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 $M=Q$, 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, $E_{\rm cr}$, 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 $r$ is the orbital separation and $R$ 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