Primordial Black Hole Evaporation and Spontaneous Dimensional Reduction

Several different approaches to quantum gravity suggest the effective dimension of spacetime reduces from four to two near the Planck scale. In light of such evidence, this letter re-examines the thermodynamics of primordial black holes (PBHs) in specific lower-dimensional gravitational models. Unlike in four dimensions, $\done$-D black holes radiate with power $P \sim \Mbh^2$, while it is known no $(2+1)-$D (BTZ) black holes can exist in a non-anti-deSitter universe. This has important relevance to the PBH population size and distribution, and consequently on cosmological evolution scenarios. The number of PBHs that have evaporated to present day is estimated, assuming they account for all dark matter. Entropy conservation during dimensional transition imposes additional constraints. If the cosmological constant is non-negative, no black holes can exist in the $(2+1)$-dimensional epoch, and consequently a $(1+1)$-dimensional black hole will evolve to become a new type of remnant. Although these results are conjectural and likely model-dependent, they open new questions about the viability of PBHs as dark matter candidates.