Hidden Degeneracy in the Brick Wall Model of Black Holes

TL;DR

This paper reveals an additional degeneracy in the brick wall model of black holes for zero-energy states, impacting entropy calculations, while modes with complex frequencies do not show this degeneracy.

Contribution

It uncovers a new degeneracy in the brick wall model's zero-energy states, refining the understanding of black hole entropy.

Findings

States with non-zero energy show additional degeneracy.

Modes with complex frequencies lack this degeneracy.

Entropy calculations are affected by this degeneracy.

Abstract

Quantum field theory in the near-horizon region of a black hole predicts the existence of an infinite number of degenerate modes. Such a degeneracy is regulated in the brick wall model by the introduction of a short distance cutoff. In this Letter we show that states of the brick wall model with non zero energy admit a further degeneracy for any given finite value of the cutoff. The black hole entropy is calculated within the brick wall model taking this degeneracy into account. Modes with complex frequencies however do not exhibit such a degeneracy.