Metastrings, Metaparticles and Black Hole Thermodynamics: On the Road Towards a Non-singular Black Hole Remnant

Abstract

We investigate the thermodynamic evolution and endpoint of black hole evaporation in the framework of metastring theory and its particle excitations, the metaparticles. Metaparticles arise as zero modes of metastrings propagating on modular (doubled) spacetime and obey a modified dispersion relation exhibiting intrinsic UV/IR mixing controlled by a duality scale mu. Using a generalized Bekenstein argument adapted to metaparticles, we derive quantum-corrected entropy contributions associated with geometric and dual (winding-like) sectors of the underlying phase space. When treated independently, these two entropy branches lead to an incomplete thermodynamic description, exhibiting unphysical behavior at small horizon area. We show that consistently treating the metaparticle as a single entangled quantum object -- rather than as two independent sectors -- naturally resolves these pathologies. We propose a pseudo-entangled total entropy that incorporates correlations between the geometric and dual sectors. The reality requirement of the entropy dynamically enforces a minimal horizon area and, equivalently, a minimal effective length scale associated with modular spacetime. The resulting black hole thermodynamics exhibits a finite maximal temperature, a divergence of the heat capacity signaling a continuous phase transition, and a shutdown of Hawking radiation through geometric channels, leaving behind a cold, stable remnant. Unlike matter-supported or curvature-bounded regular black holes, the remnant obtained here is non-material and non-geometric in nature, corresponding to a finite modular core of spacetime rather than a dust-filled interior. We compare this scenario with mimetic gravity and other non-singular black hole models, emphasizing the distinct role played by first-class constraints, entropy, and modular geometry in the present framework.

Figures (7)

• Figure 1: Metaparticle-corrected black hole entropy as a function of mass $\tilde{M}$ in Planck units for three values of the metaparticle- duality parameter $\tilde{\mu}$. All curves include logarithmic corrections to the standard Bekenstein-Hawking entropy. We particularly show the functional behavior for small masses.
• Figure 2: Left: The Metaparticle-corrected Hawking (rescaled) temperature $\tilde{\tau}(\tilde{m})$ showing a finite maximum at $\tau_{\text{max}}=1/2\pi$ followed by a rapid decrease to zero. Right: Comparison between the rescaled metaparticle-corrected heat Capacity (vs rescaled mass $\tilde{m}$) with that of Hawking's heat capacity result.
• Figure 3: Evaporation rates $-\frac{d\tilde{M}}{d\tilde{t}}$ for various values of $\tilde{\mu}$, compared to the Hawking case (dashed line). Bottom: total evaporation time for each model, assuming $M_0 = 10 M_P$.
• Figure 4: Pseudo-entanglement entropy $S_{\mathrm{ent}}(\tilde{a})$ (green) compared with the individual branches $S^+(\tilde{a})$ and $S^-(\tilde{a})$. The vertical dashed line marks the minimum allowed area $\tilde{a}_{\min}$, below which the entangled entropy becomes non-real.
• Figure 5: Log--log plot of the pseudo-entanglement entropy $S_{\mathrm{ent}}(\tilde{a})$ (green) together with the individual branches $S^+(\tilde{a})$ and $S^-(\tilde{a})$, shown up to very large $\tilde{a}$. The vertical dashed line marks the dynamically generated minimum area $\tilde{a}_{\min}$, below which the entangled entropy becomes non-real. The log--log representation makes visible the suppressed growth of the $S^+$ branch and shows that, at sufficiently large $\tilde{a}$, all three entropies approach parallel linear behavior, signaling the recovery of the classical Bekenstein--Hawking scaling.