Revisiting Event Horizon Finders

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision

Simple and Effective Type Check Removal through Lazy Basic Block Versioning

Dynamically typed programming languages such as JavaScript and Python defer type checking to run time. In order to maximize performance, dynamic language VM implementations must attempt to eliminate redundant dynamic type checks. However, type inference analyses are often costly and involve tradeoffs between compilation time and resulting precision. This has lead to the creation of increasingly complex multi-tiered VM architectures. This paper introduces lazy basic block versioning, a simple JIT compilation technique which effectively removes redundant type checks from critical code paths. This novel approach lazily generates type-specialized versions of basic blocks on-the-fly while propagating context-dependent type information. This does not require the use of costly program analyses, is not restricted by the precision limitations of traditional type analyses and avoids the implementation complexity of speculative optimization techniques. We have implemented intraprocedural lazy basic block versioning in a JavaScript JIT compiler. This approach is compared with a classical flow-based type analysis. Lazy basic block versioning performs as well or better on all benchmarks. On average, 71% of type tests are eliminated, yielding speedups of up to 50%. We also show that our implementation generates more efficient machine code than TraceMonkey, a tracing JIT compiler for JavaScript, on several benchmarks. The combination of implementation simplicity, low algorithmic complexity and good run time performance makes basic block versioning attractive for baseline JIT compilers

Bounds on 4D Conformal and Superconformal Field Theories

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of implies a completely general lower bound on the central charge c >= f_c(d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients tau^{IJ} and flavor charges. We extend these bounds to N=1 superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Phi and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Phi x Phi* OPE, and show that there is an upper bound on the dimension of Phi* Phi when dim(Phi) is close to 1. We also present even more stringent bounds on c and tau^{IJ}. In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.Comment: 47 pages, 9 figures; V2: small corrections and clarification

Horizon Entropy

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, extend quite generally to what we call here "causal horizons". The root of this generalization is the local notion of horizon entropy density.Comment: 21 pages, one figure, to appear in a special issue of Foundations of Physics in honor of Jacob Bekenstei

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.Comment: 32 pages, 8 eps figures. Corrected Eq. (36), which is wrong in the published pape