Black Hole as a Wormhole Factory

On general grounds, one may argue that a black hole stops radiation at the Planck mass, where the radiated energy is comparable to the black hole's mass. And also, it has been argued that there would be a "wormhole-like" structure, known as "space-time foam", due to large fluctuations below the Planck length. In this paper, as an explicit example, we consider an exact classical solution which represents nicely those two properties in a recently proposed quantum gravity model based on different scaling dimensions between space and time coordinates. The solution, called "Black Wormhole", consists of two different states, depending on its mass M and an IR parameter omega: For the black hole state, a non-traversable wormhole occupies the interior region of the black hole around the singularity at the origin, whereas for the wormhole state, the interior wormhole is exposed to an outside observer as the black hole horizon is disappeared from evaporation. The black hole state becomes thermodynamically stable as it approaches to the merge point where the interior wormhole throat and the black hole horizon merges, and the Hawking temperature vanishes at the exact merge point. This solution suggests the "Generalized Cosmic Censorship" by the existence of a wormhole-like structure which protects the naked singularity even after the black hole evaporation. One could understand the would-be wormholes inside the black hole horizon as the results of microscopic wormholes created by "negative" energy quanta which have entered the black hole horizon in Hawking radiation processes: The quantum black hole could be a wormhole factory. It is found that this speculative picture may be consistent with the recent "ER=EPR" proposal for resolving the recent black hole entanglement debates.Comment: Added some more words on (1) the transition between the black hole phase and wormhole phase and (2) the notion of a wormhole "factory" in Fig. 5. Updated references, Accepted in PL

K-unstable singular del Pezzo surfaces without anticanonical polar cylinder

We prove the existence of singular del Pezzo surfaces that are neither K-semistable nor contain any anticanonical polar cylinder

Alpha invariants of birationally bi-rigid Fano 3-folds I

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold K\"{a}hler-Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.Comment: 27 page

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang \cite{SZ19} on a relation between birational superrigidity and K-stability, we prove the K-stability of a birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of index $1$.Comment: 127pages. Results on the existence of KE metrics are improved, and the applications to (birational) automorphism groups are removed (simply because they are previously known

K-polystability of the first secant varieties of rational normal curves

The first secant variety $\Sigma$ of a rational normal curve of degree $d \geq 3$ is known to be a $\mathbf{Q}$-Fano threefold. In this paper, we prove that $\Sigma$ is K-polystable, and hence, $\Sigma$ admits a weak K\"{a}hler-Einstein metric. We also show that there exists a $(-K_{\Sigma})$-polar cylinder in $\Sigma$.Comment: 17 page