相关论文: Yet another proof of Hawking and Ellis's Lemma 8.5…
Recently, Li and Bambi proposed a hypothesis that the event horizon of a regular black hole can be destroyed because these objects have no gravitational singularity and therefore they are not protected by the weak cosmic censorship…
We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global…
In this paper, we prove the global existence of H\"older continuous solutions for the Cauchy problem of a family of partial differential equations, named as $\lambda$-family equations, where $\lambda$ is the power of nonlinear wave speed.…
We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…
The new solution of the Einstein equations in empty space is presented. The solution is constructed using Schwarzschild solution but essentially differs from it. The basic properties of the solution are: the existence of a horizon which is…
We present computational results which strongly support a conjecture of Morgan and Mullen (1996), which states that for every extension $E/F$ of Galois fields there exists a primitive element of $E$ which is completely normal over $F$.
The origin of the baryon asymmetry of the universe remains one of the most pressing open questions in particle physics and cosmology. Electroweak baryogenesis offers an experimentally testable explanation, requiring new sources of CP…
Questions about black holes in quantum gravity generally presuppose the presence of a horizon. Recently Carlip has shown that enforcing an initial data surface to be a horizon leads to the correct form for the Bekenstein-Hawking entropy of…
Assuming that Siegel zeros exist, we prove a hybrid version of the Chowla and Hardy--Littlewood prime tuples conjectures. Thus, for an infinite sequence of natural numbers $x$, and any distinct integers $h_1,\dots,h_k,h'_1,\dots,h'_\ell$,…
To cure the lack of predictive power of general relativity Geroch proposed to complete the theory with an additional postulate that only "hole-free" spacetimes are permitted. I argue that this postulate is too strong -- it prohibits even…
It is widely expected that generic black holes have a non-empty but weakly singular Cauchy horizon, due to mass inflation. Indeed this has been proven by the author in the spherical collapse of a charged scalar field, under decay…
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by…
It is pointed out that the claim made by Joshi and Joshi [1], has not been rigorously demonstrated by them. A simpler and more correct proof is provided.
As well as known, the black hole evaporation problem is famous problem. Because the S.W.Hawking found the black holes emit light at the future null infinity as a thermal radiation \cite{H}, we think that the black holes may be vanish.…
This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…
The Penrose inequality has so far been proven in cases of spherical symmetry and in cases of zero extrinsic curvature. The next simplest case worth exploring would be non-spherical, non-rotating black holes with non-zero extrinsic…
First proved my Donald Martin in 1975, the result of Borel determinacy has been the subject of multiple revised proofs. Following Martin's book [1], we present a recent streamlined proof which implements ideas of Martin, Moschovakis, and…
We introduce $(r+1)$-completed cycles $k$-leaky Hurwitz numbers and prove piecewise polynomiality as well as establishing their chamber polynomiality structure and their wall crossing formulae. For $k=0$ the results recover previous results…
It has long been suggested that the Cauchy horizon of dynamical black holes is subject to a weak null singularity, under the mass inflation scenario. We study in spherical symmetry the Einstein-Maxwell-Klein-Gordon equations and…
In 1953 K. Oka IX solved in first and in a final form Levi's problem (Hartogs' inverse problem) for domains or Riemann domains over $\C^n$ of arbitrary dimension. Later on a number of the proofs were given; cf.\ e.g., Docquier-Grauert's…