Quantum-Corrected Black Holes in Higher Dimensions: From Gravitational Collapse to Remnants, WGC-Like Behavior and Accretion Signatures
We study the gravitational collapse of a homogeneous dust sphere in higher-dimensional spacetime, with the loop quantum gravity correction entered through a modified Friedmann equation. Its most striking feature is an endpoint: at a finite horizon radius the temperature vanishes and evaporation stops, leaving a remnant. Reading \(α\) as an effective charge, we find behavior reminiscent of the Weak Gravity Conjecture (WGC), although no \(U(1)\) gauge field is present in the model. Solving the degeneracy conditions with the untruncated metric function, rather than with a mass expansion that is not uniform near the endpoint, we obtain closed-form expressions for the remnant radius and mass in \(D=4,5,6,7\). The unscaled ratio \(α/M_{\text{remnant}}^2\) is constant only in four dimensions and grows as \(α^{4-D}\) elsewhere, but it carries dimension \(L^{8-2D}\), so that growth is an artifact of the units. The dimensionless combination \(\tilde{\mathcal{R}} = (α/M^2) r_0^{2D-8}\) settles instead on a finite \(α\)-independent number in every dimension, decreasing from \(27/64\) in four dimensions to \(13824/(15625π^4)\) in seven. We also deform the quantum parameter, \(α\to α+ \varepsilon\), and evaluate \(-T(\partial S/\partial \varepsilon)_M\) in the remnant limit. Because \((\partial M/\partial r)_α\) vanishes there, the fixed-entropy derivative reduces exactly to a fixed-radius one, and the resulting combination \(\mathcal{U}\) is finite in each dimension but depends on \(\varepsilon\) except for \(D=5\). What is invariant is the product \(\mathcal{R}\,\mathcal{U}\,M_{\text{remnant}} = (D-3)/2\), which we verify numerically. Lastly, we study Bondi accretion onto the quantum-corrected black hole and obtain the Eddington luminosity for each dimension.