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Register a new userNon-abelian black holes and black strings in higher dimensions
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Betti Hartmann
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We review the properties of static, higher dimensional black hole solutions in theories where non-abelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in $d > 4$, but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein-Yang-Mills models. 5-dimensional black strings with horizon topology S^2 x S^1 are also discussed. These are so-called undeformed and deformed non-abelian black strings, which are translationally invariant and correspond to 4-dimensional non-abelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axially symmetric for constant values of the extra coordinate is a new feature as compared to black string solutions of Einstein (-Maxwell) theory. It is argued that these non-abelian black strings are thermodynamically unstable.
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Starting with a Zipoy-Voorhees line element we construct and study the three parameter family of solutions describing a deformed black string with arbitrary tension.
We compute the gravitational wave energy $E_{rm rad}$ radiated in head-on collisions of equal-mass, nonspinning black holes in up to $D=8$ dimensional asymptotically flat spacetimes for boost velocities $v$ up to about $90,%$ of the speed of light. We identify two main regimes: Weak radiation at velocities up to about $40,%$ of the speed of light, and exponential growth of $E_{rm rad}$ with $v$ at larger velocities. Extrapolation to the speed of light predicts a limit of $12.9,%$ $(10.1,~7.7,~5.5,~4.5),%$. of the total mass that is lost in gravitational waves in $D=4$ $(5,,6,,7,,8)$ spacetime dimensions. In agreement with perturbative calculations, we observe that the radiation is minimal for small but finite velocities, rather than for collisions starting from rest. Our computations support the identification of regimes with super Planckian curvature outside the black-hole horizons reported by Okawa, Nakao, and Shibata [Phys.~Rev.~D {bf 83} 121501(R) (2011)].
Two lectures given in Paris in 1985. They were circulated as a preprint Solitons And Black Holes In Four-Dimensions, Five-Dimensions. G.W. Gibbons (Cambridge U.) . PRINT-85-0958 (CAMBRIDGE), (Received Dec 1985). 14pp. and appeared in print in De Vega, H.J. ( Ed.), Sanchez, N. ( Ed.) : Field Theory, Quantum Gravity and Strings*, 46-59 and Preprint - GIBBONS, G.W. (REC.OCT.85) 14p. I have scanned the original, reformatted and and corrected various typos.
Recently introduced classical theory of gravity in non-commutative geometry is studied. The most general (four parametric) family of $D$ dibensional static spherically symmetric spacetimes is identified and its properties are studied in detail. For wide class of the choices of parameters, the corresponding spacetimes have the structure of asymptotically flat black holes with a smooth event horizon hiding the curvature singularity. A specific attention is devoted to the behavior of components of the metric in non-commutative direction, which are interpreted as the black hole hair.
We consider (n+1)--dimensional, stationary, asymptotically flat, or Kaluza-Klein asymptotically flat black holes, with an abelian $s$--dimensional subgroup of the isometry group satisfying an orthogonal integrability condition. Under suitable regularity conditions we prove that the area of the group orbits is positive on the domain of outer communications, vanishing only on its boundary and on the symmetry axis. We further show that the orbits of the connected component of the isometry group are timelike throughout the domain of outer communications. Those results provide a starting point for the classification of such black holes. Finally, we show non-existence of zeros of static Killing vectors on degenerate Killing horizons, as needed for the generalisation of the static no-hair theorem to higher dimensions.
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