Curved Spacetime Research Articles

Klein–Gordon equation in the presence of a vector generalized Yukawa and a scalar generalized Hulthen potentials in the rotating cosmic string space–time

In this paper, we explore the relativistic quantum dynamics of spin-0 oscillator fields within the framework of a rotating cosmic string space–time, taking into account the presence of scalar and vector potentials. We solve the Klein–Gordon oscillator equation in this curved space–time, incorporating generalized versions of the Yukawa and Hulthen potentials as vector and scalar potentials, respectively. The analytical solution of the quantum system yields the energy eigenvalue and corresponding eigenfunction, which is expressed in terms of confluent Heun functions. The resulting energy spectrum is shown to depend on various parameters associated with the cosmic string space–time and the confining potentials. We graphically illustrate how the energy spectrum varies with changes in both the potential parameters and the cosmic string parameters.

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

On gravity implication in the wavefunction collapse

Abstract Inspired by an ontic view of the wavefunction in quantum mechanics and motivated
by the universal e¤ect of gravity, we discuss a possible gravity implication in the reduc-
tion scenario of the quantum state. Concretely, we investigate the stability of the spatial
superposition of a massive quantum state under the gravity e¤ect. In this context, we
argue that the stability of the spatially superposed state jYi =
nå
i=1
ai jyii, ai 2 C, depends
on its gravitational self-energy UG
Y originating from the effective mass density distribution
r m (x) through the spatially localized eigenstates jyii. We reveal that the gravitational
self-interaction between the di¤erent spacetime curvatures jGii created by the eigenstate
e¤ective masses m y leads to the reduction of the superposed state to one of the possible
localized states jyki jGki. Among others, we discuss such a gravity-driven state reduc-
tion. Then, we approach the corresponding collapse time t Collapse Y and the induced effective electric current I Y in the case of a charged state, as well as the possible detection aspects.

Black holes - from relativity to Hawking radiation

Abstract. Black Hole (BH for short) is a kind of compact body in the universe predicted by the general theory of relativity. The gravitational pull of a black hole is extremely strong. A black hole is a celestial body whose curvature of space-time is so great that light cannot escape from its event horizon. There are four main ideas about how black holes form: collapsing stars, exploding supernovae, merging multiple black holes, and primordial black holes. In this article, we will start with Einstein's theory of relativity to analyze black holes, and focus on Schwarzschild black holes.

Quantum-induced revisiting spacetime curvature in relativistic regime

Quantum-induced revisiting spacetime curvature in relativistic regime

Unravelling the Enigmatic Nexus: Black Holes, Dark Matter, and the Interplay of Light, Gravity, and Electromagnetic Forces in Astrophysics and Astronomy

This research introduces a mathematical model positioning our physical reality within a ten-dimensional hyperspace, in which time acts as the unifying coordinate linking three-dimensional electric, magnetic, and gravitational spaces. Each domain is characterized by its respective field—electric, magnetic, or gravitational—and governed by intrinsic divergences and rotations, leading to a universal property known as Force Density, expressed in [N/m³]. This Force Density facilitates interactions among the distinct spaces while adhering to the principle of equilibrium, which posits that cumulative force densities from disturbances must consistently sum to zero. Building upon Einstein's General Relativity—which describes the curvature of spacetime by gravitational fields and assumes a constant light speed—this study proposes a perspective wherein light speed may vary during coherent laser beam interactions, prompting a re-examination of gravitational and luminous interactions across scales. The proposed model integrates the Stress-Energy Tensor and Gravitational Tensor, introducing a new tensor representation for black holes, termed Gravitational Electromagnetic Confinements, incorporating electromagnetic energy gradients and Lorentz transformations. This framework transcends traditional General Relativity, particularly evident in gravitational lensing. By reinterpreting Einstein's incorporation of the Gravitational Constant within the Energy-Stress Tensor, this work harmonizes gravity and light, offering insights into black hole solutions resonating with John Archibald Wheeler's 1955 research. Empirical data from Galileo satellites and MASER frequency measurements underscore discrepancies between established theories and this new model, enhancing the precision of gravitational observations. Through the confluence of Quantum Physics and General Relativity, as seen in approaches like String Theory, this interdisciplinary endeavor revisits the gravitational constant "G," redefining it while bridging theoretical frameworks, thus paving the way for breakthroughs in astronomical and astrophysical sciences.

Quantum geometric approach: Nature and characteristics of emerged quantum-conditioned spacetime curvatures on three-sphere

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein’s GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR’s spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed.

Gravitational redshift revisited: Inertia, geometry, and charge

Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects—the most famous of which being the Pound–Rebka experiment—are extremely well-known. Nonetheless—and perhaps surprisingly—there remains a great deal of confusion in the literature regarding what these experiments really establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound–Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes does in fact require more. Second, although typically this ‘more’ is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called ‘geometric trinity’ of gravitational theories, in fact curvature is not necessary to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat (indeed, Minkowskian), this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner–Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded (and even be repulsive or blueshifted, respectively) in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.

The non-relativistic geometric trinity of gravity

The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) describing gravity in terms of spacetime non-metricity. In this article, we complete a geometric trinity of non-relativistic gravity, by (a) taking the non-relativistic limit of STEGR to determine its non-relativistic analogue, and (b) demonstrating that this non-metric theory is equivalent to Newton–Cartan theory and its teleparallel equivalent, i.e., the curvature and the torsion based non-relativistic theories that are both geometrised versions of classical Newtonian gravity.

Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’.

Probing general relativistic spin–orbit coupling with gravitational waves from hierarchical triple systems

ABSTRACT Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These phenomena, well known in optics and condensed matter physics, are referred to as spin Hall effects. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will have profound implications for astrophysics and tests of general relativity.

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

Relativistic generalized uncertainty principle for a test particle in four-dimensional spacetime

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, [Formula: see text], becomes uncertain. There exists a specific range of coordinates where the accessibility to [Formula: see text] is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value [Formula: see text]. This expectation value is dependent on [Formula: see text], which is itself limited by a minimum measurable length [Formula: see text]. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between [Formula: see text] and [Formula: see text] is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between [Formula: see text] and the Planck length [Formula: see text] is established with a proportionality factor of [Formula: see text], where [Formula: see text] denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction [Formula: see text], leading to an unrealistic [Formula: see text]. It is also noted that the lower limit of [Formula: see text] is directly proportional to the fundamental tensor.

Joule–Thomson expansion in a mimetic black hole

This paper investigates some implications of mimetic gravity on the black hole thermodynamics. We begin with an analysis of the mimetic action and its relationship to the spacetime curvature, highlighting the field equations and their contributions to the black hole solutions. Then we explore the behavior of various thermodynamic parameters including pressure, temperature and heat capacity, revealing some intriguing features of the system near the event horizon. We analyze also the inversion temperatures, inversion curves and the Joule–Thomson coefficients to enrich our comprehension of thermodynamic phenomena in this context. By extending coordinates close to the event horizon, we study the Joule–Thomson expansion, demonstrating how strong gravitational fields create pressure gradients similar to gas cooling processes. Comparison between mimetic black hole and Schwarzschild black hole in this setup provides a deeper understanding of the unique characteristics of the mimetic gravity.

Complex refractive index with the presence of nonlinear effects.

The refractive index during self-focusing was considered as a component of the metric tensor, it means, as a curvature of space-time. However, there was an interest – what will be, if the refractive index is complex. If we introduce a complex metric tensor, then the complex part will not curve space-time. At the same time, with the presence of nonlinear effects, damping modes will occur, it means, if n is linear, then the absorption will be α, but if n = n1 + n2I, then the absorption will be different, which will be discussed in this article.

Testing General Relativity with Juno at Jupiter

The Juno spacecraft has been orbiting Jupiter since 2016 July to deepen our comprehension of the solar system by studying the gas giant. The radio science experiment enables the determination of Jupiter’s gravitational field, thus shedding light on its interior structure. The experiment relies on determining the orbit of the spacecraft during its pericenter passages. Previous gravity data analyses assumed the correctness of the general theory of relativity, which was used for trajectory integration and radio signal propagation modeling. In this work, we aim to test general relativity within the unique context of a spacecraft orbiting Jupiter, by employing the parameterized post-Newtonian (PPN) formalism, an established framework for comparing various gravitational theories. Within this framework, we focus our attention toward the PPN parameters γ and β, which offer insights into the curvature of spacetime and the nonlinearity of gravitational effects, respectively. Additionally, we extend our investigation to the Lense–Thirring effect, which models the dragging of spacetime induced by a rotating mass. By measuring the relativistic frequency shift on Doppler observables caused by Jupiter during Juno’s perijove passes, we estimate γ = 1 + (1.5 ± 4.9) × 10−3, consistent with the general theory of relativity. Our estimated γ is primarily influenced by its effect on light-time computation, with a negligible contribution from spacecraft dynamics. Furthermore, we also present a modest level of accuracy for the β parameter, reflecting the minimal dynamical perturbation on Juno from general relativity. This also applies to the Lense–Thirring effect, whose signal is too small to be confidently resolved.

Persistent gravitational wave observables: nonlinearities in (non-)geodesic deviation

Abstract The usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, ‘persistent’ observables which measure permanent effects on idealized detectors have been introduced, each probing distinct physical effects. These observables can be defined in (regions of) any spacetime where there exists a notion of radiation, such as perturbation theory off of a fixed background, nonlinear plane wave spacetimes, or asymptotically flat spacetimes. Many of the persistent observables defined in the literature have only been considered in asymptotically flat spacetimes, and the perturbative nature of such calculations has occasionally obscured deeper relationships between these observables that hold more generally. The goal of this paper is to show how these more general results arise, and to do so we focus on two observables related to the separation between two, potentially accelerated observers. The first is the curve deviation, which is a natural generalization of the displacement memory, and also contains what this paper proposes to call drift memory (previously called ‘subleading displacement memory’) and ballistic memory. The second is a relative proper time shift that arises between the two observers, either at second order in their initial separation and relative velocity, or in the presence of relative acceleration. The results of this paper are, where appropriate, entirely non-perturbative in the curvature of spacetime, and so could be used beyond leading order in asymptotically flat spacetimes.

Circular motion and collisions of charged spinning particles near Kerr Newman black holes

We investigate the dynamics of spinning particles with an electric charge orbiting electrically charged Kerr–Newman black holes. First, we derive the equations of motion for the test particles using the Mathisson-Papapetrou-Dixon (MPD) equations, taking into account electromagnetic interaction and the interaction between the particle spin and the spacetime curvature known as the Lorentz coupling term in the MPD equation. We analyze the related effective potential in various scenarios of particle spin, angular momentum, and black hole spin orientation. In addition, we provide graphical analyses of the radius of innermost stable circular orbits (ISCOs) of the particles, their angular momentum, and energy at ISCOs and superluminal bounds. The ISCOs for positive and negatively charged particles are almost the same. The combined effects of the black hole and particle spins enhance the Coulomb interaction effect on the ISCO radius. The ISCO energy and angular momentum decrease with the increase in particle spin. In the Reissner–Nordström (RN) black hole limit, the decreasing rate is faster at positive values of the particle spin, and the spin limit changes in the Kerr–Newman black hole case. Finally, we study collisions between spinning charged particles near Kerr–Newman black holes. The critical values of the angular momentum of spinning charged particles are explored, and the particles can collide in various cases of particle and black hole spin, as well as the particle angular momentum. We also analyze electromagnetic and spin effects on the center-of-mass energy of the colliding particles.

Fermions with electric dipole moment in curved space–time

Fermions with electric dipole moment in curved space–time