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Matching stationary spacetimes

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 Added by Jose Natario
 Publication date 2020
  fields Physics
and research's language is English




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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.



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In 1981 Wyman classified the solutions of the Einstein--Klein--Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.
136 - Marco Astorino 2014
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the Bekenstein black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.
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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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