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Register a new userA snapping cosmic string in a de Sitter or anti-de Sitter universe
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We present and describe an exact solution of Einsteins equations which represents a snapping cosmic string in a vacuum background with a cosmological constant $Lambda$. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of $Lambda$ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson-Trautman waves. It is also derived as a limit of the C-metric with $Lambda$, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.
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The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.
We give in this paper an explicit construction of the covariant quantization of the rank-two massless tensor field on de Sitter space (linear covariant quantum gravity on a de Sitter background). The main ingredient of the construction is an indecomposable representation of de Sitter group. We here make the choice of a specific simple gauge fixing. We show that our gauge fixing eliminates any infrared divergence in the two-point function for the traceless part of this field. But it is not possible to do the same for the pure trace part (conformal sector). We describe the related Krein space structure and covariant field operators. This work is in the continuation of our previous ones concerning the massless minimally coupled scalar fields and the massive tensor field on de Sitter.
We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss in detail the black hole properties and obtain the following main results: (i) From the horizon equation $g_{rr}=0$, we derive the relation between the perfect fluid dark matter parameter $alpha$ and the cosmological constant $Lambda$ when the cosmological horizon $r_{Lambda}$ exists. For $Lambda=0$, we find that $alpha$ is in the range $0<alpha<2M$ for $alpha>0$ and $-7.18M<alpha<0$ for $alpha<0$. For positive cosmological constant $Lambda$ (Kerr-AdS BH), $alpha_{max}$ decreases if $alpha>0$, and $alpha_{min}$ increases if $alpha<0$. For negative cosmological constant $-Lambda$ (Kerr-dS BH), $alpha_{max}$ increases if $alpha>0$ and $alpha_{min}$ decreases if $alpha<0$; (ii) An ergosphere exists between the event horizon and the outer static limit surface. The size of the ergosphere evolves oppositely for $alpha>0$ and $alpha<0$, while decreasing with the increasing $midalphamid$. When there is sufficient dark matter around the black hole, the black hole spacetime changes remarkably; (iii) The singularity of these black holes is the same as that of rotational black holes. In addition, we study the geodesic motion using the Hamilton-Jacobi formalism and find that when $alpha$ is in the above ranges for $Lambda=0$, stable orbits exist. Furthermore, the rotational velocity of the black hole in the equatorial plane has different behaviour for different $alpha$ and the black hole spin $a$. It is asymptotically flat and independent of $alpha$ if $alpha>0$ while is asymptotically flat only when $alpha$ is close to zero if $alpha<0$.
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected AdS3 appears to be singled out.
The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-$frac{3}{2}$ field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic.
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