Related papers: The 1965 Penrose singularity theorem
In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This…
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
After a historical discussion of Einstein's 1907 principle of equivalence, a homogeneous gravitational field in Minkowski spacetime is constructed. It is pointed out that the reference frames in gravitational theory can be understood as…
The first part of this paper contains a brief description of the beginnings of modern cosmology, which, the author will argue, was most likely born in the Year 1912. Some of the pieces of evidence presented here have emerged from recent…
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in…
The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized…
This article, the first in a series, analyzes the general theory of plane wave spacetimes. Following Dmitri Aleekseevsky, these are defined as spacetimes admitting a group of dilations leaving invariant a smooth curve. If this curve is…
We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship hypothesis and the Penrose inequality,…
In the traditional formalism of quantum mechanics, a simple direct proof of (a version of) the Spin Geometry Theorem of Penrose is given; and the structure of a model of the `space of the quantum directions', defined in terms of elementary…
In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of…
There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose…
A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a…
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive…
Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…
According to the cosmic censorship hypothesis of Penrose, naked singularities should never occur in realistic collapse situations. One of the major open problems in this context is the existence of a naked singularity in the Kerr solution…
The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
In 1971 I announced what I described as a nice proof of Tychonoff's Theorem, an immediate corollary of a result concerning closed projections combined with Mrowka's characterization of compactness: a space X is compact if and only if for…
In this short survey paper, we discuss certain recent results in classical gravity. Our main attention is restricted to two topics: the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture…