Narrow Results

Quantum gravitational effects, on the one hand, lead to a limitation in the accuracy of measuring spatial and time intervals, and, on the other hand, they generate a discrete of spacetime structure (quantum foam). The common source of both measurement limitations and discreteness of spacetime is quantum fluctuations, so their characteristics must be related to each other. We study such a relationship using Barrow entropy as a source of fractal spacetime structure. The minimum inaccuracy in measuring spacetime intervals is expressed through the Barrow entropy parameter. The connection between the level of fractality and the speed of information processing is considered.

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. Here we propose and analyse a generalisation of Heisenberg's equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenberg's equation turns out to be a delay-differential equation.

Spacetime emergence refers to the notion that classical spacetime "emerges" as an approximate macroscopic entity from a non-spatio-temporal structure present in a more complete theory of interacting fundamental constituents. In this paper, we propose a novel mechanism involving the "soldering" of internal and external spaces for the emergence of spacetime and the twin transmutation of general covariance. In the context of string theory, this mechanism points to a critical four-dimensional spacetime background.

Solutions are found to field equations constructed from the Pauli, Bach and Gauss–Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four-branes a solution similar to radiation Robertson–Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.

Dedicated to the memory of Lars Brink (1943–2022) for his help and friendship over many years

In this paper, we argue that the existence of solitons in theories in which local symmetries are spontaneously broken requires space–time to be enlarged by additional coordinates that are associated with large local transformations. In the context of gravity theories, the usual coordinates of space–time can be thought of arising in this way. E theory automatically contains such an enlarged space–time. We propose that space–time appears in an underlying theory when the local symmetries are spontaneously broken.

We present the theory of spacetime elasticity and demonstrate that it involves traditional thermoelasticity. Assuming linear-elastic constitutive behavior and using spacetime transversely-isotropic elastic constants, we derive all principal thermodynamic relations of classical thermoelasticity. We introduce the spacetime principle of virtual work, and use it to derive the equations of motion for both reversible and dissipative thermoelastic dynamics. We show that spacetime elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, spacetime elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity, complemented by the spectrum of boundary and interface conditions. We argue that the presented framework of spacetime elasticity should prove adequate for describing the thermoelastic phenomena occurring at low temperatures, for interpreting the results of molecular simulations of heat conduction in solids, and also for the optimal heat and stress management in the microelectronic components and the thermoelectric devices.

Nonlinear dynamical flows are often solved approximately by numerical integration based on advancing the independent variable, typically time. Here, we present a unified framework for numerical integration of differential equations based on advancing either the dependent variable, often space, or the independent variable, or any combination of the two. Spacetime stepping unifies and extends previous work. In particular, dependent variable stepping can produce better numerical results and also more faithfully describe the underlying physics, thereby providing both practical and conceptual benefits. We indicate extensions to higher dimensions.

The cosmic defect theory has been confronted with four observational constraints: primordial nuclear species abundances emerging from the big bang nucleosynthesis; large scale structure formation in the Universe; cosmic microwave background acoustic scale; luminosity distances of type Ia supernovae. The test has been based on a statistical analysis of the a posteriori probabilities for three parameters of the theory. The result has been quite satisfactory and such that the performance of the theory is not distinguishable from that of the ΛCDM theory. The use of the optimal values of the parameters for the calculation of the Hubble constant and the age of the Universe confirms the compatibility of the cosmic defect approach with observations.

It is a remarkable fact that all processes occurring in the observable universe are irreversible, whereas the equations through which the fundamental laws of physics are formulated are invariant under time reversal. The emergence of irreversibility from the fundamental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous "H" theorem. In this paper, we shall discuss some aspects of this problem and its connection with the dynamics of spacetime, within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events determined through electromagnetic processes.

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!

Using the instanton representation method, we re-construct graviton solutions about de Sitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known solutions. This paper is a precursor for its application to the construction of new General Relativity solutions in future work.

Traditional derivations of general relativity (GR) from the graviton degrees of freedom assume spacetime Lorentz covariance as an axiom. In this paper, we survey recent evidence that GR is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of GR, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of spacetime. This result has revolutionary implications for fundamental physics.

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 worldvolume. 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 (GR). 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 Einstein–Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves and the energy density of free space. By introducing a mechanical analogy of GR, we enable the application of Solid Mechanics tools to address problems in Cosmology.

In the absence of a fully fledged theory of quantum gravity, we propose a “bottom-up” framework for exploring quantum-gravitational physics by pairing two of the most fundamental concepts of quantum theory and general relativity, namely quantum superposition and spacetime. We show how to describe such “spacetime superpositions” and explore effects they induce upon quantum matter. Our approach capitalizes on standard tools of quantum field theory in curved space, and allows us to calculate physical observables like transition probabilities for a particle detector residing in curvature-superposed de Sitter spacetime, or outside a mass-superposed black hole. Crucially, such scenarios represent genuine quantum superpositions of spacetimes in contrast with superpositions of metrics that only differ by a coordinate transformation and thus are not different according to general relativity.

After recalling the principles that allow spacetime to be considered by analogy as an elastic medium, we show how the modified gravity according to the MOND theory concerning the anomaly of the velocities of stars at the periphery of galaxies can be seen as a creep of space acting on the radius of galaxies that give a creep coefficient of ${\phi }_{\mathrm{\text{space}}}=\frac{a_0}{a}\frac{{\rho }_{\mathrm{\text{local}}}}{{\rho }_{\mathrm{\text{mean}}}}-1$. The values vary between 0.2 and 9 depending on the type of galaxy and density distribution. Considering the gravitational lensing effect of the ball cluster we obtain a creep coefficient ${\phi }_{\mathrm{\text{space}}}=\frac{1-p_v}{p_v}$ with $p_v$ the percentage of visible matter and $p_{\mathrm{\text{DM}}}$ the percentage of dark matter from the global mass ($p_v+p_{\mathrm{\text{DM}}}=1$). The values vary between 0.66 and 4 for this cluster. This paper therefore raises the question, via these creep coefficients, of the possible granular nature of the vacuum and therefore of space fabric on the one hand and proposes another dark matter-free approach based on the creep of the texture of space to explain gravitational anomalies on the other hand.

In this paper, we show how it is possible to obtain mass generation in the context of non-Abelian gauge field theory, using a noncommutative spacetime. This is further confirmed by the modified dispersion relation that results from such a geometry. Other effects in the domain of ultra high energy gamma rays and cosmic rays are also deduced and it is pointed out that we might already have observed such effects.

In semiclassical gravity, the final state of black-hole evaporation cannot be described by a pure state. Nevertheless, we point out that the system can be described by a generalized pure state, which is not defined on a three-dimensional hypersurface but on the four-dimensional spacetime describing the whole Universe at all times. Unlike the conventional quantum state, such a generalized state treats time on an equal footing with space, which makes it well suited for systems that are both quantum and relativistic. In particular, such a generalized state contains a novel type of information encoded in the correlations between future and past, which avoids the black-hole information paradox.

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1-dimensional submanifolds of spacetime. This setting allows us to skip constraints.

Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialize these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

A general procedure to construct a 4-dimensional spacetime from a 3-dimensional time-oriented Lorentzian manifold and each of its timelike vector fields is exposed. It is based on the construction of the null congruence Lorentzian manifold. As an application, examples of stably causal spacetimes which obey the timelike convergence condition, are semi-symmetric, and admit an isometric spacelike circle action are obtained.

The classical phase space of general relativistic classical test particle (here called, for short, "phase space") is defined as the first jet space of motions regarded as timelike one-dimensional submanifolds of spacetime. By the projectability assumption, we define the subsheaf of special phase functions with a special Lie bracket and we compare the Lie algebra of special phase functions with the structures obtained on the phase space by the standard Hamiltonian approach.