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In a recent paper [D. Philipp, V. Perlick, D. Puetzfeld, E. Hackmann, and C. L\"ammerzahl, Phys. Rev. D 95, 104037 (2017)], a definition of a general-relativistic geoid, restricted to stationary spacetimes, was presented in terms of "isochronometric surfaces". In this note, we explicate how this definition is just a special, highly restrictive case of our earlier formulation of the general-relativistic geoid using quasilocal frames, which is valid for generic, non-stationary spacetimes [M. Oltean, R.J. Epp, P.L. McGrath, and R.B. Mann, Class. Quantum Grav. 33, 105001 (2016)]. Moreover, like the isochronometric surface geoid, we show how our "geoid quasilocal frame" (GQF) can also be defined, simply and operationally, in terms of redshift measurements., Comment: 6 pages, 1 figure

We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilocal frame -- that is, a choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume. We study the geometric properties of these geoid quasilocal frames, and construct solutions for them in some simple spacetimes. We then compare these results -- focusing on the computationally tractable scenario of a non-rotating body with a quadrupole perturbation -- against their counterparts in Newtonian gravity (the setting for current applications of the geoid), and we compute general-relativistic corrections to some measurable geometric quantities., Comment: 24 pages, 8 figures; v2: reference added; v3: introduction clarified, reference added

We determine the gyromagnetic factor of the positronium ion, a three-body system consisting of two electrons and a positron, including first relativistic corrections. We find that the g-factor is modified by a term -0.51(1)alpha^2, exceeding 15 times the alpha^2 correction for a free electron. We compare this effect with analogous results found previously in atomic positronium and in hydrogen-like ions., Comment: 7 pages

In this thesis, I examine in detail the properties of rigid quasilocal frames (RQF), which have been proposed as a geometrically natural way to define spatially extended reference frames in general relativity. I also explore their usefulness, in particular, as a tool for constructing completely general conservation laws that do not rely on the presence of spacetime symmetries and include both matter and gravitational contributions without the need for any ad hoc structures such as pseudotensors. In doing so, I show how the RQF approach affords a deeper understanding of the nature of gravitational fluxes via the equivalence principle. Finally, I apply the RQF formalism to explore Ehrenfest's rotating disk paradox, a generalization of Archimedes' law to curved spacetime, tidal interactions for Earth's and Jupiter's moons, and more., Comment: 152 pages, 7 figures, University of Waterloo PhD thesis, 2014

In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress-energy-momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear and angular momentum. In this paper we derive the form of these laws in a general first post-Newtonian (1PN) approximation, and then apply these approximate laws to the problem of gravitational tidal interactions. We obtain formulas for tidal heating and tidal torque that agree with the literature, but without resorting to the use of pseudotensors. We describe the physical mechanism of these tidal interactions not in the traditional terms of a Newtonian gravitational force, but in terms of a much simpler and universal mechanism that is an exact, quasilocal manifestation of the equivalence principle in general relativity. As concrete examples, we look at the tidal heating of Jupiter's moon Io and angular momentum transfer in the Earth-Moon system that causes a gradual spin-down of the Earth and recession of the Moon. In both examples we find agreement with observation., Comment: 22 pages, 2 figures

The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion. An RQF is defined as a two-parameter family of timelike worldlines comprising the boundary (topologically R x S^2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines be expansion- and shear-free. In other words, the size and shape of the system do not change. In previous work, such systems in Minkowski space were shown to admit precisely the same six degrees of freedom of rigid body motion that we are familiar with in Newtonian space-time, without any constraints, circumventing a century-old theorem due to Herglotz and Noether. This is a consequence of the fact that a two-sphere of any shape always admits precisely six conformal Killing vector fields, which generate an action of the Lorentz group on the sphere. Here we review the previous work in flat spacetime and extend it in three directions: (1) Using a Fermi normal coordinates approach, we explicitly construct, to the first few orders in powers of areal radius, the general solution to the RQF rigidity equations in a generic curved spacetime, and show that the resulting RQFs possess exactly the same six motional degrees of freedom as in flat spacetime; (2) We discuss how RQFs provide a natural context in which to understand the flow of energy, momentum and angular momentum into and out of a system; in particular, we derive a simple, exact expression for the flux of gravitational energy (a gravitational analogue of the Poynting vector) in terms of operationally-defined geometrical quantities on the boundary; (3) We use this new gravitational (or "geometrical") energy flux to resolve another apparent paradox, this one involving electromagnetism in flat spacetime, which we discovered in the course of this work., Comment: 21 pages

We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features. Our approach uses the Brown and York quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of gravitational energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of gravitational energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes' law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner-Nordstrom black hole., Comment: 24 pages, 3 figures

We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects. We construct a general quasi}local conservation law based on the Brown and York total (matter plus gravity) stress-energy-momentum tensor (characterized by energy and momentum per unit area), and argue that it does properly account for gravitational effects. As a simple example of the explanatory power of this quasilocal approach, consider that, when we accelerate toward a freely-floating massive object, the kinetic energy of that object increases (relative to our frame). But how, exactly, does the object acquire this increasing kinetic energy? Using the energy form of our quasilocal conservation law, we can see precisely the actual mechanism by which the kinetic energy increases: It is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic Poynting flux, and involves the general relativistic effect of frame dragging caused by the object's motion relative to us., Comment: 20 pages, 1 figure

We extend the recent D=5 results of Dias, Horowitz and Santos by finding asymptotically AdS rotating black hole and boson star solutions with scalar hair in arbitrary odd spacetime dimension. Both the black holes and the boson stars are invariant under a single Killing vector field which co-rotates with the scalar field and, in the black hole case, is tangent to the generator of the horizon. Furthermore, we explicitly construct boson star and small black hole ($r_+ \ll \ell$) solutions perturbatively assuming a small amplitude for the scalar field, resulting in solutions valid for low energies and angular momenta. We find that just as in D=5, the angular momentum is primarily carried by the scalar field in $D>5$, whereas unlike D=5 the energy is also primarily carried by the scalar field in $D>5$; the thermodynamics in D=5 are governed by both the black hole and scalar field whereas in $D>5$ they are governed primarily by the scalar field alone. We focus on cataloguing these solutions for the spacetime dimensions of interest in string theory, namely $D=5,7,9,11$., Comment: 28 pages, 1 table, 2 Appendices. v2: minor typos corrected, references added, small discussion added to section 4. v3: typos corrected, thermodynamic discussion expanded, accepted in PRD

We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering the questions what is in motion (a rigid two-dimensional system boundary), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions has only three degrees of freedom instead of the six we are familiar with from Newtonian mechanics. We argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers) - with precisely the expected three translational and three rotational degrees of freedom - provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume., Comment: 10 pages (two column), 24 pages (preprint), 1 figure

This drill (see Figure 1) is the primary sample acquisition element of the Mars Science Laboratory (MSL) that collects powdered samples from various types of rock (from clays to massive basalts) at depths up to 50 mm below the surface. A rotary-percussive sample acquisition device was developed with an emphasis on toughness and robustness to handle the harsh environment on Mars. It is the first rover-based sample acquisition device to be flight-qualified (see Figure 2). This drill features an autonomous tool change-out on a mobile robot, and novel voice-coil-based percussion. The drill comprises seven subelements. Starting at the end of the drill, there is a bit assembly that cuts the rock and collects the sample. Supporting the bit is a subassembly comprising a chuck mechanism to engage and release the new and worn bits, respectively, and a spindle mechanism to rotate the bit. Just aft of that is a percussion mechanism, which generates hammer blows to break the rock and create the dynamic environment used to flow the powdered sample. These components are mounted to a translation mechanism, which provides linear motion and senses weight-on-bit with a force sensor. There is a passive-contact sensor/stabilizer mechanism that secures the drill fs position on the rock surface, and flex harness management hardware to provide the power and signals to the translating components. The drill housing serves as the primary structure of the turret, to which the additional tools and instruments are attached. The drill bit assembly (DBA) is a passive device that is rotated and hammered in order to cut rock (i.e. science targets) and collect the cuttings (powder) in a sample chamber until ready for transfer to the CHIMRA (Collection and Handling for Interior Martian Rock Analysis). The DBA consists of a 5/8-in. (.1.6- cm) commercial hammer drill bit whose shank has been turned down and machined with deep flutes designed for aggressive cutting removal. Surrounding the shank of the bit is a thick-walled maraging steel collection tube allowing the powdered sample to be augured up the hole into the sample chamber. For robustness, the wall thickness of the DBA was maximized while still ensuring effective sample collection. There are four recesses in the bit tube that are used to retain the fresh bits in their bit box. The rotating bit is supported by a back-to-back duplex bearing pair within a housing that is connected to the outer DBA housing by two titanium diaphragms. The only bearings on the drill in the sample flow are protected by a spring-energized seal, and an integrated shield that diverts the ingested powdered sample from the moving interface. The DBA diaphragms provide radial constraint of the rotating bit and form the sample chambers. Between the diaphragms there is a sample exit tube from which the sample is transferred to the CHIMRA. To ensure that the entire collected sample is retained, no matter the orientation of the drill with respect to gravity during sampling, the pass-through from the forward to the aft chamber resides opposite to the exit tube.