TY - JOUR

T1 - N-black hole stationary and axially symmetric solutions of the Einstein/Maxwell equations

AU - Weinstein, Gilbert

N1 - Funding Information:
This research was supported in part by XSF grant DMS-9404523 The author would like to express his thanks for the support and hospitality of the Erwin Schrodinger Institute where part of this work was completed.

PY - 1996

Y1 - 1996

N2 - The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ: ℝ3 \ Σ → ℍ2ℂ, where Σ is a subset of the axis of symmetry, and ℍ2ℂ is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ: ℝn \ Σ → ℍ, where Σ is a submanifold of ℝn of co-dimension ≥ 2, and ℍ is a classical Riemannian globally symmetric space of noncompact type and rank one. This result, when applied to the black hole problem, yields solutions which can be interpreted as equilibrium configurations of multiple co-axially rotating charged black holes held apart by singular struts.

AB - The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ: ℝ3 \ Σ → ℍ2ℂ, where Σ is a subset of the axis of symmetry, and ℍ2ℂ is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ: ℝn \ Σ → ℍ, where Σ is a submanifold of ℝn of co-dimension ≥ 2, and ℍ is a classical Riemannian globally symmetric space of noncompact type and rank one. This result, when applied to the black hole problem, yields solutions which can be interpreted as equilibrium configurations of multiple co-axially rotating charged black holes held apart by singular struts.

UR - http://www.scopus.com/inward/record.url?scp=0000841230&partnerID=8YFLogxK

U2 - 10.1080/03605309608821232

DO - 10.1080/03605309608821232

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AN - SCOPUS:0000841230

SN - 0360-5302

VL - 21

SP - 1389

EP - 1430

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 9-10

ER -