Hawking Temperature, Sparsity and Energy Emission Rate of Regular Black Holes Supported by Primordial Dark Matter
Faizuddin Ahmed, Ahmad Al-Badawi, Edilberto O. Silva
TLDR
This paper explores regular black holes supported by primordial dark matter, revealing suppressed Hawking temperature and emission rates, and persistent instability.
Key contributions
- Investigated Hawking temperature, entropy, heat capacity, sparsity, and energy emission rate for PDM black holes.
- PDM suppresses Hawking temperature and spectral energy emission rate compared to the Schwarzschild case.
- Fixed-alpha heat capacity is negative, indicating persistent local thermodynamic instability.
- Geometrical sparsity parameter shows a slight reduction in the intermittency of the Hawking flux.
Why it matters
This paper advances our understanding of regular black holes by modeling them with primordial dark matter. It reveals how PDM impacts their thermodynamic stability and radiation, offering insights into exotic black hole physics. These findings are crucial for theoretical models and future astrophysical observations.
Original 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 \(α\) 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-\(α\) 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 \(α\ll 2M\), 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.
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