Related papers: The 1965 Penrose singularity theorem
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
Five topics: A rigid body does not exist in the special theory of relativity; distant simultaneity defined with respect to a given frame of reference without any reference to synchronized clocks; challenges on Einstein's connection of…
In 1973, R. Penrose presented an argument that the total mass of a space-time which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16\pi}$. An important special case of this physical statement…
We point out that algebraically special Einstein fields with twisting rays exhibit the basic properties of conformal Universes considered recently by Roger Penrose.
It is shown as experiments and theories about the nature of light led to the special theory of relativity. The most important facts for the emergence of the theory proposed by Einstein in 1905 are presented.
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
We retrace the first steps towards understanding neutrinos, particles predicted by Pauli in 1930 to avoid a supposed violation of time-translation symmetry. Despite the tendency to reduce the whole story to his intuition and the skill of…
We present a historical review of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a…
The interior of the Kerr solution is singular and achronological. The classic singularity theorem by Hawking and Penrose relies on chronology, and thus does not apply to the Kerr solution. An improvement of their theorem by Kriele partially…
I consider the isolation of general relativity research from the rest of theoretical physics during the 1930s-1950s, and the subsequent reinvigoration of the field. I suggest that the main reason for the isolation was that relativists of…
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…
This note is based on a relatively unknown paper of Albert Einstein published in 1941 in the Revista de la Universidad Nacional de Tucuman. That work can be regarded as the prequel of the one written in 1943 in collaboration with Wolfgang…
Trapped surface formation in general relativity can be studied through a coupled set of nonlinear equations, where various terms can be neglected, as was proved by a rigorous mathematical analysis of Christodoulou. This paper is devoted to…
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more…
The theory of General Relativity has successfully passed a large number of observational tests without requiring any adjustment from its original version proposed by Einstein in 1915. The past 8 years have seen significant advancements in…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavour than the original analytic…
This article presents a brief review of some historical and philosophical aspects of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity', a landmark work that denoted the starting point of modern…
We introduce a generalized version of the Jang equation, designed for the general case of the Penrose Inequality in the setting of an asymptotically flat space-like hypersurface of a spacetime satisfying the dominat energy condition. The…