Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-
dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.
The mysterious `dark energy needed to explain the current observations, poses a serious confrontation between fundamental physics and cosmology. The present crisis may be an outcome of the (so far untested) prediction of the general theory of relativ
ity that the pressure of the matter source also gravitates. In this view, a theoretical analysis reveals some surprising inconsistencies and paradoxes faced by the energy-stress tensor (in the presence of pressure) which is used to model the matter content of the universe, including dark energy.
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, s
quashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)times U(1)simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.
This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the distribution
function and summarize the construction of the gauge-invariant distribution function. The Liouville operator which describes the free streaming of electrons, and the collision term which describes the scattering of photons on free electrons are computed up to second order. Finally, the remaining dependence in the direction of the photon momentum is handled by expanding in projected symmetric trace-free multipoles and also in the more commonly used normal modes components. The results obtained remain to be used for computing numerically the contribution in the cosmic microwave background bispectrum which arises from the evolution of second order perturbations, in order to disentangle the primordial non-Gaussianity from the one generated by the subsequent non-linear evolution.
A scalar field gravitational analog of the Reissner-Nordstrom solution is investigated. The nonlinear Newtonian model has an upper-limit of charge for a central mass which agrees with the general relativistic condition required for the existence of t
he black hole horizon. The maximum limit for accumulation by bombardment of charged particles is found. The aim is to investigate the resulting physics after severing the effects of curvature from the effects of energy-mass equivalence.
We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra
of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensure conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators.
This research aims to introduce a new principle in the flat space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the quantum world. This limit, unattainable by the particles,
represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. There emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting consequences of the existence of such a minimum speed is that it prevents the absolute zero temperature for an ultracold gas according to the third law of thermodynamics. So we will be able to provide a fundamental dynamical explanation for the third law through a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed.
We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman-Penrose formalism. Gravitational instantons are exact solutions of Einsteins vacuum field equations with Euclidean signature. The Newman-Penrose formalism, w
hich supplies a toolbox for studying the exact solutions of Einsteins field equations, was adopted to the instanton case and our code translates it for the computational use.
In cosmology, the cosmic curvature $K$ and the cosmological constant $Lambda$ are two important parameters, and the values have strong influence on the behavior of the universe. In the context of normal cosmology, under the ordinary assumptions of po
sitive mass-energy and initial negative pressure, we find the initial singularity of the universe is certainly absent and we have $K=1$. This means total spatial structure of the universe should be a 3-dimensional sphere $S^3$. For the cyclic cosmological model, we have $Lambdalesssim 10^{-24} {rm ly}^{-2}$. Obviously, such constraints would be helpful for the researches on the properties of dark matter and dark energy in cosmology.
The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolution
s of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.
