13 research outputs found
Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
We describe the first convergent numerical method to determine static black
hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a
family of solutions parametrized by the ratio of the black hole size and the
size of the compact extra dimension. The solutions satisfy the demanding
integrated first law. For small black holes our solutions approach the 5d
Schwarzschild solution and agree very well with new theoretical predictions for
the small corrections to thermodynamics and geometry. The existence of such
black holes is thus established. We report on thermodynamical (temperature,
entropy, mass and tension along the compact dimension) and geometrical
measurements. Most interestingly, for large masses (close to the
Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as
evidence for an approach to a physical tachyonic instability. Using
extrapolation we speculate that the system undergoes a first order phase
transition.Comment: 42 pages, 19 eps figures; v2: 3 references added, version to appear
in Phys.Rev.
Formation and Evaporation of Charged Black Holes
We investigate the dynamical formation and evaporation of a spherically
symmetric charged black hole. We study the self-consistent one loop order
semiclassical back-reaction problem. To this end the mass-evaporation is
modeled by an expectation value of the stress-energy tensor of a neutral
massless scalar field, while the charge is not radiated away. We observe the
formation of an initially non extremal black hole which tends toward the
extremal black hole , emitting Hawking radiation. If also the discharge
due to the instability of vacuum to pair creation in strong electric fields
occurs, then the black hole discharges and evaporates simultaneously and decays
regularly until the scale where the semiclassical approximation breaks down. We
calculate the rates of the mass and the charge loss and estimate the life-time
of the decaying black holes.Comment: 23 pages, 7 eps figures, RevTex, accepted for publication in Phys.
Rev.
Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
In backgrounds with compact dimensions there may exist several phases of
black objects including the black-hole and the black-string. The phase
transition between them raises puzzles and touches fundamental issues such as
topology change, uniqueness and Cosmic Censorship. No analytic solution is
known for the black hole, and moreover, one can expect approximate solutions
only for very small black holes, while the phase transition physics happens
when the black hole is large. Hence we turn to numerical solutions. Here some
theoretical background to the numerical analysis is given, while the results
will appear in a forthcoming paper. Goals for a numerical analysis are set. The
scalar charge and tension along the compact dimension are defined and used as
improved order parameters which put both the black hole and the black string at
finite values on the phase diagram. Predictions for small black holes are
presented. The differential and the integrated forms of the first law are
derived, and the latter (Smarr's formula) can be used to estimate the ``overall
numerical error''. Field asymptotics and expressions for physical quantities in
terms of the numerical ones are supplied. Techniques include ``method of
equivalent charges'', free energy, dimensional reduction, and analytic
perturbation for small black holes.Comment: 23 pages. v3: version to be published in PRD, 3 references adde
Effects of Pair Creation on Charged Gravitational Collapse
We investigate the effects of pair creation on the internal geometry of a
black hole, which forms during the gravitational collapse of a charged massless
scalar field. Classically, strong central Schwarzschild-like singularity forms,
and a null, weak, mass-inflation singularity arises along the Cauchy horizon,
in such a collapse. We consider here the discharge, due to pair creation, below
the event horizon and its influence on the {\it dynamical formation} of the
Cauchy horizon. Within the framework of a simple model we are able to trace
numerically the collapse. We find that a part of the Cauchy horizon is replaced
by the strong space-like central singularity. This fraction depends on the
value of the critical electric field, , for the pair creation.Comment: LaTex, 27 pages, including 14 figures. Some points are clarified,
typos corrected. Version accepted for publication in Phys.Rev.
New Phase Diagram for Black Holes and Strings on Cylinders
We introduce a novel type of phase diagram for black holes and black strings
on cylinders. The phase diagram involves a new asymptotic quantity called the
relative binding energy. We plot the uniform string and the non-uniform string
solutions in this new phase diagram using data of Wiseman. Intersection rules
for branches of solutions in the phase diagram are deduced from a new Smarr
formula that we derive.Comment: 19 pages, 6 figures, v2: typos corrected, v3: refs. added, comment on
bounds on the relative binding energy n added in end of section
Dynamics & Predictions in the Co-Event Interpretation
Sorkin has introduced a new, observer independent, interpretation of quantum
mechanics that can give a successful realist account of the 'quantum
microworld' as well as explaining how classicality emerges at the level of
observable events for a range of systems including single time 'Copenhagen
measurements'. This 'co-event interpretation' presents us with a new ontology,
in which a single 'co-event' is real. A new ontology necessitates a review of
the dynamical & predictive mechanism of a theory, and in this paper we begin
the process by exploring means of expressing the dynamical and predictive
content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein
Equilibrium and stability of supermassive stars in binary systems
We investigate the equilibrium and stability of supermassive stars of mass M
\agt 10^5M_{\odot} in binary systems. We find that corotating binaries are
secularly unstable for close, circular orbits with r \alt
4R(M/10^6M_{\odot})^{1/6} where is the orbital separation and the
stellar radius. We also show that corotation cannot be achieved for distant
orbits with r \agt 12 R (M/10^6M_{\odot})^{-11/24}, since the timescale for
viscous angular momentum transfer associated with tidal torques is longer than
the evolution timescale due to emission of thermal radiation. These facts
suggest that the allowed mass range and orbital separation for corotating
supermassive binary stars is severely restricted. In particular, for
supermassive binary stars of large mass M \agt 6\times 10^6M_{\odot},
corotation cannot be achieved, as viscosity is not adequate to mediate the
transfer between orbital and spin angular momentum. One possible outcome for
binary supermassive stars is the onset of quasi-radial, relativistic
instability which drives each star to collapse prior to merger: We discuss
alternative outcomes of collapse and possible spin states of the resulting
black holes. We estimate the frequency and amplitude of gravitational waves
emitted during several inspiral and collapse scenarios.Comment: 20 pages, to be published in PR
Twistor form of massive 6D superparticle
The massive six-dimensional (6D) superparticle with manifest (n, 0) supersymmetry is shown to have a supertwistor formulation in which its “hidden” (0, n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin; for n = 1 it propagates the 6D Proca supermultiplet.PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society.This is the final version of the article. It was first available from IOP Science via http://dx.doi.org/10.1088/1751-8113/49/2/02540
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress is traced from
the early stage of 1D feasibility studies to 2D axisymmetric codes that
accurately simulate the oscillations and gravitational collapse of relativistic
stars and to current 3D codes that provide pieces of a binary black spacetime.
A prime application of characteristic evolution is to compute waveforms via
Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1