Are Astrophysical "Black" Holes Leaky?

TL;DR

This paper investigates how scale invariant dark energy modifications affect black hole horizons, suggesting they may be 'leaky' and have observable astrophysical consequences, including potential particle winds and impacts on star formation.

Contribution

It demonstrates that modified black holes lack trapped surfaces and horizons, and develops a formalism for analyzing rotating black holes under scale invariant dark energy.

Findings

Modified black holes have no trapped surfaces or event horizons.

Potential existence of particle winds from 'leaky' black holes.

Framework for analyzing rotating black holes with dark energy modifications.

Abstract

We continue a study by Adler and Ramazano\uglu (AR) of "black" holes as modified by a scale invariant dark energy action. For the spherically symmetric Schwarzschild-like case, (AR) found that there is no event horizon; hence spacetime is not divided by the "black" hole into causally disconnected regions. We review the formalism for locating trapped surfaces and apparent horizons, and show that the modified "black" hole has no trapped surfaces. Thus one suspects that it is "leaky", and that there will be a "black hole wind" of particles streaming out from the location of the nominal horizon. This will have astrophysical consequences, for example, the wind may feed and stabilize star formation in the vicinity of the "black" hole. We initiate a study of the stationary axially-symmetric rotating "black" hole as modified by a scale invariant dark energy action, i.e, one that is Kerr-like. To set up the axial case, we note that the conserving completion of the dark energy stress energy tensor can be calculated algebraically by solving a $2 \times 2$ matrix equation. Using Mathematica we calculate and simplify the modified system of Einstein equations for the axial case in quasi-isotropic coordinates, and give appropriate boundary conditions. Solution of these equations, which may require developing a special purpose numerical program, is rendered tricky by a residual general coordinate invariance of quasi-isotropic coordinates. This leads to the interesting mathematical question of representing a positive planar function as the gradient squared of a harmonic function.