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Surprisingly, the relict cosmological constant has a crucial influence on properties of accretion discs orbiting black holes in quasars and active galactic nuclei. We show it by considering basic properties of both the geometrically thin and thick accretion discs in the Kerr–de Sitter black hole (naked-singularity) spacetimes. Both thin and thick discs must have an outer edge allowing outflow of matter into the outer space, located nearby the so-called static radius, where the gravitational attraction of a black hole is balanced by the cosmological repulsion. Jets produced by thick discs can be significantly collimated after crossing the static radius. Extension of discs in quasars is comparable with extension of the associated galaxies, indicating a possibility that the relict cosmological constant puts an upper limit on extension of galaxies.

Investigations of the possibility that some novel "quantum" properties of space–time might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n<6) rotation-boost symmetry group. More recently several studies have also considered the possibility of a "doubly special relativity," in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. Here we show that the analysis of the experimental limits could be significantly different in a doubly-special-relativity framework. We find that the study of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, should not provide significant constraints on a doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts should be sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of κ-Poincaré Hopf algebras, two frameworks which are often confused with each other in the literature.

We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the nonrelativistic source velocities, the mathematical system is still seen to be nonlinear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is 10^-21.75kg · m^-3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. This is determined by examining the rotation curves at different galactic latitudes, bringing into consideration the global dynamical structure of the galaxy. The demand for global consistency applies not only to our own but also to all proposed models and theories. Various comments and criticisms from colleagues are addressed.

In this paper, we present a model of a compact relativistic anisotropic star in the presence of an electric field. In order to obtain an exact solution of the Einstein–Maxwell field equations, we assume that the stellar material inside the star obeys a Chaplygin equation of state which is a nonlinear relationship between the radial pressure and the matter density. Using Tolman’s metric potential for $g_{rr}$, we obtain the other metric co-efficient by employing the Karmarkar condition which is a necessary and sufficient condition for the interior spacetime of our model to be of embedding class I. Our stellar model is free from central singularity and obeys all the conditions for a realistic stellar object.

Here we study some general properties of spherical shear-free collapse. Its general solution when imposing conformal flatness is re-obtained (Refs. 1 and 2) and matched to the outgoing Vaidya spacetime. We propose a simple model satisfying these conditions and study its physical consequences. Special attention deserve, the role played by relaxational processes and the conspicuous link betweeen dissipation and density inhomogeneity.

The recent monumental detection of gravitational waves by LIGO, the subsequent detection by the LIGO/VIRGO observatories of a binary neutron star merger seen in the gravitational wave signal $GW170817$, the first photo of the event horizon of the supermassive black hole at the center of Andromeda galaxy released by the EHT telescope and the ongoing experiments on Relativistic Heavy Ion Collisions at the BNL and at the CERN, demonstrate that we are witnessing the second golden era of observational relativistic gravity. These new observational breakthroughs, although in the long run would influence our views regarding this Kosmos, in the short run, they suggest that relativistic dissipative fluids (or magnetofluids) and relativistic continuous media play an important role in astrophysical-and also subnuclear-scales. This realization brings into the frontiers of current research theories of irreversible thermodynamics of relativistic continuous media. Motivated by these considerations, we summarize the progress that has been made in the last few decades in the field of nonequilibrium thermodynamics of relativistic continuous media. For coherence and completeness purposes, we begin with a brief description of the balance laws for classical (Newtonian) continuous media and introduce the classical irreversible thermodynamics (CIT) and point out the role of the local-equilibrium postulate within this theory. Tangentially, we touch the program of rational thermodynamics (RT), the Clausius–Duhem inequality, the theory of constitutive relations and the emergence of the entropy principle in the description of continuous media. We discuss at some length, theories of non equilibrium thermodynamics that sprang out of a fundamental paper written by Müller in 1967, with emphasis on the principles of extended irreversible thermodynamics (EIT) and the rational extended irreversible thermodynamics (REIT). Subsequently, after a brief introduction to the equilibrium thermodynamics of relativistic fluids, we discuss the Israel–Stewart transient (or causal) thermodynamics and its main features. Moreover, we introduce the Liu–Müller–Ruggeri theory describing relativistic fluids. We analyze the structure and compare this theory to the class of dissipative relativistic fluid theories of divergent type developed in the late 1990 by Pennisi, Geroch and Lindblom. As far as theories of nonequilibrium thermodynamics of classical media are concerned, it is fair to state that substantial progress has been made and many predictions of the extended theories have been placed under experimental scrutiny. However, at the relativistic level, the situation is different. Although the efforts aiming to the development of a sensible theory (or theories) of nonequilibrium thermodynamics of relativistic fluids (or continuous media) spans less than a half-century, and even though enormous steps in the right direction have been taken, nevertheless as we shall see in this review, still a successful theory of relativistic dissipation is lacking.

Raychaudhuri equation is generalized in the parametrized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between the quantum spin of the moving particle and the torsion of the background gravitational field. The generalized Raychaudhuri equation obtained contains some extra terms, depending on the torsion of space–time, that would have some effects on the singularity theorems of general relativity. Under a certain condition, this equation could be reduced to the original Raychaudhuri equation without any need for a vanishing torsion.

Two phenomenological models of Λ, viz. and , are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time, as suggested earlier by others, including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that the model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model, , is in general attractive in nature. Moreover, it is seen that due to the combined effect of time-variable Λ and G the Universe evolved with acceleration as well as deceleration. Deceleration indicates a "big crunch".

In the study of certain noncommutative versions of Minkowski space–time a lot remains to be understood for a satisfactory characterization of their symmetries. Adopting as our case study the κ-Minkowski noncommutative space–time, on which a large literature is already available, we propose a line of analysis of noncommutative-space–time symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski). We provide new elements in favor of the expectation that the commutative-space–time notion of Lie-algebra symmetries must be replaced, in the noncommutative-space–time context, by the one of Hopf-algebra symmetries. While previous studies appeared to establish a rather large ambiguity in the description of the Hopf-algebra symmetries of κ-Minkowski, the approach here adopted reduces the ambiguity to the description of the translation generators, and our results, independently of this ambiguity, are sufficient to clarify that some recent studies which argued for an operational indistinguishability between theories with and without a length-scale relativistic invariant, implicitly assumed that the underlying space–time would be classical. Moreover, while usually one describes theories in κ-Minkowski directly at the level of equations of motion, we explore the nature of Hopf-algebra symmetry transformations on an action.

We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We then prove that if a system is strongly hyperbolic with respect to a given hypersurface, then it is also strongly hyperbolic with respect to any nearby surface.

We then study for how much these hypersurfaces can be deformed and discuss then causality, namely what the maximal propagation speed in any given direction is. In contrast with the symmetric hyperbolic case, for which the proof of causality is geometrical and direct, relaying in energy estimates, the proof for general strongly hyperbolic systems is indirect for it is based in Holmgren's theorem.

To show that the concept is needed in the area of general relativity we discuss two results for which the theory of symmetric hyperbolic systems shows to be insufficient. The first deals with the hyperbolicity analysis of systems which are second order in space derivatives; they include certain versions of the ADM and the BSSN families of equations. This analysis is considerably simplified by introducing pseudo-differential first-order evolution equations. Well-posedness for some members of the latter family systems is established by showing they satisfy the strong hyperbolicity property. Furthermore it is shown that many other systems of such families are only weakly hyperbolic, implying they should not be used for numerical modeling.

The second result deals with systems having constraints. The question posed is which hyperbolicity properties, if any, are inherited from the original evolution system by the subsidiary system satisfied by the constraint quantities. The answer is that, subject to some condition on the constraints, if the evolution system is strongly hyperbolic then the subsidiary system is also strongly hyperbolic and the causality properties of both are identical.

The more precise definition and the more fundamental understanding of the concepts of time, energy, entropy and information are building upon the new, relativistic foundation of gravity. This lecture is an attempt to explain the basic principles that underpin this progress, by focusing on the simple but subtle universal definition of energy. The principles are unearthed from Einstein’s theory and Noether’s theorems, beneath a century of misconceptions.

We use the dissipative-type theory (DTT) framework to solve for the evolution of conformal fluids in Bjorken and Gubser flows from isotropic initial conditions. The results compare well with both exact and other hydrodynamic solutions in the literature. At the same time, DTTs enforce the Second Law of thermodynamics as an exact property of the formalism, at any order in deviations from equilibrium, and are easily generalizable to more complex situations.

We know energy and mass of a particle can be connected by $E=m{c}^2$. What is the physical basis of this relation? Historically, it was thought to be based on the principle of relativity (PR). A careful examination of the literature, however, indicated that this understanding is not true. Einstein did not derive this relation from PR. Instead, his argument was mainly based on thought experiments, which focused on the similarity between radiation and matter. Following this hint, we suspect that the mass–energy equivalence could be based on the quantum property of wave–particle duality. We know photon and electron can behave as a particle as well as a wave. Such a wave property could make the particle behave differently from Newtonian mechanics. Indeed, using a wave model which treats particles as excitations of the vacuum, we show that the mass–energy equivalence relation can be directly derived based on the quantum relations of Planck and de Broglie. This wave hypothesis has several advantages; not only can it explain naturally why particles can be created in the vacuum; it also predicts that a particle cannot travel faster than the speed of light. This hypothesis can also be tested in experiment.

Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force due to the large-scale electromagnetic field which is assumed to be present in the ambient medium. The evolution of the speed of the flow relative to the ambient medium is studied. In the force-free case, the resulting equation of motion predicts rapid deceleration of the initial flow and an asymptotic relative speed with a Lorentz factor of . In the presence of the Lorentz force, the long-term relative speed of the clump tends to the ambient electrical drift speed.

The relativistic theories of light propagation are generalized by introducing two new parameters ς and η in the second post-Newtonian (2PN) order, in addition to the parametrized post-Newtonian (PPN) parameters γ and β. This new 2PN parametrized (2PPN) formalism includes the nonstationary gravitational fields and the influences of all kinds of relativistic effects. The multipolar components of gravitating bodies are taken into account as well at the first post-Newtonian (1PN) order. The equations of motion and their solutions of this 2PPN light propagation problem are obtained. Started from the definition of a measurable quantity, a gauge-invariant angle between the directions of two incoming photons for a differential measurement in astrometric observation is discussed and its formula is derived. For a precision level of a few microarcsecond (μas) for space astrometry missions in the near future, we further consider a model of angular measurement, the Laser Astrometric Test of Relativity (LATOR)-like missions. In this case, all terms with aimed at the accuracy of ~1μas are estimated.

We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi–Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.

The light time equation and frequency shift are worked out in the framework of a second parametrized post-Newtonian (2PPN) formalism in the Solar System barycentric reference system (SSBRS) developed in a recently published paper. Effects of each body’s oblateness, spin and translational motion are taken into account for the light propagation. It is found that, at the second post-Newtonian (2PN) approximation, the light time and frequency shift depend on the parameter $\eta$ only.

The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The space–time position operator acts in the Hilbert space of functions of space and time. Dynamics, however, makes eigenstates of the time operator unphysical. This poses a problem for the standard interpretation of QM and reinforces the role of alternative interpretations such as the Bohmian one. The Bohmian interpretation, despite of being nonlocal in accordance with the Bell theorem, is shown to be relativistic covariant.

Since 1964, the NASA Goddard Space Flight Center (GSFC) has been using short pulse lasers to range to artificial satellites equipped with passive retroreflectors. Today, a global network of 40 satellite laser ranging (SLR) stations, under the auspices of the International Laser Ranging Service (ILRS), routinely tracks two dozen international space missions with few-millimeter precision using picosecond pulse lasers in support of Earth science. Lunar laser ranging (LLR) began in 1969, shortly after NASA's Apollo 11 mission placed the first of five retroreflector packages on the Moon. An important LLR data product has been the verification of Einstein's equivalence principle and other tests of general relativity. In 1975, the University of Maryland used a laser ranging system to continuously transfer time between two sets of atomic clocks — one set on the ground and the other in an aircraft — to observe the predicted relativistic effects of gravity and velocity on the clock rates. Two-way asynchronous laser transponders promise to extend these precise ranging and time transfer capabilities beyond the Moon to the planets, as evidenced by two successful experiments carried out in 2005 at distances of 24 and 80 million km respectively.

We investigate the possibility that stellar mass black holes, with masses in the range of 3:8M_⊙ and 6M_⊙, respectively, could be in fact quark stars in the Color-Flavor-Locked (CFL) phase. Depending on the value of the gap parameter, rapidly rotating CFL quark stars can achieve much higher masses than standard neutron stars, thus making them possible stellar mass black hole candidates. Moreover, quark stars have a very low luminosity and a completely absorbing surface - the infalling matter on the surface of the quark star is converted into quark matter. A possibility of distinguishing CFL quark stars from stellar mass black holes could be through the study of thin accretion disks around rapidly rotating quark stars and Kerr type black holes, respectively. Strange stars exhibit a low luminosity, but high temperature bremsstrahlung spectrum, which, in combination with the emission properties of the accretion disk, may be the key signature to differentiate massive strange stars from black hole.