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We consider two most popular definitions of velocities of remote objects in General Relativity. Our work has two motivations. From a research point of view, we generalize the formula connecting these two velocities in FRW metrics found by Chodorowski to arbitrary synchronous spherically symmetric metrics. From a methodological point of view, our goal is to outline certain counter-intuitive properties of the definitions in question, which would allow to use them when it is reasonable and to avoid incorrect statements, based on inappropriate use of intuition.
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic
We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TO
This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of General Rela
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, the uniquene
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detectio