Shear-free fluids in general relativity

1986 ◽  
Vol 64 (2) ◽  
pp. 191-199 ◽  
Author(s):  
C. B. Collins
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Global Scale ◽  
Rigid Rotation ◽  
Perfect Fluids ◽  
Global Properties ◽  
Barotropic Equation ◽  
General Relativistic ◽  
Frw Models ◽  
Friedmann Robertson Walker

For a large class of shear-free general-relativistic perfect fluids that obey a barotropic equation of state, either the expansion or the rotation is zero; well-known examples include the Friedmann–Robertson–Walker (FRW) models, the Gödel solution, and stationary axisymmetric systems in rigid rotation. It has been conjectured that this is necessarily the case. Several results prove that restricted versions of this conjecture are valid, although no proof is known for the general case. A survey of these special results is given, together with physical and mathematical reasons for the study of shear-free fluids.If the conjecture is true, then there are three mutually exclusive subclasses, according to whether or not the expansion and the rotation are zero separately or simultaneously. Of these, the physically most interesting subclass is that in which the expansion is not zero, since this subclass might be thought to contain space-times that are suitable for the description of collapsing stars or expanding cosmologies. All space-times of this particular subclass are given, and their global properties are investigated. It turns out that the FRW models are the only ones in which the matter is physically reasonable on a global scale. This consequently provides a global uniqueness theorem for the FRW models.

scholarly journals Relativistic disks with two charged perfect fluids components

2019 ◽  
Vol 6 (1) ◽  
pp. 1-8
Author(s):  
A.C. Gutiérrez-Piñeres ◽  
C.S. Lopez-Monsalvo
Keyword(s):  
Equation Of State ◽  
Charged Fluids ◽  
Field Equations ◽  
Charged Fluid ◽  
Charge Densities ◽  
Two Fluids ◽  
Perfect Fluids ◽  
Barotropic Equation ◽  
Thin Disks ◽  
Relativistic Disks

A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.

scholarly journals MATTER INSTABILITIES IN GENERAL GAUSS-BONNET GRAVITY

2010 ◽  
Vol 25 (11n12) ◽  
pp. 885-899 ◽  
Author(s):  
ANTONIO DE FELICE ◽  
DAVID F. MOTA ◽  
SHINJI TSUJIKAWA
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Arbitrary Function ◽  
Ultra Violet ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Perfect Fluids ◽  
Local Gravity ◽  
Density Perturbations ◽  
Bonnet Term

We study the evolution of cosmological perturbations in [Formula: see text] gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term [Formula: see text]. We derive the equations for perturbations assuming matter to be described by a perfect fluid with a constant equation of state w. We show that density perturbations in perfect fluids exhibit negative instabilities during both the radiation and the matter domination, irrespective of the form of [Formula: see text]. This growth of perturbations gets stronger on smaller scales, which is difficult to be compatible with the observed galaxy spectrum unless the deviation from General Relativity is very small. Thus [Formula: see text] cosmological models are effectively ruled out from this Ultra-Violet instability, even though they can be compatible with the late-time cosmic acceleration and local gravity constraints.

Equilibrium stellar configurations in Rastall theory and astrophysical implications

2020 ◽  
Vol 35 (13) ◽  
pp. 2050105 ◽  
Author(s):  
Sudan Hansraj ◽  
Ayan Banerjee
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Stellar Structure ◽  
Accelerated Expansion ◽  
Standard Theory ◽  
Modified Theories Of Gravity ◽  
De Sitter ◽  
Isothermal Model ◽  
Sitter Spacetime ◽  
Barotropic Equation

Rastall theory propounded some five decades ago belongs to a class of modified theories of gravity. Such theories are motivated by the need to modify general relativity suitably in order to address some problems not explained by the standard theory. Amongst such issues are the observed accelerated expansion of the universe, motion in extremely high gravity regimes and explanations for the discrepancy in the value of the cosmological constant between quantum gravity and experimentation. Recently, it has been claimed that the Rastall theory is trivially equivalent to the standard Einstein theory. We investigate this claim in the context of stellar structure and elementary requirements for physical plausibility. We consider the analogue of the Saslaw et al. [Astrophys. J. 471, 571 (1996)] isothermal model of general relativity and show that the Rastall version satisfies the basic requirements unlike its counterpart. Then, we examine in turn the consequences of suppressing one of the inverse square law fall off of the energy density or the linear equation of state. Imposing a linear barotropic equation of state, we find a generalized de Sitter spacetime as an exact solution of the Rastall equations. In addition, the case of a constant spatial gravitational potential is studied. In each case, we note that the physics of the Rastall model differs from that of the Einstein version.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Traversable wormholes with exponential shape function in modified gravity and general relativity: A comparative study

2020 ◽  
Vol 29 (09) ◽  
pp. 2050068 ◽  
Author(s):  
Gauranga C. Samanta ◽  
Nisha Godani ◽  
Kazuharu Bamba
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Comparative Study ◽  
Modified Gravity ◽  
Shape Function ◽  
Anisotropy Parameter ◽  
Energy Conditions ◽  
Traversable Wormholes

We have proposed a novel shape function on which the metric that models traversable wormholes is dependent. Using this shape function, the energy conditions, equation-of-state and anisotropy parameter are analyzed in [Formula: see text] gravity, [Formula: see text] gravity and general relativity. Furthermore, the consequences obtained with respect to these theories are compared. In addition, the existence of wormhole geometries is investigated.

Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

2004 ◽  
Vol 17 (1-2) ◽  
pp. 165-197 ◽  
Author(s):  
Erhard Scholz
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
A Priori ◽  
Group Extension ◽  
Central Idea ◽  
German Word ◽  
General Relativistic ◽  
Empirical Turn ◽  
Relativistic Framework ◽  
Internal Symmetries

Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.

scholarly journals DARK MATTER, AND ITS DARKNESS

2006 ◽  
Vol 15 (12) ◽  
pp. 2267-2278 ◽  
Author(s):  
D. V. AHLUWALIA-KHALILOVA
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Cosmological Constant ◽  
Model Material ◽  
Representation Space ◽  
Spatial Curvature ◽  
The Standard Model ◽  
General Relativistic ◽  
Relativistic Description ◽  
Friedmann Robertson Walker

Assuming the validity of the general relativistic description of gravitation on astrophysical and cosmological length scales, we analytically infer that the Friedmann–Robertson–Walker cosmology with Einsteinian cosmological constant, and a vanishing spatial curvature constant, unambiguously requires a significant amount of dark matter. This requirement is consistent with other indications for dark matter. The same space–time symmetries that underlie the freely falling frames of Einsteinian gravity also provide symmetries which, for the spin one half representation space, furnish a novel construct that carries extremely limited interactions with respect to the terrestrial detectors made of the standard model material. Both the "luminous" and "dark" matter turn out to be residents of the same representation space but they derive their respective "luminosity" and "darkness" from either belonging to the sector with (CPT)2 = +𝟙, or to the sector with (CPT)2 = -𝟙.

scholarly journals Emergent Universe as an interaction in the dark sector

2017 ◽  
Vol 32 (28) ◽  
pp. 1750152
Author(s):  
Emiliano Marachlian ◽  
I. E. Sánchez G. ◽  
Osvaldo P. Santillán
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Equation Of State ◽  
Linear Equation ◽  
Vacuum Energy ◽  
Cosmological Parameters ◽  
Emergent Universe ◽  
Dark Sector ◽  
Cosmological Scenario ◽  
Friedmann Robertson Walker

A cosmological scenario where dark matter interacts with a variable vacuum energy for a spatially flat Friedmann–Robertson–Walker (FRW) spacetime is proposed and analyzed to show that with a linear equation of state and a particular interaction in the dark sector it is possible to get a model of an Emergent Universe. In addition, the viability of two particular models is studied by taking into account the recent observations. The updated observational Hubble data and the JLA supernovae data are used in order to constraint the cosmological parameters of the models and estimate the amount of dark energy in the radiation era. It is shown that the two models fulfil the severe bounds of [Formula: see text] at the 2[Formula: see text] level of Planck.

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