The Experts below are selected from a list of 255 Experts worldwide ranked by ideXlab platform
James Owen Weatherall - One of the best experts on this subject based on the ideXlab platform.
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On Gravitational Energy in Newtonian Theories
Foundations of Physics, 2018Co-Authors: Neil Dewar, James Owen WeatherallAbstract:There are well-known problems associated with the idea of (local) Gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian Gravitation, and particularly geometrized Newtonian Gravitation (i.e., Newton-Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian Gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian Gravitation.
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Categories and the Foundations of Classical Field Theories
arXiv: History and Philosophy of Physics, 2015Co-Authors: James Owen WeatherallAbstract:I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian Gravitation, general relativity, and Yang-Mills theories.
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are Newtonian Gravitation and geometrized Newtonian Gravitation theoretically equivalent
arXiv: History and Philosophy of Physics, 2014Co-Authors: James Owen WeatherallAbstract:I argue that a criterion of theoretical equivalence due to Clark Glymour [Nous 11(3), 227-251 (1977)] does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is "yes", at least on one natural understanding of Newtonian Gravitation.
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What is a Singularity in Geometrized Newtonian Gravitation
arXiv: Classical Physics, 2013Co-Authors: James Owen WeatherallAbstract:I discuss singular spacetimes in the context of the geometrized formulation of Newtonian Gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian Gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.
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The motion of a body in Newtonian theories
Journal of Mathematical Physics, 2011Co-Authors: James Owen WeatherallAbstract:A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian Gravitation (often called Newton-Cartan theory). It follows that in Newtonian Gravitation, as in GR, inertial motion can be derived from other central principles of the theory.
José P. S. Lemos - One of the best experts on this subject based on the ideXlab platform.
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Newtonian wormholes
General Relativity and Gravitation, 2014Co-Authors: José P. S. Lemos, Paulo LuzAbstract:A wormhole solution in Newtonian Gravitation, enhanced through an equation relating the Ricci scalar to the mass density, is presented. The wormhole inhabits a spherically symmetric curved space, with one throat and two asymptotically flat regions. Particle dynamics in this geometry is studied, and the three distinct dynamical radii, namely, the geodesic, circumferential, and curvature radii, appear naturally in the study of circular motion. Generic motion is also analyzed. A limiting case, although inconclusive, suggests the possibility of having a Newtonian black hole in a region of finite (nonzero) size.
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electrically charged fluids with pressure in Newtonian Gravitation and general relativity in d spacetime dimensions theorems and results for weyl type systems
Physical Review D, 2009Co-Authors: José P. S. Lemos, Vilson T ZanchinAbstract:Previous theorems concerning Weyl type systems, including Majumdar-Papapetrou systems, are generalized in two ways, namely, we take these theorems into d spacetime dimensions (d{>=}4), and we also consider the very interesting Weyl-Guilfoyle systems, i.e., general relativistic charged fluids with nonzero pressure. In particular within the Newton-Coulomb theory of charged gravitating fluids, a theorem by Bonnor (1980) in three-dimensional space is generalized to arbitrary (d-1)>3 space dimensions. Then, we prove a new theorem for charged gravitating fluid systems in which we find the condition that the charge density and the matter density should obey. Within general relativity coupled to charged dust fluids, a theorem by De and Raychaudhuri (1968) in four-dimensional spacetime is rendered into arbitrary d>4 dimensions. Then a theorem, new in d=4 and d>4 dimensions, for Weyl-Guilfoyle systems, is stated and proved, in which we find the condition that the charge density, the matter density, the pressure, and the electromagnetic energy density should obey. This theorem comprises, in particular cases, a theorem by Gautreau and Hoffman (1973) and results in four dimensions by Guilfoyle (1999). Upon connection of an interior charged solution to an exterior Tangherlini solution (i.e., a Reissner-Nordstroem solution in d dimensions), one is able to givemore » a general definition for Gravitational mass for this kind of relativistic systems and find a mass relation with several quantities of the interior solution. It is also shown that for sources of finite extent the mass is identical to the Tolman mass.« less
Vilson T Zanchin - One of the best experts on this subject based on the ideXlab platform.
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electrically charged fluids with pressure in Newtonian Gravitation and general relativity in d spacetime dimensions theorems and results for weyl type systems
Physical Review D, 2009Co-Authors: José P. S. Lemos, Vilson T ZanchinAbstract:Previous theorems concerning Weyl type systems, including Majumdar-Papapetrou systems, are generalized in two ways, namely, we take these theorems into d spacetime dimensions (d{>=}4), and we also consider the very interesting Weyl-Guilfoyle systems, i.e., general relativistic charged fluids with nonzero pressure. In particular within the Newton-Coulomb theory of charged gravitating fluids, a theorem by Bonnor (1980) in three-dimensional space is generalized to arbitrary (d-1)>3 space dimensions. Then, we prove a new theorem for charged gravitating fluid systems in which we find the condition that the charge density and the matter density should obey. Within general relativity coupled to charged dust fluids, a theorem by De and Raychaudhuri (1968) in four-dimensional spacetime is rendered into arbitrary d>4 dimensions. Then a theorem, new in d=4 and d>4 dimensions, for Weyl-Guilfoyle systems, is stated and proved, in which we find the condition that the charge density, the matter density, the pressure, and the electromagnetic energy density should obey. This theorem comprises, in particular cases, a theorem by Gautreau and Hoffman (1973) and results in four dimensions by Guilfoyle (1999). Upon connection of an interior charged solution to an exterior Tangherlini solution (i.e., a Reissner-Nordstroem solution in d dimensions), one is able to givemore » a general definition for Gravitational mass for this kind of relativistic systems and find a mass relation with several quantities of the interior solution. It is also shown that for sources of finite extent the mass is identical to the Tolman mass.« less
Matthew M Roberts - One of the best experts on this subject based on the ideXlab platform.
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curved non relativistic spacetimes Newtonian Gravitation and massive matter
Journal of Mathematical Physics, 2015Co-Authors: Michael Geracie, Kartik Prabhu, Matthew M RobertsAbstract:There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print arXiv:1503.02680], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
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curved non relativistic spacetimes Newtonian Gravitation and massive matter
arXiv: High Energy Physics - Theory, 2015Co-Authors: Michael Geracie, Kartik Prabhu, Matthew M RobertsAbstract:There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativisitic symmetries which supports massive matter fields. In particular, one can not impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [arXiv:1503.02680] we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Stuart L Shapiro - One of the best experts on this subject based on the ideXlab platform.
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ONE-ARMED SPIRAL INSTABILITY IN DIFFERENTIALLY ROTATING STARS
The Astrophysical Journal, 2003Co-Authors: Motoyuki Saijo, Thomas W. Baumgarte, Stuart L ShapiroAbstract:We investigate the dynamical instability of the one-armed spiral m = 1 mode in differentially rotating stars by means of 3 + 1 hydrodynamical simulations in Newtonian Gravitation. We find that both a soft equation of state and a high degree of differential rotation in the equilibrium star are necessary to excite a dynamical m = 1 mode as the dominant instability at small values of the ratio of rotational kinetic to Gravitational potential energy, T/|W|. We find that this spiral mode propagates outward from its point of origin near the maximum density at the center to the surface over several central orbital periods. An unstable m = 1 mode triggers a secondary m = 2 bar mode of smaller amplitude, and the bar mode can excite Gravitational waves. As the spiral mode propagates to the surface it weakens, simultaneously damping the emitted Gravitational wave signal. This behavior is in contrast to waves triggered by a dynamical m = 2 bar instability, which persist for many rotation periods and decay only after a radiation reaction-damping timescale.