The optimal entropy bound and the self-energy of test objects in the vicinity of a black hole

TL;DR

This paper provides a proof supporting the conjecture that the entropy bound for objects near black holes cannot be improved by additional quantum numbers, using a gedanken experiment involving scalar charges and the no-hair principle.

Contribution

It introduces a novel gedanken experiment demonstrating that scalar charges do not affect the energy bound, supporting the conjecture about the entropy bound's optimality.

Findings

Scalar charge does not contribute to self-energy.

The energy for black hole assimilation is purely gravitational.

The original entropy bound remains unaltered by scalar charge knowledge.

Abstract

Recently Bekenstein and Mayo conjectured an entropy bound for charged rotating objects. On the basis of the No-Hair principle for black holes, they speculate that this bound cannot be improved generically based on knowledge of other ``quantum numbers'', e.g. baryon number, which may be borne by the object. Here we take a first step in the proof of this conjecture. The proof make use of a gedanken experiment in which a massive object endowed with a scalar charge is lowered adiabatically towards a Schwarzschild's black hole and than dropped into the black hole from some proper distance above the horizon. Central to the proof is the intriguing fact that the self-energy of the particle receives no contribution from the scalar charge. Thus the energy with which the object is assimilated consists of its gravitational energy alone. This of course agrees with the No-scalar-Hair principle for black holes: after the object is assimilated into the black hole, any knowledge of the scalar field properties is lost. Using the GSL, we reach the conclusion that the original entropy bound was not improved by the knowledge of the scalar charge. At the end we speculate on whether or not massive vector fields may serve in the tightening of the entropy bound.