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.
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.
17271354
Spinning particles in scalar-tensor gravity
We develop a new model of a spinning particle in Brans–Dicke spacetime using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.
119240145
Quantum fluctuations in planar domain wall space–times: A possible origin of primordial preferred direction
Abstract We study the gravitational effects of a planar domain wall on quantum fluctuations of a massless scalar field during inflation. By obtaining an exact solution of the scalar field equation in de-Sitter space, we show that the gravitational effects of the domain wall break the rotational invariance of the primordial power spectrum without affecting the translational invariance. The strength of rotational violation is determined by one dimensionless parameter β , which is a function of two physical parameters, the domain wall surface tension σ and cosmological constant Λ . In the limit of small β , the leading effect of rotational violation of the primordial power spectrum is scale-invariant.
118692827
Local and global structure of domain wall space-times
We present a general proof on the equivalence of the comoving-coordinate approach, where the wall is fixed at a constant coordinate variable, and moving-wall approach, where the wall is moving in a background static space-time, in the domain wall space-times without reflection symmetry. We further provide a general procedure to construct the comoving coordinates in the domain wall space-times, where the two regions separated by an infinite thin wall have different cosmological constant $\Lambda$ and Schwartzschild mass $M$. By solving Israel's junction conditions in the thin-wall limit, the gravitational fields of spherical, planar and hyperbolic domain wall space-times with M=0 in the two different comoving coordinate systems are obtained. We finally discuss the global structure of these domain wall space-times.
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.
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.
62888680
Rayleigh–Taylor instabilities in Type Ia supernova remnants undergoing cosmic ray particle acceleration – low adiabatic index solutions
This study investigates the evolution of Rayleigh-Taylor (R-T) instabilities in Type Ia supernova remnants that are associated with a low adiabatic index γ, where γ < 5/3, which reflects the expected change in the supernova shock structure as a result of cosmic ray particle acceleration. Extreme cases, such as the case with the maximum compression ratio that corresponds to γ = 1.1, are examined. As γ decreases, the shock compression ratio rises, and an increasingly narrow intershock region with a more pronounced initial mixture of R-T unstable gas is produced. Consequently, the remnant outline may be perturbed by small-amplitude, small-wavelength bumps. However, as the instability decays over time, the extent of convective mixing in terms of the ratio of the radius of the R-T fingers to the blast wave does not strongly depend on the value of γ for γ ≥ 1.2. As a result of the age of the remnant, the unstable gas cannot extend sufficiently far to form metal-enriched filaments of ejecta material close to the periphery of Tycho's supernova remnant. The consistency of the dynamic properties of Tycho's remnant with the adiabatic model γ = 5/3 reveals that the injection of cosmic rays is too weak to alter the shock structure. Even with very efficient acceleration of cosmic rays at the shock, significantly enhanced mixing is not expected in Type Ia supernova remnants.
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.
54005042
Modular properties of 3D higher spin theory
A bstractIn the three-dimensional $ \mathfrak{s}\mathfrak{l} $(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a ‘SL(2, $ \mathbb{Z} $)’ family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus.After deriving a thermodynamics that applies to all the solutions in the ‘SL(2, $ \mathbb{Z} $)’ family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.
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.