On the origin of exponential growth in induced earthquakes in Groningen

The Groningen gas field shows exponential growth in earthquakes event counts around a magnitude M1 with a doubling time of 6-9 years since 2001. This behavior is identified with dimensionless curvature in land subsidence, which has been evolving at a constant rate over the last few decades {essentially uncorrelated to gas production.} We demonstrate our mechanism by a tabletop crack formation experiment. The observed skewed distribution of event magnitudes is matched by that of maxima of event clusters with a normal distribution. It predicts about one event $<$\,M5 per day in 2025, pointing to increasing stress to human living conditions.Comment: 12 pages, 7 figures, to appear in Earthquakes and Structure

Numerical Integration of Nonlinear Wave Equations for General Relativity

A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of one-dimensional nonlinear waves. The complete freedom in space-time slicing in the present formulation is exploited to compute in the Gowdy line-element. Second-order convergence is found by direct comparison of the results with either analytical solutions for polarized waves, or solutions obtained from Gowdy's reduced wave equations for the more general unpolarized waves. Some directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps

Uniqueness in MHD in divergence form: right nullvectors and well-posedness

Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfven waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy

Gravitational wave frequencies and energies in hypernovae

A torus develops a state of suspended accretion against a magnetic wall around a rapidly rotating black hole formed in core-collapse hypernovae. It hereby emits about 10% of the black hole spin-energy in gravitational radiation from a finite number of multipole mass moments. We quantify the relation between the frequency of quadrupole gravitational radiation and the energy output $E_w$ in torus winds by $f_{gw}\simeq 470{Hz}(E_w/4\times 10^{52}{erg})^{1/2}(7M_\odot/M)^{3/2}$, where $M$ denotes the mass of the black hole. We propose that $E_w$ irradiates the remnant stellar envelope from within. We identify $E_w$ with energies $\sim 10^{52}$ erg inferred from X-ray observations on matter injecta; and the poloidal curvature in the magnetic wall with the horizon opening angle in baryon poor outflows that power true GRB energies of $E_\gamma\simeq 3\times 10^{51}$ erg.Comment: To appear in AP

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.