Bound States of Black Holes and Other $P$-Branes

TL;DR

This work reexamines the proposal that certain extremal dilaton black holes in string theory correspond to BPS string states, showing that the four scalar/Maxwell couplings $a=\ oot{3}\{3},1,1/\root{3}\{3},0$ map to 1–4 particle bound states at threshold with zero binding energy. It demonstrates that not only masses and charges but also spins and supermultiplet structures are consistent with the bound-state interpretation, identifying Kerr-type angular momentum with the superspin $L$ and restricting black holes to $L=0$ elementary states. The authors extend the analysis to super $p$-branes in $D$ dimensions, constructing multi-centered solutions that realize $\,\Delta=4/n$ bound states of fundamental $\Delta=4$ branes; they also analyze entropy and temperature, finding reliable microscopic entropy predictions mainly for the dilaton-free case ($a=0$) and highlighting subtleties in the general case. Overall, the work integrates black hole, string, and $M$-theory perspectives, showing that bound-state formations across dimensions are consistent with dualities and supersymmetry and offering a framework for understanding black hole entropy via multi-centered branes.

Abstract

In the process of identifying heterotic and Type $II$ BPS string states with extremal dilaton black holes, it has been suggested that solutions with scalar/Maxwell parameters $a=\sqrt{3}$, $1$, $1/\sqrt{3}$ and $0$ correspond to $1-$, $2-$, $3-$ and $4$-particle bound states at threshold. (For example, the Reissner-Nordstrom black hole is just a superposition of four Kaluza-Klein black holes). Here we show that not only the masses, electric charges and magnetic charges but also the spins and supermultiplet structures of the string states are consistent with this interpretation. Their superspin $L$ corresponds to the Kerr-type angular momentum and hence only the $L=0$ elementary BPS states are black holes. Moreover, these results generalize to super $p$-branes in $D$-dimensions. By constructing multi-centered $p$-brane solitons, the new super $p$-branes found recently with various values of $a^2=Δ-2(p+1)(D-p-3)/(D-2)$ are seen to be bound states of the fundamental ones with $Δ=4$.