Gravitational Configurations Research Articles

Black bounces in Cotton gravity

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as “Cotton gravity” (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson–Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG.

Energy of gravitational radiation and the background energy of the space-time

We address the issue of gravitational radiation in the context of the Bondi-Sachs space-time, and consider the expression for the gravitational energy of the radiation obtained in the realm of the teleparallel equivalent of general relativity (TEGR). This expression is independent of the radial distance (i.e., of powers of 1/r) and depends exclusively on the functions c(u,θ,ϕ) and d(u,θ,ϕ), which yield the news functions (u is the retarded time, u=t−r). We investigate the mathematical and physical features of this energy expression in the simpler framework of axial symmetry. Once a burst of gravitational radiation takes place in a self gravitating system, that leads to a loss of the Bondi mass, gravitational radiation is emitted throughout the whole space-time. The existence and presence of this radiation in the background structure of the space-time is consistent with the analysis developed by Papapetrou, and Hallidy and Janis, who found no proof that a gravitational system that emits a burst of gravitational radiation is preceded and followed by two stationary gravitational field configurations, namely, it seems that it is impossible for a gravitational system, which is initially stationary, to return to a stationary state after emitting a burst of axially symmetric gravitational radiation, in which case the space-time is not even asymptotically stationary. Therefore, it is plausible that the gravitational energy of radiation is present in the background structure of the space-time, and this is the energy predicted in the TEGR. This analysis leads us to conjecture that the noise detected in the large terrestrial gravitational wave observatories is intrinsically related to the background gravitational radiation.

Extracting work from two gravitational cat states

Gravitational cat states in the context of gravity are superpositions of quantum states that exhibit macroscopically distinct gravitational fields. These states represent a unique blend of quantum mechanics and general relativity, providing insights into the behavior of quantum systems under gravitational influences. This study investigates the impact of thermal environments on the extractable work from gravitational cat states, which are quantum superpositions of distinct gravitational configurations. It aims to offer a comprehensive analysis of how temperature and gravitational interactions between states with masses m influence work extraction. The findings indicate that both an increase in temperature and the interactions between states reduce the amount of work that can be extracted from gravitational cat states, highlighting the delicate balance between thermal and gravitational effects in quantum systems.

Shell and tube heat exchange comparison with gravitational water vortex flow configuration

As a recent addition to the heat exchanger family, gravitational water vortex heat exchangers may be considered a potential alternative to shell-and-tube heat exchangers in the process industry. Their shared reliance on the turbulent fluid flow for heat transfer and comparable sizes indicates the need to compare the two thermal systems in terms of input energy requirement, heat exchange effectiveness, temperature distribution, log-mean temperature difference and overall heat transfer coefficient. The present study reports an experimental comparison of the performance of a shell-and-tube heat exchanger with a gravitational water vortex heat exchanger for the same heat exchange area, mass flowrates and reference temperatures. The validation of the experiments is supported by the analytical results for both heat exchangers. The experimental findings highlight the importance of the presence of air core in the gravitational water vortex heat exchanger, which performs 40 % better than in the absence of air core. Moreover, the same air core provides support in outperforming the shell-and-tube configuration by a margin of 22 % and 24 % more heat transfer rate for the same hot-side inlet temperatures of 313 K and 323 K, respectively. The study concludes that the gravitational water vortex heat exchanger performs better than the shell-and-tube heat exchanger at high inlet flow rates, whereas the latter is more effective in terms of log-mean temperature difference with better heat loss counter measures.

High-efficiency silicon metasurface mirror on a sapphire substrate

For a possible implementation of high-efficiency Si-nanosphere metasurface mirrors functioning at telecom wavelengths in future gravitational wave detectors, exact dimensional and configuration parameters of the total system, including substrate and protective coating, have to be determined a priori. The reflectivity of such multi-layer metasurfaces with embedded Si nanoparticles and their potential limitations need to be investigated. Here we present the results on how the substrate and protective layer influence optical properties and demonstrate how dimensional and material characteristics of the structure alter light reflectivity. Additionally, we consider the impact of manufacturing imperfections, such as fluctuations of Si nanoparticle sizes and their exact placement, on the metasurface reflectivity. Finally, we demonstrate how high reflectivity of the system can be preserved under variations of the protective layer thickness, incident angle of light, and its polarization.

On the Black Hole Acceleration in the C-Metric Space-Time

We consider the C-metric as a gravitational field configuration that describes an accelerating black hole in the presence of a semi-infinite cosmic string, along the accelerating direction. We adopt the expression for the gravitational energy-momentum developed in the teleparallel equivalent of general relativity (TEGR) and obtain a possible explanation for the acceleration of the black hole. The gravitational energy enclosed by surfaces of constant radius around the black hole is evaluated, and in particular the energy contained within the gravitational horizon is obtained. This energy turns out to be proportional to the square root of the area of the horizon. We find that the gravitational energy of the semi-infinite cosmic string is negative and dominant for large values of the radius of integration. This negative energy may explain the acceleration of the black hole, that moves towards regions of lower gravitational energy along the string.

Charged and rotating multi-black holes in an external gravitational field

We construct analytical and regular solutions in four-dimensional General Relativity which represent multi-black hole systems immersed in external gravitational field configurations. The external field background is composed by an infinite multipolar expansion, which allows to regularise the conical singularities of an array of collinear static black holes. A stationary rotating generalisation is achieved by adding independent angular momenta and NUT parameters to each source of the binary configuration. Moreover, a charged extension of the binary black hole system at equilibrium is generated. Finally, we show that the binary Majumdar–Papapetrou solution is consistently recovered in the vanishing external field limit. All of these solutions reach an equilibrium state due to the external gravitational field only, avoiding in this way the presence of any string or strut defect.

Quantum variational solving of the Wheeler-DeWitt equation

One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to the Wheeler-DeWitt equation. However, solutions to the equation are known only for specific symmetry-reduced systems, including models of quantum cosmology. Novel methods, which enable solving the equation for complex gravitational configurations, are therefore worth seeking. Here, we propose and investigate a new method of solving the Wheeler-DeWitt equation for minisuperspace models (with a finite number of classical degrees of freedom). The approach employs variational quantum algorithms and is possible to implement on quantum computers. For this purpose, the gravitational system is regularized, by performing spherical compactification of the phase space. This makes the system's Hilbert space finite dimensional and allows to use $SU(2)$ variables, which are easy to handle in quantum computing. The validity of the method is examined in the case of the flat de Sitter universe. Both an emulator of a quantum computer and the IBM superconducting quantum computer have been used. The advantages and limitations of the approach are discussed.

Nonrelativistic Boson stars as N-body quantum systems

In this work, we show that the structural configuration of a collection of generic nonrelativistic bosons forming a gravitationally bound Bose–Einstein condensate can be interpreted as a nonrelativistic boson star. With the approach followed in this work, we can analyze with a concise and straightforward procedure the equilibrium properties of nonrelativistic boson stars viewed as a Bose–Einstein condensate. The system’s behavior is obtained by analyzing its fundamental constituent properties, i.e. the associated single-particle properties. Additionally, we show that by expressing the corresponding Newtonian gravitational potential, under certain circumstances, as a harmonic oscillator potential one, we can describe the conditions in which the nonrelativistic boson star can form equilibrium configurations. In order to analyze the boson star’s structural configuration, we employ four different ansätzes commonly used in the literature. These ansätzes allow us to compare the cloud’s structural properties of the boson star, which leads us to obtain several gravitational equilibrium configurations from compact objects matching the size of typical stars to gigantic systems comparable to the size of galaxy cluster dark matter halos. Finally, we show that these ansätzes predict, qualitatively speaking, the same structural and gravitational equilibrium configurations for different values of the parameters involved.

Time-space duality in 2D quantum gravity

An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global Z 2 symmetry of 1 + 1D quantum gravity, we show that gravitational path integral configurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a Universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.

Integrable Systems and Spacetime Dynamics.

It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy can be obtained as the dynamical equations of three-dimensional general relativity with a negative cosmological constant. This geometrization of the AKNS system is possible through the construction of novel boundary conditions for the gravitational field. These are invariant under an asymptotic symmetry group characterized by an infinite set of AKNS commuting conserved charges. Gravitational configurations are studied by means of SL(2,R) conjugacy classes. Conical singularities and black hole solutions are included in the boundary conditions.

Hamiltonian analysis of fermions coupled to the Holst action

We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the Lorentz connection, which allows us to integrate out some auxiliary fields without spoiling the local Lorentz symmetry. They have the peculiarity that their noncanonical symplectic structures as well as the phase-space variables for the gravitational sector are real. Moreover, two of these Hamiltonian formulations involve half-densitized fermion fields. We also impose the time gauge on these formulations, which leads to real connections for the gravitational configuration variables. Finally, we perform a symplectomorphism in one of the manifestly Lorentz-invariant Hamiltonian formulations and analyze the resulting formulation, which becomes the Hamiltonian formulation of fermion fields minimally coupled to the Palatini action for particular values of the coupling parameters.

Gravitational waves in metric-affine gravity theory

We derive the exact gravitational wave solutions in a general class of quadratic metric-affine gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion, nonmetricity and the curvature. The ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding ansatz and the properties of the plane-fronted electromagnetic wave.

On generalized Melvin solutions for Lie algebras of rank 4

We consider generalized Melvin-like solutions associated with Lie algebras of rank 4 (namely, A 4, B 4, C 4, D 4, and the exceptional algebra F 4 ) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically-symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs (z) ( s = 1,…,4) of squared radial coordinate z = ρ 2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n 1, n 2, n 3, n 4) = (4, 6, 6, 4), (8, 14, 18, 10), (7, 12, 15, 16), (6, 10, 6, 6), (22, 42, 30, 16) for Lie algebras A 4, B 4, C 4, D 4, F 4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4 × 4 matrix v connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A 4 case) the matrix representing a generator of the ℤ2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained. We also presented 2-form flux integrals over 2-dimensional discs.

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

We investigate gravity models emerging from nonholonomic (subjected to non-integrable constraints) Ricci flows. Considering generalizations of G. Perelman’s entropy functionals, relativistic geometric flow equations, nonholonomic Ricci soliton and equivalent (modified) Einstein equations are derived. There are studied nonholonomic configurations which allow explicit modeling of entropic scenarios for gravity and dark matter (in the E. Verlinde approach and/or other variants). It is shown that using the anholonomic frame deformation method, the systems of nonlinear partial differential equations for geometric flow evolution of nonlinear stationary gravitations systems can be decoupled and integrated in general forms. In this and a series of partner works, we elaborate on stationary models of emergent gravity with quasi-periodic gravitational, matter fields and dark energy/matter structure. Such configurations cannot be described thermodynamically using the concept of Bekenstein-Hawking entropy if area-entropy, holographic or duality relations are not involved. Nevertheless, generalizing G. Perelman statistic thermodynamic approach to models of relativistic Ricci flows and nonholonomic solitons, we can compute respective thermodynamic variables for all types of gravitational and matter field configurations and their geometric evolution. Nonholonomic deformations of the F- and W-entropy considered and relativistic thermodynamic models are studied in more general cases when physically important solutions with quasi-periodic and pattern forming structure are found in modified gravity theories (MGT) and general relativity (GR).

One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry

We point out that the successful generation of the electroweak scale via gravitational instanton configurations in certain scalar-tensor theories can be viewed as the aftermath of a simple requirement: the existence of a quadratic pole with a sufficiently small residue in the Einstein-frame kinetic term for the Higgs field. In some cases, the inflationary dynamics may also be controlled by this residue and therefore related to the Fermi-to-Planck mass ratio, up to possible uncertainties associated with the instanton regularization. We present here a unified framework for this hierarchy generation mechanism, showing that the aforementioned residue can be associated with the curvature of the Einstein-frame target manifold in models displaying spontaneous breaking of dilatations. Our findings are illustrated through examples previously considered in the literature.

Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.

Metrics with Zero and Almost-Zero Einstein Action in Quantum Gravity

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action SE « ћ. This is obtained through a Metropolis algorithm with weight exp(−β2S2E) and β » ћ−1. The squared action in the exponential allows to circumvene the problem of the non-positivity of SE. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition SE = 0 exactly, or in certain cases even the stronger condition R(x) = 0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler’s “spacetime foam”.

The work-energy relation for particles on geodesics in the pp-wave spacetimes

A non-linear gravitational wave imparts gravitational acceleration to all particles that are hit by the wave. We evaluate this acceleration for particles in the pp-wave space-times, and integrate it numerically along the geodesic trajectories of the particles during the passage of a burst of gravitational wave. The time dependence of the wave is given by a Gaussian, so that the particles are free before and after the passage of the wave. The gravitational acceleration is understood from the point of view of a flat space-time, which is the initial and final gravitational field configuration. The integral of the acceleration along the geodesics is the analogue of the Newtonian concept of work per unit mass. Surprisingly, it yields almost exactly the variation of the non-relativistic kinetic energy per unit mass of the free particle. Therefore, the work-energy relation Δ K = Δ W of classical Newtonian physics also holds for a particle on geodesics in the pp-wave space-times, in a very good approximation, and explains why the final kinetic energy of the particle may be smaller or larger than the initial kinetic energy.

Black holes with MDRs and Bekenstein–Hawking and Perelman entropies for Finsler–Lagrange–Hamilton Spaces

New geometric and analytic methods for generating exact and parametric solutions in generalized Einstein–Finsler like gravity theories and nonholonomic Ricci soliton models are reviewed and developed. We show how generalizations of the Schwarzschild–(anti) de Sitter metric can be constructed for modified gravity theories with arbitrary modified dispersion relations, MDRs, and Lorentz invariance violations, LIVs. Such theories can be geometrized on cotangent Lorentz bundles (phase spaces) as models of relativistic Finsler–Lagrange–Hamilton spaces. There are considered two general classes of solutions for gravitational stationary vacuum phase space configurations and nontrivial (effective) matter sources or cosmological constants. Such solutions describe nonholonomic deformations of conventional higher dimension black hole, BH, solutions with general dependence on effective four dimensional, 4-d, momentum type variables. For the first class, we study physical properties of Tangherlini like BHs in phase spaces with generic dependence on an energy coordinate/parameter. We investigate also BH configurations on base spacetime and in curved cofiber spaces when the BH mass and the maximal speed of light determine naturally a cofiber horizon. For the second class, the solutions are constructed with Killing symmetry on an energy type coordinate. There are analyzed the conditions when generalizations of Bekenstein–Hawking entropy (for solutions with conventional horizons) and/or Grigory Perelman’s W-entropy (for more general generic off-diagonal solutions) can be defined for phase space stationary configurations.