Narrow Results

The simplest, i.e. the Abelian, i.e. the commutative, i.e. the integrable, i.e. the flat and torsion-free, i.e. the symmetric teleparallel affine connection has been considered in many recent works in the literature. Such an affine connection is characterized by the property that it can be vanished by a general coordinate transformation, by fixing the so-called coincident gauge. This paper focuses on the subtleties involved in the applications of the coincident gauge.

Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein’s theory of gravity that does not assume weak fields and which admits an action principle.

We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the thermodynamics of self-gravitating fermions. We stress the inequivalence of statistical ensembles for systems with long-range interactions, like gravity. In particular, we contrast the microcanonical evolution of stellar systems from the canonical evolution of self-gravitating Brownian particles. At low energies, self-gravitating Hamiltonian systems experience a gravothermal catastrophe in the microcanonical ensemble. At low temperatures, self-gravitating Brownian systems experience an isothermal collapse in the canonical ensemble. For classical particles, the gravothermal catastrophe leads to a binary star surrounded by a hot halo while the isothermal collapse leads to a Dirac peak containing all the mass. For self-gravitating fermions, the collapse stops when quantum degeneracy comes into play through the Pauli exclusion principle. The end-product of the collapse is a fermion ball, resembling a cold white dwarf star, surrounded by a halo. We can thus describe a phase transition from a gaseous phase to a condensed phase. At high energies or high temperatures, the condensate can experience an explosion, reverse to the collapse, and return to the gaseous phase. Due to the existence of long-lived metastable states, the points of collapse and explosion differ. This leads to a notion of hysteretic cycle in microcanonical and canonical ensembles.

Pulsars are wonderful gravitational probes. Their tiny size and stellar mass give their rotation periods a stability comparable to that of atomic frequency standards. This is especially true of the rapidly rotating "millisecond pulsars" (MSPs). Many of these rapidly rotating pulsars are in orbit with another star, allowing pulsar timing to probe relativistic perturbations to the orbital motion. Pulsars have provided the most stringent tests of theories of relativistic gravitation, especially in the strong-field regime, and have shown that Einstein's general theory of relativity is an accurate description of the observed motions. Many other gravitational theories are effectively ruled out or at least severely constrained by these results. MSPs can also be used to form a "Pulsar Timing Array" (PTA). PTAs are Galactic-scale interferometers that have the potential to directly detect nanohertz gravitational waves from astrophysical sources. Orbiting super-massive black holes in the cores of distant galaxies are the sources most likely to be detectable. Although no evidence for gravitational waves has yet been found in PTA data sets, the latest limits are seriously constraining current ideas on galaxy and black-hole evolution in the early universe.

We deform the anti-de Sitter algebra by adding additional generators , forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein–Cartan action with Holst term, and the gauge fields associated with the Maxwell generators appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain: $O_Q=o_P^2{O}_G^{-1}$, $o_P$ being the Planck scale. This duality is universal. From the gravity (G) and quantum (Q) variables $(O_G,O_Q)$, we define new quantum gravity (QG) variables $O_{\mathrm{\text{QG}}}=(1/2)(O_G+O_Q)$ which include all (classical, semiclassical and QG) domains passing through the Planck scale and the elementary particle domain. The QG variables are more complete than the usual ($O_Q$, $O_G$) ones which cover only one domain (Q or G). Two$O_G$ or $O_Q$ values $(\pm )$ are needed for each value of $O_{\mathrm{\text{QG}}}$ (reflecting the two dual ways of reaching the Planck scale). We perform the complete analytic extension of the QG variables through analytic (holomorphic) mappings which preserve the light-cone structure. This allows us to reveal the classical-quantum duality of the Schwarzschild–Kruskal spacetime: exterior regions are classical or semiclassical while the interior is totally quantum: its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon: four Planck scale hyperbolae border the horizons as a quantum dressing or width: “l’horizon habillé”. QG variables are naturally invariant under $O_G\to O_Q$. Spacetime reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight on the global properties of the Kruskal manifold and its present renewed interest.

In this study, we investigate the influences of fermionic q-deformation on the Einstein equations by taking into account of Verlinde’s entropic gravity approach and Strominger’s proposal on quantum black holes. According to Verlinde’s proposal, gravity is interpreted as an entropic force. Moreover, Strominger’s suggestion claims that extremal black holes obey deformed statistics instead of the standard Bose or Fermi statistics. Inspired by Verlinde’s and Strominger’s suggestions, we represent some thermostatistical functions of VPJC-type q-deformed fermion gas model for the high-temperature limit. Applying the Verlinde’s entropic gravity approach to the q-deformed entropy function, q-deformed Einstein equations with the effective cosmological constant are derived. The results obtained in this work are compared with the related works in the literature.

In the recently introduced gauge theory of translations, dubbed Coincident General Relativity (CGR), gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein–Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics and quantum theory. This paper reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, (1) energy–momentum is described locally by a conserved, symmetric tensor, (2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and (3) it is possible to identify a canonical frame for quantization.

We consider some of the obstacles that will have to be overcome in order to perform a direct measurement of the gravitational free-fall of positronium atoms. Foremost among these are the production of positronium atoms in a cryogenic environment, efficient excitation of these atoms to suitably long-lived Rydberg states, and their subsequent control via the interaction of their large electric dipole moments with inhomogeneous electric fields. Recent developments in all of these areas can be directly applied to a positronium free-fall gravity measurement, making such an endeavour both timely and feasible.

This paper examines the extent to which cultural proximity influences, and is influenced by, bilateral trade flows. Variables measuring common language or religion, commonly considered to be measures of cultural proximity, have been found to be highly significant in explaining the volume of trade between countries, but these measures have the distinct disadvantage of being static; they do not change over time. In fact, however, culture does change, possibly in response to exposure to the foreign goods, methods, and ideas brought across borders by trade; the cultural "distance" between two countries can therefore be seen to fall or rise over time. In this paper, responses to World Values Survey questions regarding trust, respect, control, and obedience are used to create a measure of cultural distance. I use this cultural distance variable in gravity regressions and show that more culturally-distant countries trade less, but that more traditional measures of culture are more significant in explaining trade. I then explore the determinants of cultural distance, finding that exports reduce cultural distance.

For the Poincaré gauge theory of gravity we consider the dynamical scalar torsion mode in a cosmological context. We explore in particular the possibility of using dynamical torsion to explain the current state of the accelerating Universe. With certain suitable sets of chosen parameters, this model can give a (qualitatively) proper description of the current universe without a cosmological constant, and the universe described is oscillating with a period of the Hubble time.

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number $S_t$, Sisko fluid parameter $\beta$ and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and $S_t$ while their positions relocate towards the fluid–air interface with increasing $\beta$ and n. Thickness of uniform film decreases when the values of C and $S_t$ are increased whilst it increases with the increase of $\beta$ and n. Analogy between the Newtonian fluid and the Sisko fluid’s shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made.

General Relativity (GR) and the Standard Model (SM) of particle physics are two enormously successful frameworks for our understanding the fundamental laws of nature. However, these theoretical schemes are widely disconnected, logically independent and unrelated in scope. Yet, GR and SM at some point must intersect, producing claims about phenomena that should be reconciled. Be it as it may, both schemes share a common basic ground: symmetry under local Lorentz transformations. Here, we will focus on the consequences of assuming this feature from the beginning to combine geometry, matter fields and gauge interactions. We give a rough description of how this could be instrumental for the construction of a unified scheme of gravitation and particle physics.

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

The vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies are hard to work out in most of the theories featuring absolute parallelism. The difficulty is traced in the fact that these theories are not invariant under local Lorentz transformations of the vierbein. We illustrate this issue in the framework of f(T) theories and Born-Infeld determinantal gravity. In particular, we show that the early Universe as described by the Born-Infeld scheme is singularity free and naturally inflationary as a consequence of the very nature of Born-Infeld gravitational action.

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld parameter λ bounds the dynamics of Hubble parameter H(t) and establishes a maximum attainable spacetime curvature.

I briefly discuss some attempts to construct a consistent modification to general relativity (GR) that might explain the observed late-time acceleration of the Universe and provide an alternative to dark energy. I describe the issues facing extensions to GR, illustrate these with a specific example, and discuss the resulting observational and theoretical obstacles.

By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, Λ and spacetime is completely free of dynamics. Thus c and Λ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity, the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of free spacetime is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area, the Universe measures 10¹²⁰ units!

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.