Related papers: Recent Developments in the Penrose Conjecture
This paper is a tribute to Robert Bartnik and his work and conjectures on quasi-local mass. We present a framework in which to clearly analyse Bartnik's static vacuum extension conjecture. While we prove that this conjecture is not true in…
The Riemannian Penrose inequality is a fundamental result in mathematical relativity. It has been a long-standing conjecture of G. Huisken that an analogous result should hold in the context of extrinsic geometry. In this paper, we resolve…
We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.
The recent progress in establishing the existence of finite neutrino masses and mixing between generations of neutrinos has been remarkable, if not astounding. The combined results from studies of atmospheric neutrinos, solar neutrinos, and…
After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's…
The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface $\Omega$ extending to past null infinity. We…
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…
We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: A shell of null dust collapses in Minkowski space and a marginally trapped…
In this contribution we assess the current experimental status of Special and General Relativity. Particular emphasis is put on putative extensions of these theories and on how these could be detected experimentally.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…
In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…
In this paper we investigate Arzela Ascoli Theorem in quasi cone metric space, which is a generalization of metric space. We prove some interesting results using forward and backward toplologies, forward and backward continuity and forward…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent extension to Lorentzian metrics of low regularity. The latter is motivated by the quest to…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
In this talk, we review recent results in testing spacetime symmetries in gravitational physics. Topics discussed include new signals for hypothetical Lorentz and diffeomorphism symmetry violations in short-range gravity tests. We review…
Under certain conditions, we give a new way to prove the uniqueness of static black hole in higher dimensional asymptotically flat spacetimes. In the proof, the Penrose inequality plays a key role in higher dimensions as well as four…
In this paper we show positive mass theorems and Penrose type inequalities for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW}, for asymptotically flat CF manifolds and its rigidity.
This PhD thesis contains a collection of work related to the algebraic classification of spacetimes in higher dimensions, including an up-to-date review of various aspects of the field. The work discussed includes the higher-dimensional…