119282479
Momentum-space representation of the Feynman propagator in Riemann-Cartan spacetime
We first construct generalized normal coordinates by using autoparallels, instead of geodesics, in an arbitrary Riemann-Cartan spacetime. With the aid of generalized normal coordinates and their associated orthonormal frames, we obtain a momentum-space representation of the Feynman propagator for scalar fields, which is a direct generalization of Bunch and Parker's works to curved spacetime with torsion. We further derive the proper-time representation in n-dimensional Riemann-Cartan spacetime from the momentum-space representation. It leads us to obtain the renormalization of the one-loop effective Lagrangians of free scalar fields by using dimensional regularization. When the torsion tensor vanishes, our resulting momentum-space representation returns to the standard Riemannian results.
118403301
Domain wall space-times with a cosmological constant
We solve the vacuum Einstein's field equations with the cosmological constant in space-times admitting three-parameter group of isometries with two-dimensional spacelike orbits. The general exact solutions, which are represented in the advanced and retarded null coordinates, have two arbitrary functions due to the freedom of choosing null coordinates. In the thin-wall approximation, the Israel's junction conditions yield one constraint equation on these two functions in spherical, planar, and hyperbolic domain wall space-times with reflection symmetry. The remain freedom of choosing coordinates is completely fixed by requiring that, when the surface energy density {sigma}{sub 0} of domain walls vanishes, the metric solutions will return to some well-known solutions. It leads us to find a planar domain wall solution, which is conformally flat, in the de Sitter universe.
119297780
Brans-Dicke theory of gravity with torsion: A possible solution of $\omega$-problem
We study the Brans-Dicke theory of gravity in Riemann-Cartan space-times, and obtain general torsion solutions, which are completely determined by Brans-Dicke scalar field $\Phi$, in the false vacuum energy dominated epoch. The substitution of the torsion solutions back to our action gives the original Brans-Dicke action with $\Phi$-dependent Brans-Dicke parameter $\omega(\Phi)$. The evolution of $\omega(\Phi)$ during the inflation is studied and it is found that $\omega$ approaches to infinity at the end of inflation. This may solve the $\omega$-problem in the extended inflation model.
118253971
How can one observe gravitational angular momentum radiation from a dynamical source near null infinity
To answer a question of how can one observed angular momentum radiation near null infinity, one can first transform the dynamical twisting vacuum solution and make it satisfy Bondi coordinate conditions in the asymptotical region of the null infinity. We then obtain the Bondi-Sachs news function and also find the relationship of how does the angular momentum contribute to the news functions from the exact solution sense. By using the Komar's integral of angular momentum, the gravitational angular momentum flux of the dynamical twisting space-time can be obtained. All of our results can be compared with the Kerr solution, Robbinson-Trautmann or Schwarzschild solution. This study can provide a theoretical basis to understand the correlations of gravitational radiations near a rotating dynamical horizon and null infinity.
119297093
Gravitational radiations of generic isolated horizons and nonrotating dynamical horizons from asymptotic expansions
Instead of using a three-dimensional analysis on quasilocal horizons, we adopt a four-dimensional asymptotic expansion analysis to study the next order contributions from the nonlinearity of general relativity. From the similarity between null infinity and horizons, the proper reference frames are chosen from the compatible constant spinors for an observer to measure the energy-momentum and flux near quasilocal horizons. In particular, we focus on the similarity of Bondi-Sachs gravitational radiation for the quasilocal horizons and compare our results with Ashtekar-Kirshnan flux formula. The quasilocal energy-momentum and flux of generic isolated horizons and nonrotating dynamical horizons are discussed in this paper.
16484534
Cosmological dynamics with propagating Lorentz connection modes of spin zero
The Poincare gauge theory of gravity has a Lorentz connection with both torsion and curvature. For this theory two good propagating connection modes, carrying spin-0+ and spin-0−, have been found. The possible effects of the spin-0+ mode in cosmology were investigated in a previous work by our group; there it was found that the 0+ mode could account for the presently accelerating universe. Here, we extend the analysis to also include the spin-0− mode. The resulting cosmological model has three degrees of freedom. We present both the Lagrangian and Hamiltonian form of the dynamic equations for this model, find the late-time normal modes, and present some numerical evolution cases. In the late time asymptotic regime the two dynamic modes decouple, and the acceleration of the Universe oscillates due to the spin-0+ mode.
119126382
Twisting singular solutions of Betheʼs equations
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
119131032
Algebraic Bethe ansatz for singular solutions
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be determined using a generalization of the Bethe equations. These generalized Bethe equations provide a practical way of determining which singular solutions correspond to eigenvectors of the model.
119331321
Boundary energy of the open XXX chain with a non-diagonal boundary term
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson–Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
17362035
Existence of the Solution for the 't Hooft-Polyakov Monopole
Author(s): McLeod, J. Bryce; Wang, Chie Bing | Abstract: In this paper we give a mathematical proof of the existence of the time independent and spherically symmetric solution to the 't Hooft-Polyakov model of magnetic monopole by using 2D-shooting method.
14842099
Bullets in a Core-Collapse Supernova Remnant: The Vela Remnant
We use two-dimensional hydrodynamical simulations to investigate the properties of dense ejecta clumps (bullets) in a core-collapse supernova remnant, motivated by the observation of protrusions probably caused by clumps in the Vela supernova remnant. The ejecta, with an inner flat and an outer steep power-law density distribution, were assumed to freely expand into an ambient medium with a constant density, ~0.1 H atoms cm-3 for the case of Vela. At an age of 104 yr, the reverse shock front is expected to have moved back to the center of the remnant. Ejecta clumps with an initial density contrast χ ~ 100 relative to their surroundings are found to be rapidly fragmented and decelerated. In order to cause a pronounced protrusion on the blast wave, as observed in the Vela remnant, χ ~ 1000 may be required. In this case, the clump should be near the inflection point in the ejecta density profile, at an ejecta velocity ~3000 km s-1. These results apply to moderately large clumps; smaller clumps would require an even larger density contrast. Clumps can create ring structure in the shell of the Vela remnant, and we investigate the possibility that RX J0852-4622, an apparent supernova remnant superposed on Vela, is actually part of the Vela shell. Radio observations support this picture, but the possible presence of a compact object argues against it. The Ni bubble effect or compression in a pulsar wind nebula are possible mechanisms to produce the clumping.