According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in ...astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.
We consider a universal relation between moment of inertia and quadrupole moment of arbitrarily fast rotating neutron stars. Recent studies suggest that this relation breaks down for fast rotation. ...We find that it is still universal among various suggested equations of state for constant values of certain dimensionless parameters characterizing the magnitude of rotation. One of these parameters includes the neutron star radius, leading to a new universal relation expressing the radius through the mass, frequency, and spin parameter. This can become a powerful tool for radius measurements.
We derive a family of post-Newtonian (PN) Dedekind ellipsoids to first order. They describe non-axially symmetric, homogeneous, and rotating figures of equilibrium. The sequence of the Newtonian ...Dedekind ellipsoids allows for an axially symmetric limit in which a uniformly rotating Maclaurin spheroid is recovered. However, the approach taken by Chandrasekhar & Elbert to find the PN Dedekind ellipsoids excludes such a limit. In a previous work, we considered an extension to their work that permits a limit of 1 PN Maclaurin ellipsoids. Here we further detail the sequence and demonstrate that a choice of parameters exists with which the singularity formerly found by Chandrasekhar & Elbert along the sequence of PN Dedekind ellipsoids is removed.
We consider the post-Newtonian approximation for the Dedekind ellipsoids in the case of axisymmetry. The approach taken by Chandrasekhar & Elbert excludes the possibility of finding a uniformly ...rotating (deformed) spheroid in the axially symmetric limit, though the solution exists at the point of axisymmetry. We consider an extension to their work that permits the possibility of such a limit.
In our previous work N. Gürlebeck and M. Scholtz, Phys. Rev. D 95, 064010 (2017), we have shown that electric and magnetic fields are expelled from the horizons of extremal, stationary and axially ...symmetric uncharged black holes; this is called the Meissner effect for black holes. Here, we generalize this result in several directions. First, we allow that the black hole carries charge, which requires a generalization of the definition of the Meissner effect. Next, we introduce the notion of almost isolated horizons, which is weaker than the usual notion of isolated horizons, since the geometry of the former is not necessarily completely time independent. Moreover, we allow the horizon to be pierced by strings, thereby violating the usual assumption on the spherical topology made in the definition of the weakly isolated horizon. Finally, we spell out in detail all assumptions entering the proof and show that the Meissner effect is an inherent property of black holes even in full nonlinear theory.
It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The ...particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.
Black holes are important astrophysical objects describing an end state of stellar evolution, which are observed frequently. There are theoretical predictions that Kerr black holes with high spins ...expel magnetic fields. However, Kerr black holes are pure vacuum solutions, which do not include accretion disks, and additionally previous investigations are mainly limited to weak magnetic fields. We prove for the first time in full general relativity that generic rapidly spinning black holes including those deformed by accretion disks still expel even strong magnetic fields. Analogously to a similar property of superconductors, this is called the Meissner effect.
The description of an observer’s measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret ...measurements, which test the metric structure of the spacetime, like the classical Michelson-Morley, Ives-Stilwell, Kennedy-Thorndike experiments or frequency comparison experiments in general, it is necessary to describe them in theories, which go beyond the Lorentzian metric structure. However, this requires a description of an observer’s measurement without relying on a metric. We provide such a description of an observer’s measurement of the fundamental quantities time and length derived from a premetric perturbation of Maxwell’s electrodynamics and a discussion on how these measurements influence classical relativistic observables like time dilation and length contraction. Most importantly, we find that the modification of electrodynamics influences the measurements at two instances: the propagation of light is altered as well as the observer’s proper time normalization. When interpreting the results of a specific experiment, both effects cannot be disentangled, in general, and have to be taken into account.
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