spintwo.net jens boos | gauge structures in gravity


    • Stationary black holes with stringy hair
    • Nov 16, 2017 | Jens Boos and Valeri P. Frolov
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      We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without cosmological constant. This solution is a warped product of two metrics. One of them is a deformed two-sphere whose Gaussian curvature is determined by the energy-density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-A(d)S generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

    • [ pdf | 1711.06357 [gr-qc] ]
    • Kerr principal null directions from Bel–Robinson and Kummer surfaces
    • Mar 31, 2017 | Jens Boos and Alberto Favaro
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      In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter fields. Moreover, we demonstrate that the principal null directions of the Kerr geometry can be obtained by projections involving either the Bel–Robinson or the Kummer tensor. We conjecture that this is also possible in more general settings.

    • [ pdf | 1703.10791 [gr-qc] ]
    • Plebański–Demiański solution of general relativity and its expressions quadratic and cubic in curvature: analogies to electromagnetism
    • Dec 5, 2014 | Jens Boos
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      Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution—the exact seven parameter solution of Plebański–Demiański (PD)—to demonstrate these analogies for a physically meaningful spacetime:

      The two quadratic curvature invariants B2 - E2 and E·B are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitational electric mass and gravitational electric current of the PD solution, respectively, if there are no gravitational magnetic monopoles present.

      Furthermore, the square of the Bel--Robinson tensor reads (B2 + E2)2 for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy-momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel–Robinson 3-form, from which the Bel–Robinson tensor can be calculated.

      We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition.

      The calculations are carried out in two coordinate systems: in the original polynomial PD coordinates, and in a modified Boyer–Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.

    • [ pdf | 1412.1958 [gr-qc] | Int. J. Mod. Phys. D 24 (2015) no.10 1550079 | inspire ]


    • Quasi-normal modes: what can ringing black holes tell us about quantum gravity?
    • Seventh Annual Symposium for Graduate Physics Research, University of Alberta, Sept 23, 2016
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      The recent detection of gravitational waves [1] is truly mind-boggling: ripples in spacetime itself were directly detected for the first time, with an instrument sensitive enough to measure dislocations the size of an atomic nucleus over a distance of a few kilometers. This discovery can also be considered the first direct detection of black holes.

      In this talk, we will discuss one aspect of black hole physics: so-called quasi-normal modes [2]. These are characteristic frequencies emitted by black holes when they are subject to perturbations: much like the ringing of a wine glass, when struck by a solid object.

      We will describe how to calculate quasi-normal modes, and in a second step elucidate as to what information these frequencies may contain. As it turns out, if measured precisely enough, they might be able to give us crucial insight into the still elusive quantum theory of gravity [3].

      1. B. P. Abbott et al. [LIGO Scientific and Virgo Collaborations], “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 061102 (2016) no. 6, arXiv:1602.03837 [gr-qc].
      2. K. D. Kokkotas and B. G. Schmidt, “Quasi-Normal Modes of Stars and Black Holes”, Living Rev. Relativity 2 2 (1999).
      3. C. Corda, “Quasi-Normal Modes: The 'Electrons' of Black Holes as 'Gravitational Atoms'? Implications for the Black Hole Information Puzzle,” Adv. High Energy Phys. 2015 867601 (2015), arXiv:1503.00565 [gr-qc].
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    • Classical aspects of Poincaré gauge theory of gravity
    • Quantum gravity group meeting, Perimeter Institute, Nov 11, 2015
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      I will briefly highlight a few cornerstones in the development of gauge theory, and then proceed to the gauge structure present in gravity. Following [1], I will argue that if one wishes to take the fermionic character of matter into account, the Poincaré group will give rise to a satisfactory gauge-theoretical description of gravity. This will include both energy-momentum and spin-angular momentum as sources of the gravitational field.

      In a second step, I will elaborate on the emerging structure of a Riemann-Cartan geometry. Einstein-Cartan theory will be sketched, a minimal and viable gauge-theoretical extension of Einstein's General Relativity. If time permits, I will briefly mention its implications for cosmology and the possible resolution of singularities.

      I will close by pointing out the deformed Lie algebra of the Poincare group as a result of the gauging procedure: unlike in Yang-Mills theory with its internal symmetry groups, here the Lie algebra is deformed due to the presence of curvature and torsion. The implications of this deformation, both in the classical and quantum regime, remain to be seen.

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    • Differential forms: from classical force to the Wilson loop
    • PSI student seminar, Perimeter Institute, Sept 2, 2015
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      We start by reviewing basic properties of differential forms in three dimensions. Using the Hodge star and thereby deriving a visualization procedure, we move on to classical mechanics and vacuum electrodynamics. Therein, differential forms can be interpreted operationally, and their full physical significance becomes clear.

      We now move on to more abstract grounds: we revisit electrodynamics as a gauge theory, and discuss its connection 1-form and its relation to the group U(1). We close by motivating the geometric interpretation of connection 1-forms in gauge theories using the Wilson loop, and sketch its application to General Relativity and beyond.

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    • Quasi-normal modes of the BTZ black hole with torsion
    • Feb 3, 2015
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      The basic structures of the Mielke–Baekler model of topologically massive gravity in (2+1) dimensions [1, 2] are reviewed, and its Bañados–Teitelboim–Zanelli(BTZ)-like black hole solution [3, 4] is briefly presented.

      We then present quasi-normal modes as applied to asymptotically anti de Sitter black hole spacetimes: they are solutions to scalar, electromagnetic, spinorial or tensorial wave equations with specific boundary conditions.

      The associated frequency to each mode is called quasi-normal frequency, and their imaginary part is relevant for the stability question of the black hole under consideration. They turn out to be negative for the BTZ black hole [5, 6], making it stable against perturbations. It remains to be seen how tensorial modes affect the stability issue.


      1. E. W. Mielke and P. Baekler, “Topological gauge model of gravity with torsion,” Phys. Lett. A 156 (1991) 399, inspire.
      2. P. Baekler, E. W. Mielke and F. W. Hehl, “Dynamical symmetries in topological 3-D gravity with torsion,” Nuovo Cim. B 107 (1992) 91, inspire.
      3. M. Bañados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69 (1992) 1849, [hep-th/9204099].
      4. A. A. García, F. W. Hehl, C. Heinicke and A. Macías, “Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion,” Phys. Rev. D 67 (2003) 124016, [gr-qc/0302097].
      5. D. Birmingham, “Choptuik scaling and quasinormal modes in the AdS / CFT correspondence,” Phys. Rev. D 64 (2001) 064024, [hep-th/0101194].
      6. R. Becar, P. A. Gonzalez and Y. Vasquez, “Dirac quasinormal modes of Chern-Simons and BTZ black holes with torsion,” Phys. Rev. D 89 (2014) 2, [arXiv:1306.5974 [gr-qc]].
    • Second order curvature invariants for the Plebański–Demiański solution
    • Nov 11, 2014
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      The Plebański–Demiański (PD) solution is a seven parameter type D solution of the Einstein–Maxwell equations [1]. It can be used to describe a uniformly accelerating Kerr–Newman black hole in a de Sitter spacetime with an additional NUT parameter.

      Recently, Griffiths & Podolský introduced new coordinates to recover the well-known Boyer–Lindquist coordinates from the polynomial PD coordinates [2]. The necessary coordinate transformations will be sketched briefly.

      In the following, I will present a computer algebra-based calculation (Reduce with Excalc [3, 4]) yielding second order curvature (pseudo-)invariants for this spacetime. The result will be of remarkably simple structure very similar to electrodynamics.


      1. J. F. Plebański and M. Demiański, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98 (1976) 98, DOI: 10.1016/0003-4916(76)90240-2.
      2. J. B. Griffiths and J. Podolský, “A New look at the Plebański-Demiański family of solutions,” Int. J. Mod. Phys. D 15 (2006) 335 [arXiv:gr-qc/0511091].
      3. A. C. Hearn, REDUCE User's Manual, Version 3.5 RAND Publication CP78 (Rev. 10/93). The RAND Corporation, Santa Monica, CA 90407-2138, USA (1993). Nowadays Reduce is freely available for download; for details see [reduce-algebra.com] and [sourceforge.net].
      4. J. Socorro, A. Macias and F. W. Hehl, “Computer algebra in gravity: Programs for (non-)Riemannian space-times. 1,” Comput. Phys. Commun. 115 (1998) 264 [arXiv:gr-qc/9804068].