Related papers: Einstein spacetimes with weak regularity

We consider weakly regular Gowdy-symmetric spacetimes on T3 satisfying the Einstein-Euler equations of general relativity, and we solve the initial value problem when the initial data set has bounded variation, only, so that the…

Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ``spacetime''. His general theory of relativity further taught us that spacetime is not just a stage on…

In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations…

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive…

A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving…

A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented…

The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…

We define the class of weakly regular spacetimes with T2 symmetry, and investigate their global geometry structure. We formulate the initial value problem for the Einstein vacuum equations with weak regularity, and establish the existence…

We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…

The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the…

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved…

We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends…

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate…

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the…

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection…

Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…

It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…

In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not ``fundamental'' but rather is an almost automatic low-energy long-distance consequence of a wide class of theories.…

It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…