Positive Spin-induced Quadrupole Moment in String Theory

TL;DR

The study addresses whether string-theory microstate geometries can realize a positive spin-induced quadrupole moment distinct from Kerr. It develops rotating Running-Kerr-Taub-Bolt solutions on an Euclidean-Kerr-Taub-Bolt base with self-dual fluxes, then reduces to four-dimensional asymptotically flat spacetimes and computes the multipole moments using ACMC coordinates; the results show $M_2>0$ for small running and possible sign flips as the rotation parameter grows, with $M_2$ diverging near $|oldsymbol{eta}| o 1$. The work provides an infinite family of regular, horizonless, rotating five-dimensional solutions parameterized by an integer $p$, along with explicit expressions for charges, angular momenta, and higher multipoles, and establishes the Taub-NUT/SUSY limits as cross-checks. This demonstrates a concrete string-theoretic mechanism for positive quadrupole moments in spinning objects, linked to the presence of nontrivial topology and fluxes, and lays groundwork for exploring duality-related families and multi-bubble configurations with potential connections to black-hole physics.

Abstract

We identify singularity-free Running-Kerr-Taub-Bolt solutions of eleven-dimensional supergravity that descend to four-dimensional rotating solutions with flat-space asymptotics. We compute their spin-induced quadrupole moment and find that for a certain range of charges this quadrupole moment is positive. This behavior differs from the Kerr black hole and from most other spinning objects constructed with ``normal'' four-dimensional matter, and we discuss the top-down physics of these solutions that could be responsible for this unusual behavior.

Figures (6)

• Figure 1: Solutions $m(\alpha)$ to equation (\ref{['N and kappa']}), for $N$ and $P_{r_{+}}$ having the same sign. Magenta curves have $N=1>0$ and orange dashed curves have $N=-1<0$.
• Figure 2: Solutions $m(\alpha)$ to equation (\ref{['N and kappa']}), for $N$ and $P_{r_{+}}$ having opposite signs. Magenta curves have $N=1>0$ and orange dashed curves have $N=-1<0$.
• Figure 3: We intersect the $m(\alpha)$ curves from the previous figures, with the condition \ref{['periodicity of phi']} represented in in dashed blue lines. We only plot the curves corresponding to ${p}=1, 2,3$ and to $\alpha\geq 0$. The results are independent of the sign of $N$, since the red curve can be obtained either by superposing the $N=1$ magenta curves in Figures \ref{['fig:N>0 pr+>0 m(alpha)']} and \ref{['fig:N>0 pr+<0 m(alpha)']}, or by superposing the $N=-1$ orange curves. The symmetry comes because $N\rightarrow-N$ and $m\rightarrow-m$ flip \ref{['same-sign']} with \ref{['opp-sign']}.
• Figure 4: Plot of $R$ with respect to $\gamma$, for the solutions with $(m',\alpha')=(0.766044,0.742227)$ (${p}=2$) for $|{\gamma}|< 1$. The ratio diverges when the boost becomes infinite, $|{\gamma}|\rightarrow 1$.
• Figure 5: Right figure: more $N=1$ solutions $(m,\alpha)$ for values of ${p}$ from 4 to 100. Square red points are solutions of type 1, and blue round points are solutions of type 2.