Search Results (35)

Within the framework of string theory, a number of new fields can arise that correct the Einstein–Hilbert action, including the Kalb–Ramond two-form field. In this work, we derive explicitly first-order relativistic corrections to conservative dynamics in the presence of a Kalb–Ramond field using the effective field theory approach. The resulting additional terms in the Lagrangian governing conservative binary dynamics are presented explicitly. Full article

In this study, we discuss a series of eight energy scales, some of which are our own speculations, and fit the logarithms of these energies as a straight line versus a quantity related to the dimensionalities of action terms in a way to be defined in the article. These terms in the action are related to the energy scales in question. So, for example, the dimensionality of the Einstein–Hilbert action coefficient is one related to the Planck scale. In fact, we suppose that, in the cases described with quantum field theory, there is, for each of our energy scales, a pair of associated terms in the Lagrangian density, one “kinetic” and one “mass or current” term. To plot the energy scales, we use the ratio of the dimensionality of, say, the “non-kinetic” term to the dimensionality of the “kinetic” one. For an explanation of our phenomenological finding that the logarithm of the energies depends, as a straight line, on the dimensionality defined integer q, we give an ontological—i.e., it really exists in nature in our model—“fluctuating lattice” with a very broad distribution of, say, the link size a. We take the Gaussian in the logarithm, $ln\left(a\right)$. A fluctuating lattice is very natural in a theory with general relativity, since it corresponds to fluctuations in the gauge depth of the field of general relativity. The lowest on our energy scales are intriguing, as they are not described by quantum field theory like the others but by actions for a single particle or single string, respectively. The string scale fits well with hadronic strings, and the particle scale is presumably the mass scale of Standard Model group monopoles, the bound state of a couple of which might be the dimuon resonance (or statistical fluctuation) found in LHC with a mass of 28 GeV. Full article

This paper is devoted to the study of stationary trajectories of free particles. From a classical point of view, this appears to be an almost trivial problem: Free particles should follow straight lines as predicted by Newton’s first law, and straight lines are indeed the stationary trajectories of the standard action integrals in the classical theory. In the following, however, a general relativistic approach is studied, and in this situation it is much less evident what action integral should be used. As it turns out, using the traditional Einstein–Hilbert principle gives us stationary states very much in line with the classical theory. But it is suggested that a different action principle, and in fact one which is closer to quantum mechanics, gives stationary states with a much richer structure: Even if these states in a sense can represent particles which obey the first law, they are also inherently rotating. Although we may still be far from understanding how general relativity and quantum mechanics should be united, this may give an interesting clue to why rotation (or rather spin, which is a different but related concept) seems to be the natural state of motion for elementary particles. Full article

I propose a possible way to introduce the effect of temperature (defined through the virial theorem) into Einstein’s theory of general relativity. This requires the computation of a path integral on a ten-dimensional flat space in a four-dimensional spacetime lattice. Standard path integral Monte Carlo methods can be used to compute this. Full article

Under the announcement by Alain Connes that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein–Hilbert action of general relativity, we derive the Lichnerowicz-type formula for the Witten deformation of the non-minimal de Rham–Hodge operator and the gravitational action in the case of n-dimensional compact manifolds without boundary. Finally, we present the proof of the Kastler–Kalau–Walze-type theorem for the Witten deformation of the non-minimal de Rham–Hodge operator on four- and six-dimensional oriented compact manifolds with boundary. Full article

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation. Full article

We consider the discrete $Z_4$ symmetry $\widehat{\mathbf{i}}$, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, $\widehat{\mathbf{i}}$, the emerging tetrads are multiplied by the imaginary unit, $\widehat{\mathbf{i}}{e}_{\mu }^a=-i{e}_{\mu }^a$. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid ³He-B. The order parameter in ³He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The $\widehat{\mathbf{i}}$-symmetry operation changes the phase of the complex order parameter by $\pi /2$, which corresponds to the $Z_4$ discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this $Z_4$ symmetry, in which the $\widehat{\mathbf{i}}$-operation changes sign of the scalar curvature, $\widehat{\mathbf{i}}\mathcal{R}=-\mathcal{R}$, and thus the Einstein–Hilbert action violates the $\widehat{\mathbf{i}}$-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling $K=1/16\pi G$ plays the role of the order parameter, which changes sign under $\widehat{\mathbf{i}}$-transformation. Full article

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered “anomalous”. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein–Hilbert action, which is based on a fractional derivative action, and add a scalar field, $\varphi$, to create a non-minimal interaction theory with the coupling, $\xi R{\varphi }^2$, between gravity and the scalar field, where $\xi$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism. Full article

Kaluza–Klein theory attempts a unification of gravity and electromagnetism through the hypothesis that spacetime has five dimensions, of which only four are observed. The original model gives rise to the standard Einstein–Maxwell theory after dimensional reduction. However, in five dimensions, the Einstein–Hilbert action is not unique, and one can add to it a Gauss–Bonnet term, giving rise to nonlinear corrections in the dimensionally reduced action. We consider such a model, which reduces to Einstein gravity nonminimally coupled to nonlinear electrodynamics. The black hole solutions of the four-dimensional model modify the Reissner–Nordström solutions of general relativity. We show that in the modified solutions, the gravitational field presents the standard singularity at $r=0$, while the electric field can be regular everywhere if the magnetic charge vanishes. Full article

We explore the duality invariance of the Maxwell and linearized Einstein–Hilbert actions on a non-rotating black hole background. On-shell, these symmetries are electric–magnetic duality and Chandrasekhar duality, respectively. Off-shell, they lead to conserved quantities; we demonstrate that one of the consequences of these conservation laws is that even- and odd-parity metric perturbations have equal Love numbers. Along the way, we derive an action principle for the Fackerell–Ipser equation and Teukolsky–Starobinsky identities in electromagnetism. Full article

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multifluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein–Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called “$3+1$” form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed “flow-of-time”. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the “$3+1$” form of the field equations, which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe. Full article

An investigation has been carried out on a reconfigured form of the Einstein-Hilbert action, denoted by $f(R,T^{\varphi })$, where $T^{\varphi }$ represents the energy-momentum tensor trace of the scalar field under consideration. The study has focused on how the structural behavior of the scalar field changes based on the potential’s shape, which has led to the development of a new set of Friedmann equations. In the context of modified theories, researchers have extensively explored the range of gravitational wave polarization modes associated with relevant fields. In addition to the two transverse-traceless tensor modes that are typically observed in general relativity, two additional scalar modes have been identified: a massive longitudinal mode and a massless transverse mode, also known as the breathing mode. Full article

We investigate the phase space of a scalar field theory obtained by minisuperspace deformation. We consider quintessence or phantom scalar fields in the action that arises from minisuperspace deformation on the Einstein–Hilbert action. We use a modified Poisson algebra where Poisson brackets are the $\alpha$-deformed ones and are related to the Moyal–Weyl star product. We discuss early- and late-time attractors and reconstruct the cosmological evolution. We show that the model can have the $\mathrm{\Lambda CDM}$ model as a future attractor if we initially consider a massless scalar field without a cosmological constant term. Full article

A theory of the initial state of the universe is proposed within the framework of the Euclidean quantum theory of gravity. The theory is based on a quantum representation in which the action functional is implemented as an operator on the space of wave functionals depending on the 4D space metric and matter fields. The initial construction object is the eigenvalue of the action operator in the area of the origin of the universe with the given values of the 3D metric and matter fields on the boundary. The wave function of the initial state is plotted as an exponential of this eigenvalue, after a Wick rotation in the complex plane of the radial variable of the Euclidean 4D space. An estimate of the initial radius of the universe is proposed. Full article