Year: 2026
Type: article
Abstract: The paper develops a model to understand the effective quantum geometry of a black hole horizon and the emission of Hawking spectrum in $$2+1$$ 2 + 1 dimensions. Using the algebra of Hamiltonian charges on the horizon, we establish that one should view the black hole horizon as formed out of quantised lengths of elementary quanta of value $$8\pi \ell _{P}\, n$$ 8 π ℓ P n , where $$n\in \mathbb {N}$$ n ∈ N , and $$\ell _{P}$$ ℓ P is the Planck length. We determine the black hole entropy using this equidistant length spectrum in the microcanonical ensemble and show that its value is close to the Bekenstein-Hawking entropy. To evaluate the Hawking spectrum, we note that, to an observer near the black hole horizon, the entropy (or length of horizon cross-section) is related to the black hole energy. Hence, one may develop a formulation of length ensemble (similar to the area canonical ensemble of Krasnov) from which the black body spectrum may be obtained directly. This local observer perceives a Hawking spectrum whose temperature is modified by the Tolman factor.
Source: The European Physical Journal C
Authors: Akriti Garg, Ayan Chatterjee
Institution: Central University of Himachal Pradesh
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G6160989398
OpenAlex ID: W7165763867