Book contents
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
Non existence of static multi-black-hole solutions in 2+1 dimensions
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
Summary
Abstract
It is shown that there is no static pure multi-black-hole solution of the (2+1)-Einstein equations with negative cosmological constant. The result is extended to the stationnary case and to the Einstein-Maxwell theory, for which the absence of pure multi-black hole solutions with freely specifiable positions is also established.
Introduction
Four-dimensional Einstein-Maxwell theory admits remarkable static multiblack-hole metrics in which the electrostatic repulsion exactly balances the gravitational attraction [1, 2, 3]. These solutions have the following important properties.
(i) each black hole contained in the solutions is of the extreme Reissner-Nordstrom type, i.e., has its mass equal to its charge;
(ii) the relative positions of the individual black holes are free parameters that can be specified independly of their masses (the exact balance between the electromagnetic repulsion and the gravitational attraction holds for any configuration); and
(ii) all the multi-black hole solutions have some exact supersymmetries [4, 5, 6]; actually, they are the only black hole solutions with this property.
Recently, three-dimensional metrics describing single black holes have been found in the context of the Einstein theory with a negative cosmological constant [7]. Even though the single (2+1)-black hole solutions occur in a much simpler setting, they share global causal properties quite similar to their (3+1)-parents [8].
The purpose of this note is to investigate whether one can construct static multi-black-hole solutions in 2+1 dimensions. We show that this is not possible, in spite of the fact that multiparticle solutions are known to exist for (2+1)-Einstein theory with zero cosmological constant [9].
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- Information
- Geometry of Constrained Dynamical Systems , pp. 150 - 157Publisher: Cambridge University PressPrint publication year: 1995