Exact Supersymmetric Massive and Massless White Holes

TL;DR

This paper identifies exact supersymmetric, non-Abelian, four-dimensional configurations arising from heterotic-string backgrounds that saturate the BPS bound at special moduli where $M^2=Z^A{\cal R}_{AB}(\Phi_0)Z^B\to0$. By leveraging ten-dimensional SSW and GFS solutions with $SO(8)$ holonomy and embedding the spin connection into the gauge group, the authors derive massless and massive BPS states that remain anomaly-free due to Green–Schwarz cancellation. A key finding is a new class of supersymmetric white-hole (repulson) solutions exhibiting gravitational repulsion, with a repulsive core and a singular surface at $r_0=2(\sqrt{M^2+q^2}-M)$, suggesting an antigravity regime for these objects. They also obtain exact mass formulas for these states and show that non-Abelian vector multiplets are essential for nontrivial massless configurations, offering a framework for exploring nonperturbative dynamics at special moduli. Overall, the work demonstrates the existence of exact, non-Abelian SUSY configurations that challenge conventional black-hole intuition and open avenues for studying universal gravitational repulsion in string theory.

Abstract

We study special points in the moduli space of vacua at which supersymmetric electric solutions of the heterotic string theory become massless. We concentrate on configurations for which supersymmetric non-renormalization theorem is valid. Those are ten-dimensional supersymmetric string waves and generalized fundamental strings with SO(8) holonomy group. From these we find the four dimensional spherically symmetric configurations which saturate the BPS bound, in particular near the points of the vanishing ADM mass. The non-trivial massless supersymmetric states in this class exist only in the presence of non-Abelian vector fields.We also find a new class of supersymmetric massive solutions, closely related to the massless ones. A distinctive property of all these objects, either massless or massive, is the existence of gravitational repulsion. They reflect all particles with nonvanishing mass and/or angular momentum, and therefore they can be called white holes (repulsons), in contrast to black holes which tend to absorb particles of all kinds. If such objects can exist, we will have the first realization of the universal gravitational force which repels all particles with the strength proportional to their mass and therefore can be associated with antigravity.