arXiv research

Gravitational instantons collapse to a punctured plane with a special Kahler metric.

The paper constructs gravitational instantons with unique collapse patterns.

Deep learning predicts nuclear equation of state from rotating core collapse GW signals.

The paper proves extremal black holes form at a critical point of gravitational collapse.

Study on curvature blow-up rates in black hole interiors from gravitational collapse.

The paper studies gravitational instantons with flat limits and finds elliptic regularity estimates.

Study collapsing geometry of hyperkähler 4-manifolds and prove conjectures.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

Penrose's conjecture links black holes and gravitational singularities.

We construct large families of new collapsing hyperkähler metrics on the K3 surface. The limit space is the quotient of a flat 3-torus by an involution. Away from finitely many exceptional points the collapse occurs with bounded curvature. There are at most 24 exceptional points where the curvature concentrates, which …

New estimates quantify blow-up rates of spacelike singularities in gravitational collapse.

Study nondifferentiable metrics in general relativity, resolving causality issues and limits evolution scenarios.

Study gluing event horizons of Minkowski and Schwarzschild spacetimes.

We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smoo…

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the exi…

Study shows no closed trapped submanifolds can be tangent to certain spacelike hypersurfaces.

The study finds polynomial upper bounds for singularities in Einstein-scalar field system.

Paper studies apparent horizon dynamics and introduces a null comparison principle.

We reinterpret the proof of the Riemannian Penrose inequality by H. Bray. The modified argument turns out to have a nice feature so that the flow of Riemannian metrics appearing Bray's proof gives a Lorentzian metric of a spacetime. We also discuss a possible extension of our approach to charged black holes.

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capt…

Study shows large extra dimensions are hidden from view by black holes.

Vacuum gravity shows black holes can form without collapse.

Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that obser…

The inequality $m^3\geq \frac{27π}{4} |\mathcal{J}_{2}||\mathcal{J}_{1}-\mathcal{J}_{2}|$ relating total mass and angular momenta, is established for (possibly dynamical) spacetimes admitting black holes of ring ($S^1\times S^2$) topology. This inequality is shown to be sharp in the sense that it is saturated precisely…

For gravitational collapse, we observe a correspondence between region close to past null infinity and region close to central singularity. In line with this philosophy, we construct a new ansatz, with which we first present a 40-page self-contained proof of trapped surface formation in a far-from-center region. A syst…

For surfaces, we brush a reasonably sharp picture of the influence of the fundamental group upon the complexity of foliated-dynamics. A metaphor emerges with phase-changes through the solid-liquid-gaseous states. Groups of ranks $0\le r\le 1$ are frozen with intransitivity reigning ubiquitously. When $2\le r \le 3$, th…

New theorem shows black holes are real, with clearer event horizon.

New black hole models with both null and spacelike singularities.

Proof confirms cosmic censorship for charged gravitational collapse.

Classifies gravitational instantons with quadratic volume growth.

Survey of recent progress in gravitational instantons

The paper proves unique characterization of gravitational instantons with specific volume growth.

Period maps surjective for certain gravitational instantons.

Authors prove Torelli theorem for a specific type of gravitational instantons.

This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.

Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.

Existence proved for specific types of gravitational instantons.

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkäler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instant…

Proves infinitesimal rigidity of Hermitian gravitational instantons.

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…

Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.

New approach proves existence of gravitating vortices on Riemann surfaces.

Review of gravitational instantons in physics.

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …

Charge measurements for instantons and gravitational perturbations.