Showing papers on "Introduction to the mathematics of general relativity published in 2016"
TL;DR: In this article, the authors studied compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John") and theories involving the double-dual of the Riemann tensor (Paul).
Abstract: Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the $\Lambda$CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John") and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.
91 citations
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11 Feb 2016TL;DR: The history of attempts to algebraically extend General Relativity is reviewed in this paper, where the philosophy of the pseudo-complex extension is introduced and the basic assumptions, including for example a generalized variational principle and how to map to real observables.
Abstract: The history of of attempts to algebraically extend General Relativity is reviewed. The philosophy of the pseudo-complex extension is introduced and the basic assumptions, including for example a generalized variational principle and how to map to real observables. The appearance of a minimal length and the advantages of the pseudo-complex theory are discussed.
71 citations
TL;DR: The first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system was provided by as discussed by the authors.
Abstract: The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group.
54 citations
TL;DR: An alternative approach to the theory of General Relativity (GR) is reviewed in this article, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions.
Abstract: An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to T i k . Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation R i k = 0 as the field equation of gravitation plus inertia in the very presence of matter.
51 citations
TL;DR: In this article, a scaling method was proposed to identify dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in a modified Horndeski action.
Abstract: The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new and surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.
41 citations
01 Jan 2016
TL;DR: The mass and motion in general relativity is universally compatible with any devices to read as mentioned in this paper and it is available in our book collection and an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading mass and motion in general relativity. Maybe you have knowledge that, people have search hundreds times for their chosen readings like this mass and motion in general relativity, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their laptop. mass and motion in general relativity is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the mass and motion in general relativity is universally compatible with any devices to read.
40 citations
TL;DR: In this paper, the functional setting customarily adopted in General Relativity (GR) is discussed and basic physical implications of nonlocal point transformations (NLPTs) are considered, which are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems.
Abstract: A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and the diagonalization of nondiagonal metric tensors.
20 citations
TL;DR: In this article, the authors verify the consistency of the Godel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical ChernSimons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field.
Abstract: We verify the consistency of the Godel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
17 citations
TL;DR: The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail in this paper, where the action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born-infeld constant λ goes to infinity.
16 citations
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TL;DR: In this paper, a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations was developed for the case of an arbitrary curved spacetime and the nonrelativistic (Newtonian) limit.
Abstract: We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of weak gravitational fields in a static or expanding background, and the nonrelativistic (Newtonian) limit. The Klein-Gordon-Maxwell-Einstein equations govern the evolution of a complex scalar field, possibly describing self-gravitating Bose-Einstein condensates, coupled to an electromagnetic field. They may find applications in the context of dark matter, boson stars, and neutron stars with a superfluid core.
14 citations
TL;DR: In this paper, a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance was established, and it was shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations.
Abstract: We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.
TL;DR: In this paper, the Levi-Civita Lagrangian points were used as observables to test general relativity and effective field theories of gravity in the solar system, and the resulting nonlinear ordinary differential equations for the motion of planets and satellites were solved for the Earth's orbit about the Sun, written down in detail for the Sun-Earth-Moon system and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies.
Abstract: Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder-Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of celestial bodies, showing in detail under which conditions the effects of internal structure and finite extension get cancelled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth's orbit about the Sun, written down in detail for the Sun-Earth-Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies.
07 Jan 2016
TL;DR: In this paper, a non-relativistic version of Newton-Cartan gravity was proposed. But it is invariant under general coordinate transformations and cannot move faster than the speed of light.
Abstract: This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinate systems. While point i) is by definition the necessary difference between relativistic and non-relativistic theories, one might wonder if there exists a version of Newtonian gravity that allows point ii), a theory of non-relativistic gravity that is invariant under general coordinate transformations. Indeed, such a theory was constructed a few years after Einstein's theory of general relativity and it is called Newton-Cartan gravity. This theory finds applications e.g. in models of condensed matter physics that describe systems which exhibit non-relativistic symmetries. It is also used in generalizations of the holographic principle to non-relativistic settings. With these motivations in mind we study Newton-Cartan structures in this thesis. We present a non-relativistic limiting procedure that enables us to get Newton-Cartan gravity from Einstein's relativistic theory. In addition we focus our study on supersymmetric extensions of Newton-Cartan gravity. We study non-relativistic versions of cosmological and conformal supergravity in three dimensions. We also look at off-shell formulations and a non-relativistic version of the superconformal tensor calculus which we call Schroedinger tensor calculus.
01 Jan 2016
TL;DR: The special relativity from einstein to strings is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you for downloading special relativity from einstein to strings. Maybe you have knowledge that, people have look hundreds times for their favorite readings like this special relativity from einstein to strings, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they are facing with some malicious virus inside their desktop computer. special relativity from einstein to strings is available in our digital library an online access to it is set as public so you can download it instantly. Our digital library spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the special relativity from einstein to strings is universally compatible with any devices to read.
01 Jan 2016
TL;DR: In this article, some properties of generalized quasi-Einstein manifold spacetimes have been studied and two non-trivial examples have been constructed to prove the existence of generalized quasi-einstein manifolds.
Abstract: Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss $G(QE)_{4}$ with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.
TL;DR: Advanced Relativity (AR) as discussed by the authors is the model which fully integrates matter and consciousness by applying Hilbert spaces, where space is measured by roads and time is measured with clocks and is characterized by a variable energy density which gives origin to energy, mass and gravity from the micro to the macro scale.
Abstract: Advanced Relativity (AR) is the model which fully integrates matter and consciousness by applying Hilbert spaces. Advancer Relativity reviews the key concepts of Einstein’s Relativity, namely, space and time. In AR, space is what we measure with roads and time is what we measure with clocks. Space is not empty and deprived of physical properties; it is characterized by a variable energy density which gives origin to energy, mass and gravity from the micro to the macro scale. Time is merely numerical order of material changes, i.e. motion running in space. AR describes all phenomena of special relativity (SR) and general relativity (GR) and opens new perspectives in cosmology and astronomy, namely, no signal can move in time as time is merely numerical order of a given signal moving in space.
01 Jan 2016
TL;DR: In this article, a systematic review of the theoretical framework, major predictions, experimental evidences of general relativity and its implications to other branches of science is presented, and the review concludes that the Newtonian law of gravity is built upon the Keplers laws and has stood hundreds of years' test by scientific research and engineering practice.
Abstract: This article gives a systematic review of the theoretical framework, major predictions, experimental evidences of general relativity and its implications to other branches of science. It has been pointed out that, other than the (0,0) component of Einstein’s tensor field equation which reduces to the Newtonian law of gravitation under linear approximation, all other components either lead to divergence, or are in conflict with the fundamental postulation of relativity that no speed should exceed the speed of light, or defies physical interpretation. The review gives a detailed analysis of the three classical evidences of general relativity and has shown that none of these experimental evidences can stand scrutiny. The article also analyzed the two recent experiments (BICEP2 and LIGO) that claimed to have found experimental evidences of gravitational wave and black hole, and demonstrated their fallacies. It has been pointed out that the principle of relativity demands that any viable theory must have translational as well as rotational relativity, which requires general relativity to have a rotational transformation that can transform the Schwarzschild metric into the Kerr metric and vice versa. Calculations show that a general rotational transformation is in conflict with one of the fundamental postulations of relativity—no speed should exceed the speed of light, i.e., general relativity violates the principle of relativity. The article also gives a thorough analysis of one of the most important concept of general relativity—gravity comes from the curvature of space time, and gravity warps the space time. It has been pointed out that the curving of a geodesic is merely the bending of the trajectory of an object moving in gravitational field, which is not the curving of the space time itself. Moreover, the field equation describes the shape of equipotential, the curving of which is not the curving of space time either. The measure of curvature of space time is the Riemann curvature scalar R. Calculations show that the Riemann curvature and Ricii tensor of both the Schwarzschild metric and the Kerr metric—the only two known analytical solutions to Einstein’s field equation, vanish, which means that the space time is flat. The concept that gravity comes from the curvature of space time and gravity warps the space time is invalid. The review concludes that the Newtonian law of gravity is built upon the Keplers laws that represent enormous results of observational astronomy and has stood hundreds of years’ test by scientific research and engineering practice. It is still been checked every day by science and engineering, and has never failed the test. On the other hand, Einstein’s general relativity has a multitude of unsolvable inconsistencies in its fundamental postulations, theoretical framework, experimental tests, and it is completely powerless in practical applications. It is therefore incorrect to say that the Newtonian law of gravitation is only
TL;DR: In this article, the energy concept in the case of a continuum or a system of fields is reviewed, and the definitions of the canonical and Hilbert energymomentum tensors from a Lagrangian through the principle of stationary action in a general spacetime.
Abstract: We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame, and that, however, they can be given a rigorous meaning. Then we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in a general spacetime. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially of the fields.
01 Jan 2016
TL;DR: The geometry of spacetime as mentioned in this paper is an introduction to special and general relativity, but it is not suitable for reading in a classroom environment, as it is unsuitable for children's reading.
Abstract: Thank you very much for reading geometry of spacetime an introduction to special and general relativity. Maybe you have knowledge that, people have look hundreds times for their chosen readings like this geometry of spacetime an introduction to special and general relativity, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some harmful bugs inside their computer.
TL;DR: In this article, a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, Eotvos experiment, Newcomb's improved observation of the Newcomb-Newcomb-Eisenstein divergence, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) is given.
Abstract: This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eotvos experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; A...
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TL;DR: In this article, the authors recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discussed their properties, illustrated with simple examples, in the context of general relativity.
Abstract: We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples.
TL;DR: In this article, the concept of timespace manifold is introduced and the fundamental concepts of global relativity theory with respect to this general situation are defined, including affine connection, parallel transport, curvature tensor, and Einstein equation.
Abstract: In this paper we introduce the concept of timespace manifold. We study the affine connection, parallel transport, curvature tensor, and Einstein equation, respectively. In the case homogeneous, a time-space manifold with such tangent spaces which have a certain fixed time-space structure. We redefine the fundamental concepts of global relativity theory with respect to this general situation.
TL;DR: In this paper, two kinds of conserved currents are derived in de Sitter (dS) special relativity (SR), and an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current.
Abstract: In de Sitter (dS) special relativity (SR), two kinds of conserved currents are derived. The first kind is a 5-dimensional dS-covariant angular momentum (AM) current, which unites the energy-momentum (EM) and 4d AM current in an inertial-type coordinate system. The second kind is a dS-invariant AM current, which can be generalized to a conserved current for the coupling system of the matter field and gravitational field in dS gravity. Moreover, an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current. All the above results are compared to the ordinary SR with Lorentz invariance.
01 Jan 2016
TL;DR: Einstein this article showed that time is no more than a relative measure, namely that whenever we have to do with speed equal to or close to that of light, time is not a variable absolute and independent of the reference system adopted, but depends on the variable position.
Abstract: In 1905 Albert Einstein, in a paper entitled “On the Electrodynamics of Moving Bodies”, as a solution to the disagreement between classical mechanics and the results of the Michelson's experiment, who showed the invariance of the speed of light in vacuum measured in different inertial reference systems, developed the theory of special relativity. In this essay Einstein expounded a theory that, instead of introducing a privileged system, required the revision of the concepts of space and time of classical physics. Combining the principle of Galilean relativity, according to which the laws of physics are invariant in all inertial reference systems, with the physics of electromagnetism, according to which the speed of light in a vacuum is constant, Einstein concluded that time is no more than a relative measure, namely that whenever we have to do with speed equal to or close to that of light, time is no longer a variable absolute and independent of the reference system adopted, but depends on the variable position. This is what Einstein shows through the critical examination of the concept of simultaneity. The abandonment of the traditional conception of space and time based on the idea of a spatial continuum flowing through a temporal continuum coherently leads to the assumption of a space-time continuum (chronotope) in which distances and time intervals vary with the changing the reference system, and together vary, of course, all other sizes to those connected (speed, acceleration, mass).
TL;DR: In this article, the authors studied the dynamics of self-gravitating fluids bounded by spherically symmetric surface in the background of f (G) gravity and found that their results are consistent with general relativity for constant f (g) model (regular distribution of dark energy in the universe).
Abstract: We study the dynamics of self-gravitating fluids bounded by spherically symmetric surface in the background of f (G) gravity. The link between physical and geometrical variables, such as anisotropy, density inhomogeneity, dissipation, the Weyl tensor, expansion scalar, shear tensor and modified (Gauss-Bonnet) curvature terms, is given. We also investigate some particular fluid models according to various dynamical conditions. It is found that our results are consistent with general relativity for constant f (G) model (regular distribution of dark energy in the universe). Any other choice of the model leads to irregular distribution of dark energy and deviates from general relativity.
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Abstract: In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance.'. The dichotomy can be resolved by introducing a scalar field/potential algebraically related to the Ricci tensor for which the corresponding metric is free of additional singularities. Hence, although a fundamentally nonlinear theory, the scalar field/potential provides an analytic framework for interacting particles; described by linear superposition. The stress tensor for the scalar field includes both the sources of and the energy-momentum for the gravitational field, and has zero covariant and ordinary divergence. Hence, the energy-momentum for the gravitational field and sources are conserved. The theory's predictions agree with the experimental results for General Relativity. By introducing the corresponding Lagrangian to analytic mechanics, what is experimentally known for GR can be accounted for.
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06 Sep 2016
TL;DR: In this article, a dialectical perspective of the internal dynamics of Space-Time-Matter-Motion of the infinite universe, mediated by the virtual particles of the quantum vacuum, is presented.
Abstract: From the macrocosm to the microcosm, natural science has so far confirmed the most fundamental assertion of materialist dialectics that there can be no matter without motion and no motion without matter. This view of the objective reality is in sharp conflict with the one proposed by Albert Einstein in his theory of General Relativity (GR). According to Einstein, “Since the theory of general relativity (GR) implies the representation of physical reality by a continuous field, the concept of particles and material points cannot play a fundamental part and neither can the concept of motion. The particle can only appear as a limited region in space in which the field strength or energy density is particularly high”(1). This article offers a dialectical perspective of the internal dynamics of Space-Time-Matter-Motion of the infinite universe, mediated by the virtual particles of the quantum vacuum. It is at the same time a refutation of the finite, non-material and abstract four dimensional spacetime geometric manifold as the ontological basis of objective reality, proposed by Minkowski and Einstein.
TL;DR: In this paper, the authors compare the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi, with the Entwurf Lagrangian.
Abstract: Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. As a result, it also has 3 ghosts, failing a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work.
This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right.
Particle physics also can be useful in the historiography of gravity and space-time. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like.
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TL;DR: In this paper, the center of mass and angular momentum at both the quasi-local and total levels are derived from first principles in general relativity and by the method of geometric analysis, and the classical formula p=mv is shown to be consistent with the field equation for the first time.
Abstract: These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain these difficulties and progresses that have been made. In particular, I shall introduce new definitions of center of mass and angular momentum at both the quasi-local and total levels, which are derived from first principles in general relativity and by the method of geometric analysis. With these new definitions, the classical formula p=mv is shown to be consistent with Einstein's field equation for the first time. This paper is based on joint work [14][15] with Po-Ning Chen and Shing-Tung Yau.