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

TL;DR

This paper demonstrates that certain extremal black holes and super p-branes can be understood as bound states of fundamental BPS states, with consistent mass, charge, spin, and supersymmetry properties, extending to higher dimensions.

Contribution

It shows that the properties of extremal black holes and super p-branes align with bound state interpretations, including their superspin and supermultiplet structures, generalizing previous results.

Findings

Masses, charges, spins, and supermultiplet structures are consistent with bound state interpretation.

Elementary BPS states are only the L=0 black holes.

Results extend to super p-branes in arbitrary dimensions.

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 $a^2=\Delta-2(p+1)(D-p-3)/(D-2)$ are seen to be bound states of the fundamental ones with $\Delta=4$.