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1.
The comoving-frame equations of radiative transfer and moment equations to accurate terms of all orders inv/c are derived in the modified Lagrangian form. The equations exactly describe the interaction of radiation with matter in a relativistically moving medium in flat or curved spacetime. Two specialized sets of equations are presented: (1) the equation of radiative transfer and moment equations accurate to terms of second order (v 2/c 2), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric.  相似文献   

2.
Our Universe consistes of particles, space and time. Ever since Descartes we have known that true emptiness cannot exist; ever since Einstein we have known that space and time are part of the stuff of our world. Efforts to determine the structure of particles go in parallel with the search for the structure of spacetime. Einstein gave us a geometrical answer regarding the structure of spacetime: a distance recipe (Lorentz-Minkowski) suffices. The theory boils down to a patching together of local Lorentz frames into a global whole, which gives it the form of a gauge field theory based on local Lorentz symmetry. On large scales, the Einstein Equation seems to work well. The structure of particles is described by a gauge field. too. On small scales the Standard Model seems to work very well.However, we know from Newtonian gravity that the presence of particles must be related to the structure of spacetime. Einstein made a conjecture for the form of this connection using the Newtonian limit of small speeds and weak fields. The right hand side of his equation for the bulk theory of matter (the energy-momentum tensor), is equated to the Einstein tensor from non-Euclidian geometry.But that connection is wrong. The structure of spacetime cannot be equated to the density of particles if we include the Standard Model in the matter tensor. In field theory a potential is not something that can be freely changed by adding an arbitrary scalar term; due to the local (as opposed to global) character of the fields, a potential becomes an entity in itself. Einstein's conjecture runs into profound trouble because the reality of potentials implies that the zero point energy of the vacuum must be included in the Einstein equation. The net result is the appearance of a term equivalent to a cosmological constant A of stupendous size, some 10118 times the critical cosmic density.The crisis due to the zero point fluctuations in the energy-momentum tensor is a clash of titans: Einstein's geometrical ideas on spacetime structure vs the behaviour of particles and the vacuum discribed by Dirac and followers. Someone, or everyone, is wrong. In my opinion the straightforward quantization of spacetime will always be impossible because the usual particle symmetries (U(1), SU(2), SU(3) and relatives) connect fermions and bosons, whereas relativistic analogies of these symmetries (the Lorentz symmetry) says something about spacetime and not about particles.  相似文献   

3.
On the largest scales there is evidence of discrete structure, examples of this are superclusters and voids and also by redshift taking discrete values. In this paper it is proposed that discrete redshift can be explained by using the spherical harmonic integer l; this occurs both in the metric or density perturbations and also in the solution of wave equations in Robertson-Walker spacetime. It is argued that the near conservation of energy implies that l varies regularly for wave equations in Robertson-Walker spacetime, whereas for density perturbations l cannot vary regularly. Once this is assumed then perhaps the observed value of discrete redshift provides the only observational or experimental data that directly requires an explanation using both gravitational and quantum theory. In principle a model using this data could predict the scale factor R (or equivalently the deceleration parameter q). Solutions of the Klein-Gordon equation in Robertson-Walker spacetimes are used to devise models which have redshift taking discrete values, but they predict a microscopic value for R. A model in which the stress of the Klein-Gordon equation induces a metrical perturbation of Robertson-Walker spacetime is devised. Calculations based upon this model predict that the Universe is closed with 2 q0 - 1=10-4. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

4.
We investigate the influence of the cosmological constant, Λ, on the bending of light by a charged black hole in a de Sitter spacetime. Despite vanishing of the cosmological constant in the second order null geodesic equation, considering the method introduced by Rindler and Ishak (2007), we obtain an expression for the deflection angle, consistent with previous results for Schwarzschild, Schwarzschild-de Sitter (SdS), and Reissner-Nordstrom (RN) spacetimes.  相似文献   

5.
A spacetime manifold generated by the pencil of conics defined by two distinct pairs of complex-conjugated lines and a pair of real lines is considered. The manifold, originally endowed with two spatial and two temporal dimensions, is shown to substantially change its properties as we change the affine properties of the pencil. Two kinds of transformation are of particular interest. A dimensionality-preserving process, characterized by the transmutation of a temporal coordinate into a spatial one and leading to familiar (3+1)D spacetime, and a dimensionality-reducing scenario, featuring simultaneous annihilation of one temporal and one spatia dimension and ending up with a (1+1)D spacetime. A striking difference between the nature of temporal and spatial is revealed; whereas we find purely spatial manifolds, those comprising exclusively temporal dimensions donot exist.  相似文献   

6.
We find the stress-energy tensor of a perfect fluid in the 6-dimensional spacetime proposed by Cole. Using the weak-field Newtonian approximation of general relativity gives a constant of proportionality in Einstein's field equations that differs by a factor of 4/6 from the usual one and shows that Cole's extension of the Schwarzschild metric to 6 dimensions is not valid for a gravitating mass of ordinary matter. A subsequent evaluation of the deflection of starlight for the 6-d spacetime gives a result that is 4/6 of the 4-d result. We conclude that if spacetime is 6-dimensional, one must find a different way to deal with gravity.  相似文献   

7.
We formulate the general relativistic force-free electrodynamics in a new 3 1 language. In this formulation,when we have properly defined electric and magnetic fields,the covariant Maxwell equations could be cast in the traditional form with new vacuum con-stitutive constraint equations. The fundamental equation governing a stationary,axisymmet-ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3 1 system of Thorne and MacDonald,the new system of 3 1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applica-tions in flat spacetime. We investigate its application to disk wind,black hole magnetosphere and solar physics in both flat and curved spacetime.  相似文献   

8.
A U(1)-symmetric Yang-Mills-Higgs (i.e., an Abelian Higgs) sunspot's model is recognized to originate from a massless, complex-valued scalar field coupled minimally to electromagnetic gauge potentials in the background of a (globally)conformally symmetric semi-metric spacetime, whose metric structure is described by the generalized Einstein equations with nonvanishing (positive-valued) cosmological constant. It is shown, in particular, that non-linearity (selfcoupling) of the scalar field appears due to a non-zeroness of the cosmological term, whereas its non-zero vacuum amplitude is induced by the (Ricci scalar) curvature of the Sun's spacetime manifold.  相似文献   

9.
We report a general solution in one of the gravitational potentials to the Einstein system in static spherically symmetric spacetime, modeling anisotropic strange quark matter by imposing a linear barotropic equation of state. The model generated by choosing Tolmann IV form for the gravitational potential is shown to contain the previously known anisotropic dark energy star model of Lobo (Class. Quantum Gravity 23:1525, 2006) and isotropic models of de Sitter and Einstein. Moreover, the model is shown to be physically admissible and corroborate with experimental observations on strange star candidates such as SAX J1808.4-3658 and 4U 1820-30.  相似文献   

10.
Considering the fact that there is a correlation between the black hole horizon and cosmological horizon, we discuss the thermodynamic properties of de Sitter spacetime. The equivalent temperature and energy of de Sitter spacetime are obtained. It is shown that the upper limit energy of de Sitter spacetime is equal to the energy of a pure de Sitter spacetime. The thermodynamic entropy of de Sitter spacetime is the sum of the black hole horizon thermodynamic entropy and the one of cosmological horizon.  相似文献   

11.
This paper focuses on the implications of a commutative formulation that integrates branch-cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Building on a mini-superspace structure, we explore the impact of an inflaton-type scalar field on the wave function of the Universe. Specifically analyzing the dynamical solutions of branch-cut gravity within a mini-superspace framework, we emphasize the scalar field's influence on the evolution of the evolution of the wave function of the Universe. Our research unveils a helix-like function that characterizes a topologically foliated spacetime structure. The starting point is the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as g i $$ {g}_i $$ . The corresponding wave equations are derived and are resolved. The commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. Additionally, we delve into a mini-superspace of variables, incorporating scalar-inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions for the wave equations without recurring to numerical approximations.  相似文献   

12.
This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

13.
Based on the 2nd-order post-Newtonian approximation under the DSX frame of the general relativity theory, the 2nd-order post-Newtonian orbital equation of light in the axis-symmetrical stationary spacetime is derived, and from this, the angle of deflection of light propagating in the equatorial plane is derived. The obtained results are consistent with those of the Schwarzchild and Kerr metrics within the limits of measuring precision.  相似文献   

14.
It is shown that the equation of motion Du j/Ds = (e/mc 2)F ji u i , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx j [jpi] = 0 or L v p i = 0, where p i is the conjugate momentum 4-vector and v a vector determined by the condition p i v i, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.  相似文献   

15.
We present a solution to the Einstein field equations for a massless scalar field in a Bianchi type-V spacetime, which can be interpreted as a solution for a perfect fluid with the equation of state of stiff matter. This solution complements a solution previously given by us for an anisotropic fluid.  相似文献   

16.
This paper investigates the effects of the spatial variation of the cosmological constant λ on the spacetime geometry within and outside a massive object. It is seen that the variation of λ with the radial coordinate introduces non-trivial changes leading to spacetime closing on itself around a massive object. It may also be possible to generate interior solutions that lead to flat rotation curves of galaxies  相似文献   

17.
Unno  W.  Ribes  E.  Appenzeller  I. 《Solar physics》1974,35(2):287-308

A stationary two-dimensional isothermal flow parallel to the magnetic lines of force is studied in connection with the hydrodynamic support of a spicule. Observed large extension into the corona (～ 6000 km) and high velocities (～ 25 km s-1) can be explained consistently if the effective kinetic temperature within a spicule could be about 104 K in the chromospheric region (z < 2000 km) and increase to about 2.5 × 104 K or more in the coronal region (z > 2000 km). In a special simple case, an analytic solution of equations of motion is obtained and is used for explaining why the pressure in a spicule can be higher than the normal surrounding pressure in upper levels.

Comparison between the effective kinetic temperatures for the spicule support and the empirical electron temperatures shows that they are about the same in lower levels (z < 2000 km) but contributions to the effective kinetic temperature other than the electron temperatures are necessary in higher levels (z > 2000 km). Thus, we postulate the role of acoustic waves that are enhanced by the presence of the magnetic field and are practically undamped in the accelerated flow in a spicule. The coupling between the acoustic waves and the outward expanding motion initiated at the foot of a spicule by the magnetic buoyancy and the solar oscillation is thought to be similar to the mechanism of a geyser in which the bubble formation in an ascending flow is fundamental. The magnetic field strength adequate to provide an appropriate circumstance for the occurrence of a spicule is considered to be about 200 G at the base of the chromosphere. Observational implications are briefly discussed.

  相似文献   

18.
Using the analytic extension method, we study Hawking radiation of an (n+4)-dimensional Schwarzschild-de Sitter black hole. Under the condition that the total energy is conserved, taking the reaction of the radiation of particles to the spacetime into consideration and considering the relation between the black hole event horizon and cosmological horizon, we obtain the radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer a strictly pure thermal spectrum. It is related to the change of the Bekenstein-Hawking (B-H) entropy corresponding the black hole event horizon and cosmological horizon. The result satisfies the unitary principle. At the same time, we also testify that the entropy of de Sitter spacetime is the sum of the entropy of black hole event horizon and the one of cosmological horizon.  相似文献   

19.
This article focuses on the implications of a noncommutative formulation of branch-cut quantum gravity. Based on a mini-superspace structure that obeys the noncommutative Poisson algebra, combined with the Wheeler–DeWitt equation and Hořava–Lifshitz quantum gravity, we explore the impact of a scalar field of the inflaton-type in the evolution of the Universe's wave function. Taking as a starting point the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, the corresponding wave equations are derived and solved. The noncommutative quantum gravity approach adopted preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner Formalism. In this work we delve deeper into a mini-superspace of noncommutative variables, incorporating scalar inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions to the wave equations without resorting to numerical approximations. The results indicate that the noncommutative algebraic space captures low and high spacetime scales, driving the exponential acceleration of the Universe.  相似文献   

20.
We have investigated Hawking non-thermal and purely thermal Radiations of Reissner Nordström anti-de Sitter (RNAdS) black hole by massive particles tunneling method. The spacetime background has taken as dynamical, incorporate the self-gravitation effect of the emitted particles the imaginary part of the action has derived from Hamilton-Jacobi equation. We have supposed that energy and angular momentum are conserved and have shown that the non-thermal and thermal tunneling rates are related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The results for RNAdS black hole is also in the same manner with Parikh and Wilczek’s opinion and explored the new result for Hawking radiation of RNAdS black hole.  相似文献   

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