Acceleration of particles by acceleration horizons

We consider collision of two particles in the vicinity of the extremal acceleration horizon (charged or rotating) that includes the Bertotti-Robinson space-time and the geometry of the Kerr throat. It is shown that the energy in the centre of mass frame E_{c.m.} can become indefinitely large if parameters of one of the particles are fine-tuned, so the Ba\~nados-Silk-West (BSW) effect manifests itself. There exists coordinate transformation which brings the metric into the form free of the horizon. This leads to some paradox since (i) the BSW effect exists due to the horizon, (ii) E_{c.m.} is a scalar and cannot depend on the frame. Careful comparison of near-horizon trajectories in both frames enables us to resolve this paradox. Although globally the space-time structure of the metrics with acceleration horizons and black holes are completely different, locally the vicinity of the extremal black hole horizon can be approximated by the metric of the acceleration one. The energy of one particle from the viewpoint of the Kruskal observer (or the one obtained from it by finite local boost) diverges although in the stationary frame energies of both colliding particles are finite. This suggests a new explanation of the BSW effect for black holes given from the viewpoint of an observer who crosses the horizon. It is complementary to the previously found explanation from the point of view of a static or stationary observer.Comment: 30 pages. Presentation improved and expanded, Sec. VI and VII and Appendix added. Matches version accepted in PRD. I thank the referee for helping in the improvement of this pape

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde

Regularized Nonlinear Acceleration

We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average are computed via a simple linear system, whose solution can be updated online. This acceleration scheme runs in parallel to the base algorithm, providing improved estimates of the solution on the fly, while the original optimization method is running. Numerical experiments are detailed on classical classification problems

Improved Acceleration of the GPU Fourier Domain Acceleration Search Algorithm

We present an improvement of our implementation of the Correlation Technique for the Fourier Domain Acceleration Search (FDAS) algorithm on Graphics Processor Units (GPUs) (Dimoudi & Armour 2015; Dimoudi et al. 2017). Our new improved convolution code which uses our custom GPU FFT code is between 2.5 and 3.9 times faster the than our cuFFT-based implementation (on an NVIDIA P100) and allows for a wider range of filter sizes then our previous version. By using this new version of our convolution code in FDAS we have achieved 44% performance increase over our previous best implementation. It is also approximately 8 times faster than the existing PRESTO GPU implementation of FDAS (Luo 2013). This work is part of the AstroAccelerate project (Armour et al. 2002), a many-core accelerated time-domain signal processing library for radio astronomy.Comment: proceeding from ADASS XXVII conference, 4 page

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Proton acceleration in analytic reconnecting current sheets

Particle acceleration provides an important signature for the magnetic collapse that accompanies a solar flare. Most particle acceleration studies, however, invoke magnetic and electric field models that are analytically convenient rather than solutions of the governing magnetohydrodynamic equations. In this paper a self-consistent magnetic reconnection solution is employed to investigate proton orbits, energy gains, and acceleration timescales for proton acceleration in solar flares. The magnetic field configuration is derived from the analytic reconnection solution of Craig and Henton. For the physically realistic case in which magnetic pressure of the current sheet is limited at small resistivities, the model contains a single free parameter that specifies the shear of the velocity field. It is shown that in the absence of losses, the field produces particle acceleration spectra characteristic of magnetic X-points. Specifically, the energy distribution approximates a power law ~ξ-3/2 nonrelativistically, but steepens slightly at the higher energies. Using realistic values of the “effective” resistivity, we obtain energies and acceleration times that fall within the range of observational data for proton acceleration in the solar corona