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Register a new userVelocities of distant objects in General Relativity revisited
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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.
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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 stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to a ${cal O}(10%)$ factor, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically viable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.
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 (TOV) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
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 Relativity will be described. Then, the present situation will be reviewed presenting a number of examples. The opportunities given by astrophysical and astrometric observations will be shortly discussed. Coming to terrestrial experiments the attention will be specially focused on ringlasers and a dedicated experiment for the Gran Sasso Laboratories, named by the acronym GINGER, will be presented. Mention will also be made of alternatives to the use of light, such as particle beams and superfluid rings.
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 uniqueness of black hole solutions and the stability of Kerr spacetime and the final state conjecture, critical phenomena and the Einstein-Yang--Mills equations, and a number of other problems in classical general relativity. We then broaden the scope and discuss some mathematical problems motivated by quantum gravity, including AdS/CFT correspondence and problems in higher dimensions and, in particular, the instability of anti-de Sitter spacetime, and in cosmology, including the cosmological constant problem and dark energy, the stability of de Sitter spacetime and cosmological singularities and spikes. Finally, we briefly discuss some problems in numerical relativity and relativistic astrophysics.
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 detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.
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