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1.
In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these
fundamental solutions to represent solutions of the Cauchy problem and to prove L
p
− L
q
estimates for the solutions of the equation with and without a source term. 相似文献
2.
In this paper we study the Euler-Poincaré equations in . We prove local existence of weak solutions in , and local existence of unique classical solutions in , k > N/2 + 3, as well as a blow-up criterion. For the zero dispersion equation (α = 0) we prove a finite time blow-up of the classical solution. We also prove that as the dispersion parameter vanishes, the weak solution converges to a solution of the zero dispersion equation with sharp rate as α → 0, provided that the limiting solution belongs to with k > N/2 + 3. For the stationary weak solutions of the Euler-Poincaré equations we prove a Liouville type theorem. Namely, for α > 0 any weak solution is u=0; for α= 0 any weak solution is u=0. 相似文献
3.
L<Superscript>1</Superscript> Stability of Spatially Periodic Solutions in Relativistic Gas Dynamics
Daniela Calvo Rinaldo M. Colombo Hermano Frid 《Communications in Mathematical Physics》2008,284(2):509-535
This paper proves the well posedness of spatially periodic solutions of the relativistic isentropic gas dynamics equations.
The pressure is given by a γ-law with initial data of large amplitude, provided γ − 1 is sufficiently small. As a byproduct of our techniques, we obtain the same results for the classical case. At the limit
c → + ∞, the solutions of the relativistic system converge to the solutions of the classical one, the convergence rate being
1/c
2. We also construct the semigroup of solutions of the Cauchy problem for initial data with bounded total variation, which
can be large, as long as γ − 1 is small. 相似文献
4.
I. V. Kirnos A. N. Makarenko S. A. Pavluchenko A. V. Toporensky 《General Relativity and Gravitation》2010,42(11):2633-2641
We investigate dynamics of (4 + 1) and (5 + 1) dimensional flat anisotropic Universe filled with a perfect fluid in the Gauss–Bonnet
gravity. An analytical solutions valid for particular values of the equation of state parameter w = 1/3 have been found. For other values of w structure of cosmological singularity have been studied numerically. We found that for w > 1/3 the singularity is isotropic. Several important differences between (4 + 1) and (5 + 1) dimensional cases are discussed. 相似文献
5.
Amir F. Bahrehbakhsh Mehrdad Farhoudi Hossein Shojaie 《General Relativity and Gravitation》2011,43(3):847-869
We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans–Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors
be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to
expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar
field are not constants, the 5D equations, for any kind of geometry, admit a power–law relation between the scalar field and scale factor of the fifth dimension.
Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant, [(w)\tilde]{\tilde{\omega}} . We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with
a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra
dimensions for any kind of geometry without any priori assumption among them. For non-constant scalar fields and spatially flat geometries, solutions are found to be in the form
of power–law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints
with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The power–law
solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept
a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the
solutions are more restricted. We illustrate that the accelerating power–law solutions, which satisfy the weak energy condition
and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the condition
${\tilde{\omega} > -3/2}${\tilde{\omega} > -3/2} which prevents ghost scalar fields in the equivalent 4D vacuum Brans–Dicke equations. The results are presented in a few tables and figures. 相似文献
6.
We consider a D-dimensional model of gravity with non-linear “scalar fields” as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n − 1 factor spaces are Ricci-flat, e.g. when one space M 1 of dimension d 1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically symmetric solutions is studied and a restricted version of “no-hair theorem” for black holes is proved. For the case d 1 = 2 a subclass of latent soliton solutions is singled out. 相似文献
7.
In this paper we obtain topological static solutions of some kind of pure F(R) gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS
Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-Λ-conformally invariant Maxwell
solution. In other word, starting from pure gravity leads to (charged) Einstein-Λ solutions which we interpreted them as (charged)
(a)dS black hole solutions of pure F(R) gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at r = 0. We should note that the Kreschmann scalar of charged solutions goes to infinity as r → 0, but with a rate slower than that of uncharged solutions. 相似文献
8.
E. Kyriakopoulos 《General Relativity and Gravitation》2012,44(1):157-199
We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and
applying the “Newman–Janis complex coordinate trick” we get a rotating metric g
μν
with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q
E
and magnetic Q
M
. Then we find a solution of the equations of motion having this g
μν
as metric. Our solution is asymptotically flat and has angular momentum J = M
a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics,
the vector fields and the quantity l = x+ie-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q
E
, Sen for Q
E
and Q
M
, Kerr–Newman for Q
E
and Q
M
, Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild
are the same function of a, and two functions ρ
2 = r(r + b) + a
2 cos2
θ and Δ = r(r + b) − 2Mr + a
2 + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown
that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and
that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions
outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and
for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another
a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most
physically interesting and well known solutions, are listed in an “Appendix”. 相似文献
9.
Theodoros Kolyvaris George Koutsoumbas Eleftherios Papantonopoulos George Siopsis 《General Relativity and Gravitation》2011,43(1):163-180
We present a new class of black hole solutions with a minimally coupled scalar field in the presence of a negative cosmological
constant. We consider an one-parameter family of self-interaction potentials parametrized by a dimensionless parameter g. When g = 0, we recover the conformally invariant solution of the Martinez–Troncoso–Zanelli (MTZ) black hole. A non-vanishing g signals the departure from conformal invariance. Thermodynamically, there is a critical temperature at vanishing black hole
mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch
of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on g and it is higher than the MTZ critical temperature. As g → 0, this second critical temperature diverges. 相似文献
10.
A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature
singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable
wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions
to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional
to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm
method and compute the conserved quantities of these spacetimes. 相似文献
11.
F. Rahaman Saibal Ray M. Kalam M. Sarker 《International Journal of Theoretical Physics》2009,48(11):3124-3138
We perform a survey whether higher dimensional Schwarzschild space-time is compatible with some of the solar system phenomena.
As a test we examine four well known solar system effects, viz., (1) Perihelion shift, (2) Bending of light, (3) Gravitational
redshift, and (4) Gravitational time delay. It is shown, under a N-dimensional solutions of Schwarzschild type very narrow class of metrics, that the results related to all these physical
phenomena are mostly incompatible with the higher dimensional version of general relativity. We compare all these restricted
results with the available data in the literature. 相似文献
12.
Alain Bachelot 《Communications in Mathematical Physics》2008,283(1):127-167
We investigate the global solutions of the Dirac equation on the Anti- de-Sitter Universe. Since this space is not globally
hyperbolic, the Cauchy problem is not, a priori, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio
beween the mass M of the field and the cosmological constant Λ > 0: it appears a critical value, Λ/12, which plays a role similar to the Breitenlohner-Freedman
bound for the scalar fields. When M
2 ≥ Λ/12 there exists a unique unitary dynamics. On the contrary, for the light fermions satisfying M
2 < Λ/12, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases,
the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy. 相似文献
13.
A. B. J. Kuijlaars A. Martínez-Finkelshtein F. Wielonsky 《Communications in Mathematical Physics》2011,308(1):227-279
We consider the double scaling limit for a model of n non-intersecting squared Bessel processes in the confluent case:
all paths start at time t = 0 at the same positive value x = a, remain positive, and are conditioned to end at time t = 1 at x = 0. After appropriate rescaling, the paths fill a region in the tx–plane as n → ∞ that intersects the hard edge at x = 0 at a critical time t = t
*. In a previous paper, the scaling limits for the positions of the paths at time t ≠ t
* were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as n → ∞ of the correlation kernel at critical time t
* and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections
with the Pearcey kernel. The analysis is based on the study of a 3 × 3 matrix valued Riemann-Hilbert problem by the Deift-Zhou
steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions
of a particular third-order linear differential equation, and its matching with a global parametrix. 相似文献
14.
K. Saaidi S. W. Rabiei A. Aghamohammadi 《International Journal of Theoretical Physics》2011,50(8):2514-2519
We study spherically symmetric static empty space solutions in R+ε/R model of f(R) gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there
are general solutions which are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains
a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration
of the universe. 相似文献
15.
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into
four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r = r(λ), t = t(χ), and τ= τ (χ), where λ is the true anomaly and χ is a parameter along the orbit. A very simple relation between λ and χ is also shown.
These solutions are very useful for modelling temporal evolution of transient phenomena near black holes since they are expressed
with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately. 相似文献
16.
We consider an aggregation equation in , n ≥ 2 with fractional dissipation, namely, , where 0 ≤ γ < 1 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e
−|x|. We prove that for a class of smooth initial data, the solutions develop blow-up in finite time. 相似文献
17.
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in
\mathbb R3{\mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α
th
-order fractional derivatives of the velocity for some α > 0 in the space variables in L
2, which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the L
2-equicontinuity in the time variable and the uniform bound in L
q
, for some q > 2, of the velocity independent of μ > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler
equations in
\mathbb R3{\mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star
convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only
do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical
solutions through the identification of a function space in which convergence should take place, with the bounds that are
independent of μ > 0, that is in the high Reynolds number limit. 相似文献
18.
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is possible
to reassemble the irreducible summands appearing in the unitary braid group representations from a unitary braided fusion
category with possibly different positive multiplicities to get representations that are uniformly equivalent to the ones
from a unitary R-matrix. Such an equivalence will be called a localization of the unitary braid group representations. We show that the q = e
πi/6 specialization of the unitary Jones representation of the braid groups can be localized by a unitary 9 × 9 R-matrix. Actually this Jones representation is the first one in a family of theories (SO(N), 2) for an odd prime N > 1, which are conjectured to be localizable. We formulate several general conjectures and discuss possible connections to
physics and computer science. 相似文献
19.
J. M. Baptista 《Communications in Mathematical Physics》2009,291(3):799-812
We consider the vortex equations for a U(n) gauge field A coupled to a Higgs field f{\phi} with values on the n × n matrices. It is known that when these equations are defined on a compact Riemann surface Σ, their moduli space of solutions
is closely related to a moduli space of τ-stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the matrix f{\phi} , we show that the vortex solutions are entirely characterized by the location in Σ of the zeros of det f{\phi} and by the choice of a vortex internal structure at each of these zeros. We describe explicitly the vortex internal spaces
and show that they are compact and connected spaces. 相似文献
20.
Naveen Bijalwan 《International Journal of Theoretical Physics》2012,51(1):23-34
General exact higher-dimensional (n+2), n>2 solutions in general theory of relativity of Einstein-Maxwell field equations for spherically symmetric distribution of
charged pressure perfect fluid are expressed in terms of pressure extending 4-dimensional solutions presented by Bijalwan
(Astrophys. Space Sci. 2011, doi:). Subsequently, metrics (e
λ
and e
υ
), matter density and electric intensity are expressible in terms of pressure. Consequently, Pressure is found to be an invertible
arbitrary function of ω (=c
1+c
2
r
2), where c
1 and c
2 (≠0) are arbitrary constants, and r is the radius of star, i.e. p=p(ω). We present a general solution for charged pressure fluid in terms for ω. We list and discuss some old and new solutions which fall in this category. Also, these solutions satisfy barotropic equation
of state relating the radial pressure to the energy density. But we noticed that none of these solutions in terms of pressure
for charged fluids has a well behaved neutral counter part for a spatial component of metric e
λ
i.e. choosing same spatial component for charged and neutral fluid. To illustrate the approach, we discovered a new solution
for extended charged analogues of Schwarzschild interior solution in higher dimensions which is found to be well behaved only
for n=2. The maximum mass found to be 1.512 M
Θ with linear dimension 14.964 km. Physical quantities pressure, energy density, red-shift, velocity of sound and p/c
2
ρ are well behaved and monotonically decreasing towards the surface while adiabatic index and charge density are monotonically
increasing. For brevity we don’t discuss the numerical results in detailed. 相似文献