emission of a sound signal from the falling spacecraft is shown. The blue cones correspond to the future light cones and the red cones are the future sonic cones (\ref{['eta']}). The black curve represents the world line obtained numerically from Eqs. (\ref{['4velocity']}), (\ref{['anz']}), (\ref{['F']}) for the spacecraft which moves together with a falling background field. Being between the the Schwarzschild ($r=r_{g}$) and sound ($r=r_{\ast }$) horizons the spacecraft emits an acoustic signal (shown by red) which reaches the distant observer in finite time. The trajectory of the signal is obtained by the numerical integration of Eq. (\ref{['eta']}).