New Horizons for Black Holes and Branes

TL;DR

The paper develops and applies the blackfold effective theory to map the landscape of higher-dimensional, asymptotically flat vacuum black holes, uncovering new stationary solutions such as helical black strings/rings and odd-sphere horizons, plus non-uniform black cylinders. It demonstrates how ultraspinning Myers-Perry black holes emerge as even-ball blackfolds and reveals a rich phase structure with infinite rational non-uniqueness in certain regimes, alongside static minimal blackfolds tied to horizon uniqueness. By solving intrinsic and extrinsic blackfold equations and employing matched asymptotic expansions, the authors compute masses, angular momenta, entropies, and tensions, and chart horizon topologies and entropy rankings across dimensions. The work lays a foundation for future explorations of dynamical stability, charged generalizations, and a fuller, cross-dimensional phase diagram of black holes and branes.

Abstract

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes.

Figures (7)

• Figure 1: Helical black strings (left) and helical black rings (right).
• Figure 2: Local brane pressure ($i.e.$, minus tension) of the disc (2-ball) as a function of radius (in units of $1/\Omega$) for the case $n=3$. Integrating this brane pressure over the disc gives zero, as it should according to \ref{['zeroten']}.
• Figure 3: A graphical depiction of the non-uniform black cylinder based on the numerical evaluation of the blackfold equations for $n=1$ and $\nu=0.2$.
• Figure 4: Plot of the velocity $\Omega R(z)$ based on numerical solutions of eq. \ref{['cylian']} for $n=1$ and fixed $\kappa$ and $\Omega$ . Each curve represents $\Omega R(z)$ over a half-period. The curve oscillates between a minimum $R_-$ and a maximum $R_+$. The thick solid curve represents the uniform solution and has $\nu=0$. The remaining curves, starting from the solid one to the shorter-dashed ones, represent solutions with increasing values of $\nu$, respectively, $\nu=0.01, 0.1, 0.2, 0.3, 0.4$.
• Figure 5: Plot of the radius $R(z)$ as a function of $z$ for fixed $L$ and angular momentum $J$, based on numerical solutions of eq. \ref{['cylian']}, \ref{['cyliap']}, \ref{['cyliat']} where we chose $n=1$, $L=1$, $J=1$ and $G=1$. The curve oscillates between a minimum $R_-$ and a maximum $R_+$. The thick solid curve represents the uniform solution and has $\nu=0$. The remaining curves, starting from the solid one to the shorter-dashed ones, represent solutions with increasing values of $\nu$, respectively, $\nu=0.01, 0.1, 0.2, 0.3, 0.4$. The red curve has $\nu = 0.48$ and serves to illustrate what happens near extreme non-uniformity assuming the blackfold solution is trustworthy in that regime.