The metaphysics of Machian frame-dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding

Estimates of the total gravitation radiation in the head-on black hole collision

We report on calculations of the total gravitational energy radiated in the head-on black hole collision, where we use the geometry of the Robinson-Trautman metrics.Comment: 10 pages, 2 figures, LaTeX2

Vacuum effects in an asymptotically uniformly accelerated frame with a constant magnetic field

In the present article we solve the Dirac-Pauli and Klein Gordon equations in an asymptotically uniformly accelerated frame when a constant magnetic field is present. We compute, via the Bogoliubov coefficients, the density of scalar and spin 1/2 particles created. We discuss the role played by the magnetic field and the thermal character of the spectrum.Comment: 17 pages. RevTe

Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons

We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface Sigma of constant negative or zero curvature. When horizons exist, the spacetimes are black holes with an asymptotically locally anti-de Sitter infinity, but the infinity topology differs from that in the asymptotically Minkowski case, and the horizon topology is not S^2. Maximal analytic extensions of the solutions are given. The local Hawking temperature is found. When Sigma is closed, we derive the first law of thermodynamics using a Brown-York type quasilocal energy at a finite boundary, and we identify the entropy as one quarter of the horizon area, independent of the horizon topology. The heat capacities with constant charge and constant electrostatic potential are shown to be positive definite. With the boundary pushed to infinity, we consider thermodynamical ensembles that fix the renormalized temperature and either the charge or the electrostatic potential at infinity. Both ensembles turn out to be thermodynamically stable, and dominated by a unique classical solution.Comment: 25 pages, REVTeX v3.1, contains 5 LaTeX figures. (Typos corrected, references and minor comments added. To be published in Phys. Rev. D.

Head-on collisions of black holes: the particle limit

We compute gravitational radiation waveforms, spectra and energies for a point particle of mass $m_0$ falling from rest at radius $r_0$ into a Schwarzschild hole of mass $M$. This radiation is found to lowest order in $(m_0/M)$ with the use of a Laplace transform. In contrast with numerical relativity results for head-on collisions of equal-mass holes, the radiated energy is found not to be a monotonically increasing function of initial separation; there is a local radiated-energy maximum at $r_0\approx4.5M$. The present results, along with results for infall from infinity, provide a complete catalog of waveforms and spectra for particle infall. We give a representative sample from that catalog and an interesting observation: Unlike the simple spectra for other head-on collisions (either of particle and hole, or of equal mass holes) the spectra for $\infty>r_0>\sim5M$ show a series of evenly spaced bumps. A simple explanation is given for this. Lastly, our energy vs. $r_0$ results are compared with approximation methods used elsewhere, for small and for large initial separation.Comment: 15 pages, REVTeX, 25 figure

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

On the energy of homogeneous cosmologies

An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely those with a tetrad description--for all 9 Bianchi types. Our energy is given by the value of the Hamiltonian with homogeneous boundary conditions; this value vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein's general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein's theory as an important special case, the energy for all class B models is, contrary to expectation, negative.Comment: 11 pages, reformated with minor change

Spin, gravity, and inertia

The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the non-relativistic limit of the theory. The new term describing the specific spin (gravitational moment) interaction effect is recovered in the Hamiltonian. The comparison of the true gravitational coupling with the purely inertial case demonstrates that the spin relativistic effects do not violate the equivalence principle for the Dirac fermions.Comment: Revtex, 12 pages, no figures, accepted in Phys. Rev. Let