48 research outputs found
Celestial Mechanics, Conformal Structures, and Gravitational Waves
The equations of motion for non-relativistic particles attracting
according to Newton's law are shown to correspond to the equations for null
geodesics in a -dimensional Lorentzian, Ricci-flat, spacetime with a
covariantly constant null vector. Such a spacetime admits a Bargmann structure
and corresponds physically to a generalized pp-wave. Bargmann electromagnetism
in five dimensions comprises the two Galilean electro-magnetic theories (Le
Bellac and L\'evy-Leblond). At the quantum level, the -body Schr\"odinger
equation retains the form of a massless wave equation. We exploit the conformal
symmetries of such spacetimes to discuss some properties of the Newtonian
-body problem: homographic solutions, the virial theorem, Kepler's third
law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal
Killing 2-tensors, and motions under inverse square law forces with a
gravitational constant varying inversely as time (Dirac). The latter
problem is reduced to one with time independent forces for a rescaled position
vector and a new time variable; this transformation (Vinti and Lynden-Bell)
arises from a conformal transformation preserving the Ricci-flatness
(Brinkmann). A Ricci-flat metric representing non-relativistic
gravitational dyons is also pointed out. Our results for general time-dependent
are applicable to the motion of point particles in an expanding
universe. Finally we extend these results to the quantum regime.Comment: 26 pages, LaTe
Action functionals for relativistic perfect fluids
Action functionals describing relativistic perfect fluids are presented. Two
of these actions apply to fluids whose equations of state are specified by
giving the fluid energy density as a function of particle number density and
entropy per particle. Other actions apply to fluids whose equations of state
are specified in terms of other choices of dependent and independent fluid
variables. Particular cases include actions for isentropic fluids and
pressureless dust. The canonical Hamiltonian forms of these actions are
derived, symmetries and conserved charges are identified, and the boundary
value and initial value problems are discussed. As in previous works on perfect
fluid actions, the action functionals considered here depend on certain
Lagrange multipliers and Lagrangian coordinate fields. Particular attention is
paid to the interpretations of these variables and to their relationships to
the physical properties of the fluid.Comment: 40 pages, plain Te
Abelian Higgs hair for extreme black holes and selection rules for snapping strings
It has been argued that a black hole horizon can support the long range
fields of a Nielsen-Olesen string, and that one can think of such a vortex as
black hole ``hair''. We show that the fields inside the vortex are completely
expelled from a charged black hole in the extreme limit (but not in the near
extreme limit). This would seem to imply that a vortex cannot be attached to an
extreme black hole. Furthermore, we provide evidence that it is energetically
unfavourable for a thin vortex to interact with a large extreme black hole.
This dispels the notion that a black hole can support `long' Abelian Higgs hair
in the extreme limit. We discuss the implications for strings that end at black
holes, as in processes where a string snaps by nucleating black holes.Comment: 4 pages REVTeX plus 3 figures. Additional figures and mpeg movies
available at http://www.damtp.cam.ac.uk/user/ats25/strhole.html This paper is
a condensed version of gr-qc/9706004, and is essentially the talk presented
at The Eighth Marcel Grossmann Meeting on General Relativity, 22-27 June
1997, The Hebrew University, Jerusalem, Israe
Non-Abelian Black Holes and Catastrophe Theory I : Neutral Type
We re-analyze the globally neutral non-Abelian black holes and present a
unified picture, classifying them into two types; Type I (black holes with
massless non-Abelian field) and Type II (black holes with ``massive"
non-Abelian field). For the Type II, there are two branches: The black hole in
the high-entropy branch is ``stable" and almost neutral, while that in the low
entropy branch, which is similar to the Type I, is unstable and locally
charged. To analyze their stabilities, we adopt the catastrophe theoretic
method, which reveals us a universal picture of stability of the black holes.
It is shown that the isolated Type II black hole has a fold catastrophe
structure.
In a heat bath system, the Type I black hole shows a cusp catastrophe, while
the Type II has both fold and cusp catastrophe.Comment: 27pages, LaTex style, WU-AP/39/94. Figures are available (hard
copies) upon requests [[email protected] (T.Torii)
Extrema of Mass, First Law of Black Hole Mechanics and Staticity Theorem in Einstein-Maxwell-axion-dilaton Gravity
Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we
derived the formulas for the variation of mass and other asymptotic conserved
quantities in the theory under consideration. Generalizing this kind of
reasoning to the initial dota for the manifold with an interior boundary we got
the generalized first law of black hole mechanics. We consider an
asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity
describing a black hole with a Killing vector field timelike at infinity, the
horizon of which comprises a bifurcate Killing horizon with a bifurcate
surface. Supposing that the Killing vector field is asymptotically orthogonal
to the static hypersurface with boundary S and compact interior, we find that
the solution is static in the exterior world, when the timelike vector field is
normal to the horizon and has vanishing electric and axion- electric fields on
static slices.Comment: 17 pages, Revtex, a few comments (introduction) and references adde
Abelian Higgs Hair for Black Holes
We find evidence for the existence of solutions of the Einstein and Abelian
Higgs field equations describing a black hole pierced by a Nielsen-Olesen
vortex. This situation falls outside the scope of the usual no-hair arguments
due to the non-trivial topology of the vortex configuration and the special
properties of its energy-momentum tensor. By a combination of numerical and
perturbative techniques we conclude that the black hole horizon has no
difficulty in supporting the long range fields of the Nielsen Olesen string.
Moreover, the effect of the vortex can in principle be measured from infinity,
thus justifying its characterization as black hole ``hair".Comment: 31 pages, plain tex, 7 figures included. minor corrections and
references adde
Relationships between various characterisations of wave tails
One can define several properties of wave equations that correspond to the
absence of tails in their solutions, the most common one by far being Huygens'
principle. Not all of these definitions are equivalent, although they are
sometimes assumed to be. We analyse this issue in detail for linear scalar
waves, establishing some relationships between the various properties. Huygens'
principle is almost always equivalent to the characteristic propagation
property, and in two spacetime dimensions the latter is equivalent to the
zeroth order progressing wave propagation property. Higher order progressing
waves in general do have tails, and do not seem to admit a simple physical
characterisation, but they are nevertheless useful because of their close
association with exactly solvable two-dimensional equations.Comment: Plain TeX, 26 page
Dilatonic Black Holes with Gauss-Bonnet Term
We discuss black holes in an effective theory derived from a superstring
model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term.
Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of
spherically symmetric solutions, i.e., a neutral, an electrically charged, a
magnetically charged and a ``colored'' black hole, and discuss their
thermodynamical properties and fate via the Hawking evaporation process. For
neutral and electrically charged black holes, we find critical point and a
singular end point. Below the mass corresponding to the critical point,
nosolution exists, while the curvature on the horizon diverges and anaked
singularity appears at the singular point. A cusp structure in the mass-entropy
diagram is found at the critical point and black holes on the branch between
the critical and singular points become unstable. For magnetically charged and
``colored" black holes, the solution becomes singular just at the end point
with a finite mass. Because the black hole temperature is always finite even at
the critical point or the singular point, we may conclude that the evaporation
process will not be stopped even at the critical point or the singular point,
and the black hole will move to a dynamical evaporation phase or a naked
singularity will appear.Comment: 31pages, 11figures, LaTex styl
Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black-hole solutions to the stationary Einstein
equations has been steadily increasing, sometimes in unexpected ways. In
particular, it has turned out that not all black-hole-equilibrium
configurations are characterized by their mass, angular momentum and global
charges. Moreover, the high degree of symmetry displayed by vacuum and
electro-vacuum black-hole spacetimes ceases to exist in self-gravitating
non-linear field theories. This text aims to review some developments in the
subject and to discuss them in light of the uniqueness theorem for the
Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998.
Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's
authorship. Significantly restructured and updated all sections; changes are
too numerous to be usefully described here. The number of references
increased from 186 to 32
Exactly Soluble Sector of Quantum Gravity
Cartan's spacetime reformulation of the Newtonian theory of gravity is a
generally-covariant Galilean-relativistic limit-form of Einstein's theory of
gravity known as the Newton-Cartan theory. According to this theory, space is
flat, time is absolute with instantaneous causal influences, and the degenerate
`metric' structure of spacetime remains fixed with two mutually orthogonal
non-dynamical metrics, one spatial and the other temporal. The spacetime
according to this theory is, nevertheless, curved, duly respecting the
principle of equivalence, and the non-metric gravitational connection-field is
dynamical in the sense that it is determined by matter distributions. Here,
this generally-covariant but Galilean-relativistic theory of gravity with a
possible non-zero cosmological constant, viewed as a parameterized gauge theory
of a gravitational vector-potential minimally coupled to a complex
Schroedinger-field (bosonic or fermionic), is successfully cast -- for the
first time -- into a manifestly covariant Lagrangian form. Then, exploiting the
fact that Newton-Cartan spacetime is intrinsically globally-hyperbolic with a
fixed causal structure, the theory is recast both into a constraint-free
Hamiltonian form in 3+1-dimensions and into a manifestly covariant reduced
phase-space form with non-degenerate symplectic structure in 4-dimensions.
Next, this Newton-Cartan-Schroedinger system is non-perturbatively quantized
using the standard C*-algebraic technique combined with the geometric procedure
of manifestly covariant phase-space quantization. The ensuing unitary quantum
field theory of Newtonian gravity coupled to Galilean-relativistic matter is
not only generally-covariant, but also exactly soluble.Comment: 83 pages (TeX). A note is added on the early work of a remarkable
Soviet physicist called Bronstein, especially on his insightful contribution
to "the cube of theories" (Fig. 1) -- see "Note Added to Proof" on pages 71
and 72, together with the new references [59] and [61