Gravitational waves from gamma-ray bursts

We present a mechanism for long bursts of gravitational radiation from Kerr black holes surrounded by a torus. These systems are believed to form in core-collapse of massive stars in association with gamma-ray bursts. The torus catalyzes black hole-spin energy mostly into gravitational radiation, with a minor output in winds, thermal and neutrino emissions. Torus winds impact the remnant envelope of the progenitor star from within, which may account for X-ray emission lines and leaves a supernova remnant. The frequency in gravitational radiation satisfies f_{gw}=470Hz (E_{SNR}/4\times 10^{51})^{1/2}(0.1/\beta)^{1/2}(7M_\odot/M_H)^{3/2}, where E_{SNR} is the kinetic energy in the SNR, M_H is the black hole mass and \beta\simeq0.1 the initial ejection velocity, as detected in GRB 011211. Ultimately, this leaves a black hole binary surrounded by a SNR, which is conceivably illustrated by RX J050736-6847.8.Comment: Invited talk at GRBs in the Afterglow Era: 3rd Workshop, Rome 200

Gravitational radiation from a torus around a black hole

Long gamma-ray bursts (GRBs) from rapidly spinning black hole-torus systems may represent hypernovae or black hole-neutron star coalescence. We show that the torus may radiate gravitational radiation powered by the spin-energy of the black hole in the presence of non-axisymmetries. The coupling to the spin-energy of the black hole is due to equivalence in poloidal topology to pulsar magnetospheres. Results calculated in the suspended accretion state indicate that GRBs are potentially the most powerful LIGO/VIRGO burst-sources in the Universe, with an expected duration of 10-15s on a horizontal branch of 1-2kHz in the $\dot{f}(f)-$diagram.Comment: Accepted for publication in the Phys. Rev. Let

Extreme luminosities in ejecta produced by intermittent outflows around rotating black holes

Extreme sources in the Transient Universe show evidence of relativistic outflows from intermittent inner engines, such as cosmological gamma-ray bursts. They probably derive from rotating back holes interacting with surrounding matter. We show that these interactions are enhanced inversely proportional to the duty cycle in advection of magnetic flux, as may apply at high accretion rates. We demonstrate the morphology and ballistic propagation of relativistic ejecta from burst outflows by numerical simulations in relativistic magnetohydrodynamics. Applied to stellar mass black holes in core-collapse of massive stars, it provides a robust explosion mechanism as a function of total energy output. At breakout, these ejecta may produce a low-luminosity GRB. A long GRB may ensue from an additional ultra-relativistic baryon-poor inner jet from a sufficiently long-lived intermittent inner engine. The simulations demonstrate a complex geometry in mergers of successive ejecta, whose mixing and shocks provide a pathway to broadband high energy emission from magnetic reconnection and shocks.Comment: MNRASL, to appea

Hyperbolic Hamiltonian equations for general relativity

The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new system for black hole spacetimes that are asymptotically quiescent, which introduces analyticity properties that can be exploited for numerical calculations by compactification in spherical coordinates with complex radius following a M\"obius transformation. Conformal flat initial data of two black holes are hereby invariant, and correspond to a turn point in a pendulum, up for a pair of separated black holes and down for a single black hole. Here, Newton's law appears in the relaxation of $l=2$ deformations of semi-infinite poloidal surface elements, defined by the moment of inertia of the binary.Comment: Based on an invited talk at the Federation Denis Poisson (October 2008

Global spectral representations of black hole spacetimes in the complex plane

Binary black hole coalescence produces a finite burst of gravitational radiation which propagates towards quiescent infinity. These spacetimes are analytic about infinity and contain a dimensionless coupling constant $M/s$, where $M$ denotes the total mass-energy and $s$ an imaginary distance. This introduces globally convergent Fourier series on a complex radial coordinate, allowing spectral representation of black hole spacetimes in all three dimensions. We illustrate this representation theory on a Fourier-Legendre expansion of Boyer-Lindquist initial data and a scalar wave equation with signal recovery by Cauchy's integral formula.Comment: Based on an invited talk at the Int'l Conf. Theor. Physics, 11-16 April 2005, Lebedev Physical Institute, Mosco

The Theory Of Ideal Yang-Mills Fluids In Symmetric Hyperbolic Form

The theory of ideal Yang-Mills fluids (IYMF; a Yang-Mills field coupled to a fluid in the limit of infinite conductivity) is embedded in symmetric hyperbolic form. This yields both causality and well-posedness of initial value problems in this theory. The embedding is based on a covariant, constraint-free divergence formulation of IYMF, developped by the author previously for magneto-hydrodynamics. Expressions for the small amplitude wave structure are also derived, showing that in general Alfven waves do not persist in the presence of colored magnetic fields.Comment: 36 page

Galaxy rotation curves and the deceleration parameter in weak gravity

We present a theory of weak gravity parameterized by a fundamental frequency $\omega_0 = \sqrt{1-q}H$ of the cosmoloogical horizon, where $H$ and $q$ denote the Hubble and, respectively, deceleration parameter. It predicts (i) a $C^0$ onset to weak gravity across accelerations $\alpha = a_{dS}$ in galaxy rotation curves, where $a_{dS}=cH$ denotes the de Sitter acceleration with velocity of light $c$, and (ii) fast evolution $Q(z)=dq(z)/dz$ of the deceleration parameter by $\Lambda=\omega_0^2$ satisfying $Q_0>2.5$, $Q_0=Q(0)$, distinct from $Q_0\lesssim1$ in $\Lambda$CDM. The first is identified in high resolution data of Lellie et al.(2017), the second in heterogeneous data on $H(z)$ over $0<z<2$. A model-independent cubic fit in the second rules out $\Lambda$CDM by $4.35\sigma$ and obtains $H_0=74.0\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$ consistent with Riess et al. (2016). Comments on possible experimental tests by the LISA Pathfinder are included.Comment: 15 p., 5 figs., based on invited talk Conference Cosmology, Gravitational waves and Particles, 6-10 Feb., NTU, Singapore (2017

Directed searches for broadband extended gravitational-wave emission in nearby energetic core-collapse supernovae

Core-collapse supernovae are factories of neutron stars and stellar mass black holes. Type Ib/c supernovae stand out as potentially originating in relatively compact stellar binaries and their branching ratio of about 1\% into long gamma-ray bursts. The most energetic events probably derive from central engines harboring rapidly rotating black holes, wherein accretion of fall-back matter down to the Inner Most Stable Circular Orbit (ISCO) offers a window to {\em broadband extended gravitational-wave emission} (BEGE). To search for BEGE, we introduce a butterfly filter in time-frequency space by Time Sliced Matched Filtering. To analyze long epochs of data, we propose using coarse grained searches followed by high resolution searches on events of interest. We illustrate our proposed coarse grained search on two weeks of LIGO S6 data prior to SN 2010br $(z=0.002339)$ using a bank of up to 64 thousand templates of one second duration covering a broad range in chirp frequencies and bandwidth. Correlating events with signal-to-noise ratios $>6$ from the LIGO L1 and H1 detectors each reduces to a few events of interest. Lacking any further properties reflecting a common excitation by broadband gravitational radiation, we disregarded these as spurious. This new pipeline may be used to systematically search for long duration chirps in nearby core-collapse supernovae from robotic optical transient surveys using embarrassingly parallel computing.Comment: 26 pages, 8 figures, to appear in Ap

Asymptotic harmonic behavior in the prime number distribution

We consider $\Phi(x)=x^{-\frac{1}{4}}\left[1-2\sqrt{x}\Sigma e^{-p^2\pi x}\ln p\right]$ on $x>0$, where the sum is over all primes $p$. If $\Phi$ is bounded on $x>0$, then the Riemann hypothesis is true or there are infinitely many zeros Re~$z_k>\frac{1}{2}$. The first 21 zeros give rise to asymptotic harmonic behavior in $\Phi(x)$ defined by the prime numbers up to one trillion.Comment: minor revision, 13 pages, 3 figure

Deep searches for broadband extended gravitational-wave emission bursts by heterogeneous computing

We present a heterogeneous search algorithm for broadband extended gravitational-wave emission (BEGE), expected from gamma-ray bursts and energetic core-collapse supernovae. It searches the $(f,\dot{f})$-plane for long duration bursts by inner engines slowly exhausting their energy reservoir by matched filtering on a {\em Graphics Processor Unit} (GPU) over a template bank of millions of one-second duration chirps. Parseval's Theorem is used to predict the standard deviation $\sigma$ of filter output, taking advantage of near-Gaussian noise in LIGO S6 data over 350-2000 Hz. Tails exceeding a mulitple of $\sigma$ are communicated back to a {\em Central Processing Unit} (CPU). This algorithm attains about 65\% efficiency overall, normalized to the Fast Fourier Transform (FFT). At about one million correlations per second over data segments of 16 s duration $(N=2^{16}$ samples), better than real-time analysis is achieved on a cluster of about a dozen GPUs. We demonstrate its application to the capture of high frequency hardware LIGO injections. This algorithm serves as a starting point for deep all-sky searches in both archive data and real-time analysis in current observational runs.Comment: to appear in Progress of Theoretical and Experimental Physics (PTEP), 16p., 9 fi