Hawking Temperature, Sparsity and Energy Emission Rate of Regular Black Holes Supported by Primordial Dark Matter

TL;DR

This paper analyzes the thermodynamic and radiative properties of regular black holes supported by primordial dark matter, focusing on Hawking temperature, entropy, sparsity, and emission rate, with emphasis on the effects of the regularity scale parameter.

Contribution

It provides a detailed study of how primordial dark matter influences black hole thermodynamics and Hawking radiation, including the effects of the regularity scale parameter and comparison to Schwarzschild black holes.

Findings

PDM scale suppresses Hawking temperature and energy emission rate.

Heat capacity remains negative, indicating thermodynamic instability.

Sparsity parameter slightly reduced, affecting Hawking flux intermittency.

Abstract

In this paper, we investigate the thermodynamic and radiative properties of a regular black hole sourced by primordial dark matter (PDM), modeled effectively through a Dirac--Born--Infeld (DBI) scalar field. We compute the Hawking temperature, the entropy obtained from the first law at fixed PDM scale, the specific heat capacity, the sparsity parameter of the Hawking flux, and the spectral energy emission rate. Particular attention is devoted to the role played by the regularity scale parameter \(\alpha\) and to the recovery of the Schwarzschild limit. Using the normalization in which the integration constant \(M\) is the ADM mass and \(f(r)=1-2M/r+\mathcal{O}(r^{-3})\), we find that the PDM scale suppresses the Hawking temperature and the spectral energy emission rate relative to the Schwarzschild case. The fixed-\(\alpha\) heat capacity remains negative along the physical branch, indicating the persistence of local thermodynamic instability in the canonical ensemble. Moreover, within the effective-area prescription adopted here, the geometrical sparsity parameter receives a negative leading correction in the perturbative regime \(\alpha\ll 2M\), implying a slight reduction of the intermittency of the Hawking flux. We also distinguish between the near-horizon geometrical estimate and the shadow-based high-energy absorption cross-section used in the emission rate.