Numerical evolution of matter in dynamical axisymmetric black hole spacetimes. I. Methods and tests

We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses the characteristic information of the general relativistic hydrodynamic equations to build up a linearized Riemann solver. The spacetime is evolved with an axisymmetric ADM code designed to evolve a wormhole in full general relativity. We discuss the numerical and algorithmic issues related to the effective coupling of the hydrodynamical and spacetime pieces of the code, as well as the numerical methods and gauge conditions we use to evolve such spacetimes. The code has been put through a series of tests that verify that it functions correctly. Particularly, we develop and describe a new set of testbed calculations and techniques designed to handle dynamically sliced, self-gravitating matter flows on black holes, and subject the code to these tests. We make some studies of the spherical and axisymmetric accretion onto a dynamic black hole, the fully dynamical evolution of imploding shells of dust with a black hole, the evolution of matter in rotating spacetimes, the gravitational radiation induced by the presence of the matter fields and the behavior of apparent horizons through the evolution.Comment: 42 pages, 20 figures, submitted to Phys Rev

Vacuum field energy and spontaneous emission in anomalously dispersive cavities

Anomalously dispersive cavities, particularly white light cavities, may have larger bandwidth to finesse ratios than their normally dispersive counterparts. Partly for this reason, their use has been proposed for use in LIGO-like gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze the quantum noise associated with anomalously dispersive cavity modes. The vacuum field energy associated with a particular cavity mode is proportional to the cavity-averaged group velocity of that mode. For anomalously dispersive cavities with group index values between 1 and 0, this means that the total vacuum field energy associated with a particular cavity mode must exceed $\hbar \omega/2$. For white light cavities in particular, the group index approaches zero and the vacuum field energy of a particular spatial mode may be significantly enhanced. We predict enhanced spontaneous emission rates into anomalously dispersive cavity modes and broadened laser linewidths when the linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure

Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre on the real plane, we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr. 77 (2000), 49--75). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.Comment: 22 pages, 6 figure

Influence of self-gravity on the runaway instability of black hole-torus systems

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black hole mass ratio and angular momentum distribution orbiting in equilibrium around a non-rotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical timescales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical timescales.Comment: To appear on Phys.Rev.Let

The Shapiro Conjecture: Prompt or Delayed Collapse in the head-on collision of neutron stars?

We study the question of prompt vs. delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. We discuss the insight provided by Shapiro's conjecture and its limitation. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations in the Einstein theory with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out in our study.Comment: 4 pages, 7 figure

A Comment on Continuous Spin Representations of the Poincare Group and Perturbative String Theory

We make a simple observation that the massless continuous spin representations of the Poincar\'e group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models

The effect of Wilson line moduli on CP-violation by soft supersymmetry breaking terms

The CP-violating phases in the soft supersymmetry-breaking sector in orbifold compactifications with a continuous Wilson line are investigated. In this case the modular symmetry is the Siegel modular group $Sp(4,Z)$ of genus two. In particular, we study the case that the hidden sector non-perturbative superpotential is determined by the Igusa cusp form ${\cal C}_{12}$ of modular weight 12. The effect of large non-perturbative corrections to the dilaton K\"ahler potential on the resulting CP-violating phases is also investigated.Comment: LaTeX file, 12 pages plus 7 figures, to appear in Phys.Lett.

Cosmology beyond BAO from the 3D distribution of the Lyman-α forest

We propose a new method for fitting the full-shape of the Lyman-α (Ly α) forest 3D correlation function in order to measure the Alcock-Paczynski (AP) effect. Our method preserves the robustness of baryon acoustic oscillations (BAO) analyses, while also providing extra cosmological information from a broader range of scales. We compute idealized forecasts for the Dark Energy Spectroscopic Instrument (DESI) using the Ly α autocorrelation and its cross-correlation with quasars, and show how this type of analysis improves cosmological constraints. The DESI Ly α BAO analysis is expected to measure H(zeff)rd and DM(zeff)/rd with a precision of ∼0.9 per cent⁠, where H is the Hubble parameter, rd is the comoving BAO scale, DM is the comoving angular diameter distance, and the effective redshift of the measurement is zeff ≃ 2.3. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of ∼0.5−0.6 per cent on each of H(zeff)rd and DM(zeff)/rd. Furthermore, we show that a joint full-shape analysis of the Ly α auto and cross-correlation with quasars can measure the linear growth rate times the amplitude of matter fluctuations in spheres of 8 h−1Mpc, fσ8(zeff). Such an analysis could provide the first ever measurement of fσ8(zeff) at redshift zeff > 2. By combining this with the quasar autocorrelation in a joint analysis of the three high-redshift two-point correlation functions, we show that DESI could be able to measure fσ8(zeff ≃ 2.3) with a precision of 5−12 per cent⁠, depending on the smallest scale fitted