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1.
We analyze the role of the electromagnetic field for the stability of a shearing viscous star with spherical symmetry. Matching conditions are given for the interior and the exterior metrics. We use a perturbation scheme to construct the collapse equation. The range of instability is explored in Newtonian and post Newtonian (pN) limits. We conclude that the electromagnetic field diminishes the effects of the shearing viscosity in the instability range and makes the system more unstable in both Newtonian and post Newtonian approximations. 相似文献
2.
Juan A. Navarro Gonzalez Juan B. Sancho de Salas 《Journal of Geometry and Physics》2003,44(4):595-622
We consider a smooth one-parameter family of four-dimensional manifolds X,≥0, each one endowed with a covariant metric g. It is assumed that g is a Lorentz metric for each >0, i.e., the signature of g is (+,−,−,−) for >0, while the limit metric g0 on X0 is assumed to be degenerated of rank 1, i.e., the signature of g0 is (+,0,0,0). We characterize when the limit manifold X0 inherits the geometric structure of a Newtonian gravitation. The limit manifold X0 is a Newtonian gravitation if and only if there exist the limits of the Levi-Civita connection , the curvature operator
and the contravariant Einstein tensor G2 as →0. Moreover, the existence of these limits is characterized in terms of the Taylor expansion of the family {g} with respect to the parameter . 相似文献
3.
In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature
tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic
parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system
of equations in the Newtonian limit. 相似文献
4.
Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity, but are rather guided ones by previously known results in Einstein's theory. The action-at-a-distance nature of Newton's gravity requires further verification from Einstein's theory for its use in the large-scale nonlinear regimes. We study the domain of validity of the Newtonian cosmology by investigating weakly nonlinear regimes in relativistic cosmology assuming a zero-pressure and irrotational fluid. We show that, first, if we ignore the coupling with gravitational waves the Newtonian cosmology is exactly valid even to the second order in perturbation. Second, the pure relativistic correction terms start appearing from the third order. Third, the correction terms are independent of the horizon scale and are quite small in the large-scale near the horizon. These conclusions are based on our special (and proper) choice of variables and gauge conditions. In a complementary situation where the system is weakly relativistic but fully nonlinear (thus, far inside the horizon) we can employ the post-Newtonian approximation. We also show that in the large-scale structures the post-Newtonian effects are quite small. As a consequence, now we can rely on the Newtonian gravity in analyzing the evolution of nonlinear large-scale structures even near the horizon volume. 相似文献
5.
Ramesh Chandra 《General Relativity and Gravitation》1977,8(9):787-793
On the grounds of the two correspondence limits, the Newtonian limit and the special theory limit of Einstein field equations, a modification of the cosmical constant has been proposed which gives realistic results in the case of a homogeneous universe. Also, according to this modification an explanation for the negative pressure in the steady-state model of the universe has been given. 相似文献
6.
We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using
that, we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method
for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition,
we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials
in anti-de Sitter space. 相似文献
7.
This paper explores the instability limits for the stellar objects in the background of a particular modified gravity theory. In order to accomplish the instability conditions, a spherically symmetric anisotropic charged fluid influenced by the modified gravity is taken under consideration. The modified field equations and the equations of motion are accomplished in background of the Gauss–Bonnet gravity. These equations are perturbed to constitute the collapse equation. The Newtonian and post-Newtonian limits are imposed and found that the dynamical instability of the fluid is explained by the adiabatic index which consists on analytical value depending on static profile of material variables. 相似文献
8.
Limits of the hydrodynamic no-slip boundary condition 总被引:1,自引:0,他引:1
A controversial point in fluid dynamics is to distinguish the relative importance of surface roughness and fluid-surface intermolecular interactions in determining the boundary condition. Here hydrodynamic forces were compared for flow of Newtonian fluids past surfaces of variable roughness but similar, poorly wetted, surface chemistry. The critical shear stress and shear rate to observe deviations from predictions using the no-slip boundary condition increased nearly exponentially with increasing roughness and diverged at approximately 6 nm rms roughness. We conclude that local intermolecular interactions dominated when the surface was very smooth, but roughness dominated otherwise. This quantifies the limits of both ideas. 相似文献
9.
Yu. N. Pokotilovski 《Physics of Atomic Nuclei》2006,69(6):924-931
Constraints for the constants of hypothetical Yukawa-type corrections to the Newtonian gravitational potential are obtained
from analysis of neutron scattering experiments. Restrictions are obtained for the interaction range between 10−12 and 10−7 cm, where Casimir force experiments and atomic-force microscopy are not sensitive. Experimental limits are obtained also
for nonelectromagnetic inverse-power-law neutron-nucleus potentials. Some possibilities are discussed to strengthen these
constraints.
The text was submitted by the author in English. 相似文献
10.
Thomas W. Baumgarte 《General Relativity and Gravitation》1993,25(11):1189-1204
The Newtonian limit of solutions of a model problem is studied. It is shown that under certain assumptions on the initial data relativistic solutions approach a Newtonian solution as the speed of light tends to infinity. The model problem, although having a much simpler structure than the real equations, shows many of the typical problems arising in the discussion of the Newtonian limit. The method of characteristics is applied and its limitation discussed. 相似文献
11.
12.
J. A. Carrillo M. G. Delgadino A. Mellet 《Communications in Mathematical Physics》2016,343(3):747-781
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). We prove this (and some other regularity results) by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems. 相似文献
13.
《Comptes Rendus Physique》2003,4(3):337-346
Motivated in large part by the possibility of observing signatures of compact extra dimensions, experimental searches for deviations from Newtonian gravity at short distances have improved in sensitivity by many orders of magnitude in the past five years. We review the essential features of the experiments responsible for the current limits on new effects in the range from a few microns to a few centimeters, and discuss prospects for the near future. To cite this article: J.C. Long, J.C. Price, C. R. Physique 4 (2003). 相似文献
14.
William H. Press 《General Relativity and Gravitation》1979,11(2):105-109
We show that a material with sufficiently large elastic shear modulus or shear viscosity will act like a gravitational conductor or metal. It will reflect gravitational waves, and it can be used to make gravitational waveguides and circuits. Unlike electromagnetism, a gravitational wave can be guided by a single conductor in transverse mode. Gravitational conductors can obey the dominant energy condition, and they can be larger than their Schwarzschild radius, but they must violate a new condition that is probably satisfied by all existing forms of matter. Direct-current gravitational circuits, although limits of guided gravitational waves, have a simple Newtonian interpretation.This essay is a slightly expanded version of one that received an honorable mention (1978) from the Gravity Research Foundation-Ed.Work supported in part by NSF grant No. PHY78-09616. 相似文献
15.
Thomas W. Noonan 《General Relativity and Gravitation》1984,16(11):1103-1118
The macroscopic stress-energy tensor of an astronomical medium such as a galaxy of stars is determined by the field equation of general relativity from the small-scale variations in mass and velocity. In the weak-field, slow-motion approximation, in which the gravitational fields of the stars are Newtonian, it is found that the contribution by the small-scale gravitational fields to the macroscopic density and stress are, respectively, the Newtonian gravitational energy density and the Newtonian gravitational stress tensor. This result is based on the general-relativity field equation, not conservation laws, although the general-relativity field equation has the well-known property of being consistent with conservation laws. 相似文献
16.
R. W. Hellings P. J. Adams J. D. Anderson M. S. Keesey E. L. Lau E. M. Standish V. M. Canute I. Goldman 《International Journal of Theoretical Physics》1989,28(9):1035-1041
Results are presented from the analysis of solar system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (0.2 ± 0.4) × 10–11 year–1 and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (0.1 ± 0.8) × 10–11 year–1. The error limits quoted are the result of uncertainties in the masses of the asteroids.This paper is reprinted with minor editorial modifications fromPhysical Review Letters,51, 1609 (1983). 相似文献
17.
Zbigniew Oziewicz 《Foundations of Physics》1994,24(10):1379-1402
A bivertical classical field theory includes the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows one to recognize the formal analogies among Newtonian mechanics and Maxwell's electrodynamics.On leave of absence from University of Wrocaw, Poland. Work partially supported by Polish Committee for Scientific Research K.BN, Grant #2 P302 023 07. 相似文献
18.
Jürgen Ehlers developed frame theory to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter
λ, which can be thought of as 1/c
2, where c is the speed of light. By construction, frame theory is equivalent to general relativity for λ > 0, and reduces to Newtonian gravity for λ = 0. Moreover, by setting , frame theory provides a framework to study the Newtonian limit . A number of ideas relating to frame theory that were introduced by Jürgen have subsequently found important applications
to the rigorous study of both the Newtonian limit and post-Newtonian expansions. In this article, we review frame theory and
discuss, in a non-technical fashion, some of the rigorous results on the Newtonian limit and post-Newtonian expansions that
have followed from Jürgen’s work. 相似文献
19.
In this work, we have investigated the dynamical instability of spherically symmetric gravitating object under expansion-free condition in Einstein Gauss–Bonnet gravity. In this context, the field equations and dynamical equations have been established in the Gauss–Bonnet gravity. The linear perturbation scheme has been used on the dynamical equations to construct the collapse equation. The Newtonian, post Newtonian and post Newtonian approximations have been applied to investigate the general dynamical (in)stability equations. It has been observed that the instability range of the collapsing source is independent of adiabatic index Γ (stiffness of the fluid does not play any role). The instability range can be determined by the pressure anisotropy, energy density profile, Gauss–Bonnet parameter α and some constraints at Newtonian, post Newtonian and post Newtonian order. 相似文献
20.
We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a three-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two two-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Moreover, it makes a host of mathematical tools from dynamical systems theory available, which allows us to prove several theorems about the relationship between the equation of state and properties concerning total masses and radii. 相似文献