We demonstrate that the Evans-Rosenquist formulation of the optical mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein's field equations. Some remarks including suggestions for future work are also added.
Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{μν}$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is conformally related to the metric of the ambient space. Various aspects of the optical-mechanical analogy are discussed as they relate to the geodesics of conformally related metrics. Some applications of the concepts of gradient-index optics to general relativity are examined, such as effective indices of refraction for gravitational lensing and Gordon's optic…
The problem of construction of a continuous (macroscopic) matter model for a given point-like (microscopic) matter distribution in general relativity is formulated. The existing approaches are briefly reviewed and a physical analogy with the similar problem in classical macroscopic electrodynamics is pointed out. The procedure by Szekeres in the linearized general relativity on Minkowski background to construct a tensor of gravitational quadruple polarization by applying Kaufman's method of molecular moments for derivation of the polarization tensor in macroscopic electrodynamics and to derive…
A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and instability of cold stars. Our procedure deriving the Hamiltonian is based on an analysis of the process of the observation with the background of the notion of quantum-mechanical local times compatible with general theory of relativity.
The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background field is inhomogeneous and anisotropic in the former case, whereas it is inhomogeneous but isotropic in the latter. The features of light scattering are investigated by assuming the interaction region to be sandwiched between two flat spacetime regions, where light rays propagate along straight lines. Standard tools of ordinary wave optics are used to study t…
In this paper, starting from vortices we are finally lead to a treatment of Fermions as Kerr-Newman type Black Holes wherein we identify the horizon at the particle's Compton wavelength periphery. A naked singularity is avoided and the singular processes inside the horizon of the Black Hole are identified with Quantum Mechanical effects within the Compton wavelength. Inertial mass, gravitation, electromagnetism and even QCD type interactions emerge from such a description including relative strengths and also other features like the anomalous gyromagnetic ratio, the discreteness of the charge,…
We study the analogy between propagation of light rays in a stationary curved spacetime and in a toroidal (meta-)material. After introducing a novel gravitational analog of the index of refraction of a magneto-electric medium, it is argued that light rays not only feel a Lorentz-like force in a magneto-electric medium due to the non-vanishing curl of the toroidal moment, but also there exists an optical analog of Aharonov-Bohm effect for the rays traveling in a region with a curl-free toroidal moment. Experimental realization of this effect could utilize either a multiferroic material or a tor…
The flux of angular momentum in electromagnetism cannot be expressed entirely in terms of the field's radiative degrees of freedom. Its expression also involves Coulombic pieces of the field, in the form of a charge aspect $q(θ,ϕ)$, a function of polar angles whose integral gives the total charge of the system. Guided by the strong analogy between radiative processes in electromagnetism and gravitation, we ask whether the flux of angular momentum in general relativity might also involve Coulombic pieces of the gravitational field. Further, we ask whether such terms might have been missed in th…
For distances large relative to the electron Compton wavelength, the Maxwell and gravitational fields from a bound electron in its groundstate are essentially those from a rotating, charged, massive point particle. For distances small relative to the electron Compton wavelength, the corresponding Maxwell fields and General Relativity metric, Riemann and Einstein tensors become bounded, showing that, for this example, quantum effects remove the corresponding classical singularities in electromagnetism and General Relativity. The asymptotic magnetic dipole field from the bound electron produces …
A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In particular, the action that will be considered has been extensively used during the last years to propose inflationary and dark energy models. Nevertheless, in order to keep the discussion as generic as possible, neither symmetries nor a specific form of the potential for the three-form field will be imposed. Interesting and relevant results about the number …
In the spirit of the well-known analogy between inviscid fluids and pseudo-Riemannian manifolds we study spherical singular hypersurfaces in the static superfluid. Such hypersurfaces turn out to be the interfaces dividing the superfluid into the pairs of spherical domains, examples of which are ``superfluid A - superfluid B'' or ``impurity - superfluid'' phases. It is shown that these shells form the acoustic lenses which are the sonic counterparts of the usual optical ones. The exact equations of motion of the lens interfaces are obtained. Also some quantum aspects of the theory are considere…
There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother Nature may have used the same basic pattern for her laws of gravitation and electrodynamics, in which case the CEs might be viewed as the field equations of gravitation in place of Einstein's equation. This is not a new theory of gravitation (because the curvature equations are derivable from Einstein's equation), but rather is a mild reinterpret…
The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.
We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the "cosmic fabric" and spacetime with the fabric's world volume. Using a Lagrangian formulation, we show that the fabric's behavior as derived from Hooke's Law is analogous to that of spacetime per the Field Equations of General Relativity. The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric's Lagrangian outside of inclusions is shown to have the same form as the …
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with …
Covariant Hamiltonian formulation of $F(R)$ gravity is used to find variation of surface Hamiltonian which leads to formulation of temperature and entropy of a horizon. These thermodynamic quantities are then used to establish an analogy between Einstein equation and Clausius equation. The obtained results are compared to those from classical General Relativity.
In the general case, torsion couples to the spin current of the Dirac field. In General Relativity, the apparent torsion field to which the spin current of the Dirac field couples is a mere manifestation of the tetrad anholonomy. Seen from the tetrad frame itself, it has for components the anholonomy coefficients. The latter represent mechanical characteristics of the frame. In the teleparallel equivalent of General Relativity, this coefficient turns out to be the only torsion present.
While quantum field theory could more aptly be called the "quantum field framework" $-$ as it encompasses a vast variety of varying concepts and theories $-$ in comparison, relativity, both special and general, is more commonly portrayed as less of a "general framework". Viewed from this perspective, the paradigm of "analogue space-times" is to promote the specific theory of general relativity (Einstein gravity) to a framework which covers relativistic phenomena at large. Ultimately, this then also gives rise to new proposals for experiments in the laboratory, as it allows one to move general …
Using a suitable rescaling of the independent variable, a Lagrangian is found for the nonlinear Vialov equation ruling the longitudinal profiles of glaciers and ice caps in the shallow ice approximation. This leads to a formal analogy between the (rescaled) Vialov equation and the Friedmann equation of relativistic cosmology, which is explored. This context provides a new symmetry of the (rescaled) Vialov equation and gives, at least formally, all its solutions using a generating function, which is the Nye profile for the degenerate case of perfectly plastic ice.
This work completes a serie of two papers devoted to the extension of the fundamental laws of electrodynamics in the context of Fock's nonlinear relativity (FNLR). Indeed, after having established in the previous study the exact generalizations of both Maxwell's equations and Dirac magnetic monopole, we present here the remaining exact Lorentz force. As in k-Minkowski spacetime, two different nature contributions appear in the corresponding equation of motion where the new effect is interpreted as the gravitational-type Lorentz force. This common point separately induced by the radius of the u…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed that, unlike general relativity, it agrees with Doppler tracking signals from the Pioneer 10 and 11 space probes. There a gravitational acceleration equation plays an important role, accounting for the relative motions of Earth and the probes. Here it's shown that equation also describes Mercury's orbit.
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
In the spirit of Sakharov's `metric elasticity' proposal, we draw a loose analogy between general relativity and the hydrodynamic state of a quantum gas. In the `top-down' approach, we examine the various conditions which underlie the transition from some candidate theory of quantum gravity to general relativity. Our emphasis here is more on the `bottom-up' approach, where one starts with the semiclassical theory of gravity and examines how it is modified by graviton and quantum field excitations near and above the Planck scale. We mention three aspects based on our recent findings: 1) Emergen…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This allows to introduce geometrical objects that are not invariant under General gauge transformations but they are under Special ones. We develop then a formalism that strengthens the analogy of the formalisms of the electromagnetic and the gravitational theories in a Special relativity framework. We are thus able to define the energy-momentum tensor of the gr…
Using the Dirac procedure to treat constraints dynamical sistems applied to gravitation, as described in the context of Teleparallel Equivalent of General Relativity (TEGR), we investigate, from the first class constraints, the gauge transformations in the fundamental field: the components of tetrads. We have shown that there is no an isotropy in physical space with respect to gauge transformations, i.e., given an arbitrary gravitational field, coming from a gauge transformation in the internal space, physical space reacts differently in the spatial and temporal components. By making an approp…
Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the functions describing the embedding of four dimensional spacetime in a ten or possibly higher dimensional manifold. So far, the main drawback of the formalism is that the generator of normal deformations ("fourth constraint") cannot be written down in closed form. The present approach is compared and contrasted with the usual one and with the canonical descrip…
A previous paper [1] introduced a quantum-mechanical theory of gravity, and showed it agrees with the standard experimental tests of general relativity. Doppler tracking signals returned by the Pioneer 10 and 11 space probes offer an additional test. Analysis by Anderson, Laing, Lau, Liu, Neito and Turyshev [2] finds a persistent blueshift, equivalent to an extra acceleration of the probes toward the Sun. While unexplained by general relativity or prevailing cosmology, it's shown this effect is predicted by the quantum-mechanical alternative.
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing at a space-time level the whole gauge group SO(1,3) x U(1) x SU(2) x SU(3) associated to fundamental interactions; equivalently, by assuming that internal gauge transformations are indeed local space-time transformations. The geometry naturally embodies freedoms corresponding to gravitational and non-gravitational gauge fields. As a consequence of the fact th…
We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system. We find that the tensor naturally contains essential information of the energy-momentum tensor of a classical scalar field, when the entropy data or the spectrum data of the system are embedded into the classical field as the field strength. Thus, we can regard the Einstein equation as the equation of coarse-grained states for the original microscopic system behind the classical field theory. We make some remarks on quantization of gravity and var…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric two-tensor field) but by a multiplet of such fields, or by a matrix-valued symmetric two-tensor field that satisfies certain conditions. We define the matrix extensions of standard constructions of differential geometry including connections and curvatures, and finally, an invariant functional of the new field that reduces to the standard Einstein action fun…
Recent researches suggest an analogy between the theory of general relativity (GR) and fluid dynamics. As a result of this analogy, the Navier-Stokes equations and Einstein field equations are the same, and it is possible to study the properties of space-time by using fluid mechanics. In this paper, we present a new model to describe gravitational phenomena by an inviscid and compressible fluid called space-time fluid (STF). The analogy method is used to obtain the gravity field of both static and rotating masses from the flow field of STF around static and rotating point sinks. In addition, e…
