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Register a new userEvolution of Vacuum Bubbles Embeded in Inhomogeneous Spacetimes
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Added by
Florencia Anabella Teppa Pannia
Publication date
2016
fields
Physics
and research's language is
English
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We study the propagation of bubbles of new vacuum in a radially inhomogeneous background filled with dust or radiation, and including a cosmological constant, as a first step in the analysis of the influence of inhomogeneities in the evolution of an inflating region. We also compare the cases with dust and radiation backgrounds and show that the evolution of the bubble in radiation environments is notably different from that in the corresponding dust cases, both for homogeneous and inhomogeneous ambients, leading to appreciable differences in the evolution of the proper radius of the bubble.
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In this paper, we construct a class of collapsing spacetimes in vacuum without any symmetries. The spacetime contains a black hole region which is bounded from the past by the future event horizon. It possesses a Cauchy hypersurface with trivial topology which is located outside the black hole region. Based on existing techniques in the literature, the spacetime can in principle be constructed to be past geodesically complete and asymptotic to Minkowski space. The construction is based on a semi-global existence result of the vacuum Einstein equations built on a modified version of the a priori estimates that were originally established by Christodoulou in his work on the formation of trapped surface, and a gluing construction carried out inside the black hole. In particular, the full detail of the a priori estimates needed for the existence is provided, which can be regarded as a simplification of Christodoulous original argument.
We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.
We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.
Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial tool to understand the dynamics of black hole perturbations. Spherical symmetry allows for an expansion of the perturbations in scalar, vector, and tensor harmonics. The resulting perturbative equations are decoupled for modes with different parity and different harmonic numbers. Moreover, for each harmonic and parity, the equations for the perturbations can be decoupled in terms of (gauge-invariant) master functions that satisfy 1+1 wave equations. By working in a completely general perturbative gauge, in this paper we study what is the most general master function that is linear in the metric perturbations and their first-order derivatives and satisfies a wave equation with a potential. The outcome of the study is that for each parity we have two branches of solutions with similar features. One of the branches includes the known results: In the odd-parity case, the most general master function is an arbitrary linear combination of the Regge-Wheeler and the Cunningham-Price-Moncrief master functions whereas in the even-parity case it is an arbitrary linear combination of the Zerilli master function and another master function that is new to our knowledge. The other branch is very different since it includes an infinite collection of potentials which in turn lead to an independent collection master of functions which depend on the potential. The allowed potentials satisfy a non-linear ordinary differential equation. Finally, all the allowed master functions are gauge invariant and can be written in a fully covariant form.
In this paper we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case the component of any homothetic Killing vector along the $z$ direction must be constant. Firstly, it is shown that either the component along the radial direction is constant or we have the proportionality $g_{phiphi}propto g_{rhorho}$, where $g_{phiphi}>0$. In both cases, complete analyses are carried out and the general forms of the homothetic Killing vectors are determined. The associated conformal factors are also obtained. The case of vanishing twist in the metric, i.e., $omega= 0$ is considered and the complete forms of the homothetic Killing vectors are determined, as well as the associated conformal factors.
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