Search Results (398)

The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant $d{s}^2$, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Albert Einstein initially sought a dynamical formulation in which $d{s}^2$ encoded the gravitational effects, without invoking curvature as a physical entity. The now more familiar geometrical interpretation—identifying gravitation with spacetime curvature—gradually emerged through his collaboration with Marcel Grossmann and the adoption of the Ricci tensor in 1915. Anyhow, in his 1920 Leiden lecture, Einstein explicitly reinterpreted spacetime geometry as the state of a physical medium—an “ether” endowed with metrical properties but devoid of mechanical substance—thereby actually rejecting geometry as an independent ontological reality. Building upon this mature view, gravitation is reconstructed from the Weak Equivalence Principle, understood as the exact compensation between inertial and gravitational forces acting on a body under a uniform gravitational field. From this fundamental principle, together with an extension of Fermat’s Principle to massive objects, the invariant $d{s}^2$ is obtained, first in the static case, where the gravitational potential modifies the flow of proper time. Then, by applying the Lorentz transformation to this static invariant, its general form is derived for the case of matter in motion. The resulting invariant reproduces the relativistic form of Newton’s second law in proper time and coincides with the weak-field limit of General Relativity in the harmonic gauge. This approach restores the operational meaning of Einstein’s theory: spacetime geometry represents dynamical relations between physical measurements, rather than the substance of spacetime itself. By deriving the gravitational modification of the invariant directly from the Weak Equivalence Principle, Fermat Principle and Lorentz invariance, this formulation clarifies the physical origin of the metric structure and resolves long-standing conceptual issues—such as the recurrent hole argument—while recovering all the empirical successes of General Relativity within a coherent and sound Machian framework. Full article

Rapid detection and follow-up of electromagnetic (EM) counterparts to gravitational wave (GW) signals from binary neutron star (BNS) mergers are essential for constraining source properties and probing the physics of relativistic transients. Observational strategies for these early EM searches are therefore critical, yet current practice remains suboptimal, motivating improved, coordination-aware approaches. We propose and evaluate the Two-Step Localization strategy, a coordinated observational protocol in which one wide-field auxiliary telescope and one narrow-field main telescope monitor the evolving GW sky localization in real time. The auxiliary telescope, by virtue of its large field of view, has a higher probability of detecting early EM emission. Upon registering a candidate signal, it triggers the main telescope to slew to the inferred location for prompt, high-resolution follow-up. We assess the performance of Two-Step Localization using large-scale simulations that incorporate dynamic sky-map updates, realistic telescope parameters, and signal-to-noise ratio (SNR)-weighted localization contours. For context, we compare Two-Step Localization to two benchmark strategies lacking coordination. Our results demonstrate that Two-Step Localization significantly reduces the median detection latency, highlighting the effectiveness of targeted cooperation in the early-time discovery of EM counterparts. Our results point to the most impactful next step: next-generation faster telescopes that deliver drastically higher slew rates and shorter scan times, reducing the number of required tiles; a deeper, truly wide-field auxiliary improves coverage more than simply adding more telescopes. Full article

Phosphorus-31 nuclear magnetic resonance (³¹P NMR) spectroscopy is a powerful analytical physical chemistry experimental technique that is widely used to study the structure and dynamics of phosphorus-containing compounds today. Accurate calculation of ³¹P NMR chemical shifts lies in the basis of the proper assignment of NMR signals, as they can be closely spaced to each other in the NMR spectra of systems that bear nuclei with subtly different electron environments, like complex organophosphorus compounds, nucleic acids, and phosphates, etc. The most advanced quantum chemistry (QC) methods allow us to reach the agreement between theoretical values of ³¹P NMR chemical shifts and experiments within a few ppm, which makes them a useful tool for studying chemical structure, reaction mechanisms, and catalyst design with the aid of the NMR method. This review surveys the application of both density functional and wave function methods of electron structure to the calculation of ³¹P NMR chemical shifts and proposes a thorough discussion of the latest findings related to the factors affecting the final accuracy of the ³¹P NMR chemical shifts prediction, including basis sets, the geometry factor effect, solvent, vibrational, and relativistic corrections. Full article

In Minkowski 3-space, we establish a geometric framework to osculate Type-II ruled surfaces by utilizing the Type-II Bishop frame in $\left({\mathbb{E}}_1^3\right)$. Our analysis extends to higher-order singularities such as butterflies and pyramids, including explicit singularity loci. We also compare Type-II Bishop frames with rotation-minimizing frames using timelike base curves and spacelike normals. With RK4 integration, we develop a robust computational model for Weingarten surfaces and subclasses with constant curvature. The theoretical foundation for Type-II Bishop frames is extended to higher-dimensional Minkowski spaces ${\mathbb{E}}_1^n$ for $n>3$ through generalized Frenet-type equations and curvature functions. We determine exact stability conditions under perturbations of Bishop curvature using advanced singularity theory. The numerical implementations of our methods, including geometric modeling and relativistic geometry, demonstrate their effectiveness in both theoretical and applied contexts. Full article

Large density fluctuations near the QCD critical point can be probed via intermittency analysis, which involves measuring scaled factorial moments (SFMs) of multiplicity distributions in relativistic heavy-ion collisions. Intermittency reflects the emergence of scale invariance and self-similar structures, which are closely related to symmetry principles and their breaking near a second-order phase transition. We present a systematic model study of intermittency for charged hadrons in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 $\mathrm{GeV}$. Using the cascade UrQMD model, we demonstrate that non-critical background effects can produce sizable SFMs and a large scaling exponent if they are not properly removed using the mixed-event subtraction method. To estimate the possible critical intermittency signal in experimental data, we employ a hybrid UrQMD+CMC model, in which fractal critical fluctuations are embedded into the UrQMD background. A direct comparison of the second-order SFM between the model and STAR experimental data suggests that a critical intermittency signal on the order of approximately $1.8\%$ could be present in the most central Au+Au collisions at RHIC energies. This study provides practical guidance for evaluating background contributions in intermittency measurements and offers a quantitative estimate for the critical signal fraction present in the STAR data. Full article

We revisit the premise that spacetime geometry must be quantized and show that this assumption is not physically required. Just as one does not quantize pressure or temperature, quantizing the metric treats a macroscopic continuum variable as if it were microscopic. We develop an alternative approach, Chronon Field Theory (ChFT), in which a smooth timelike covector ${\mathrm{\Phi }}_{\mu }$ obeys a unified variational principle—the Temporal Coherence Principle (TCP). In appropriate long-wavelength and low-vorticity regimes, the TCP dynamics yield an emergent Lorentzian metric and reproduce the Einstein field equations to leading order. Phase-coherent excitations exhibit a universal invariant speed and admit an eikonal limit that reproduces Hamilton–Jacobi and Schrödinger-type dynamics. Despite the presence of a microscopic causal alignment field, exact operational Lorentz invariance is preserved because all observers and measuring devices co-emerge from the same causal medium. The framework predicts small higher-order dispersive corrections to relativistic propagation while maintaining a universal causal cone, with effects constrained by fast radio burst and multi-messenger observations. ChFT thus provides a compact effective description in which gravitational and quantum dynamics emerge from a single coherence principle, without postulating quantum geometry at the fundamental level. Full article

We consider a model problem of polarization-dependent light bending and time delays in the vicinity of neutron stars endowed with magnetar-strength magnetic fields (B∼${10}^{15}\mathrm{G}$), combining an effective-metric formulation of Heisenberg–Euler nonlinear electrodynamics with general-relativistic ray tracing. The spacetime geometry is analyzed using both the Kerr metric and a quadrupole-deformed q-metric, characterized by a quadrupole parameter varying in the range $q\in [{10}^{-3},0.5]$. In addition, the impact of complex magnetic-field topologies is examined by introducing a magnetic quadrupole component alongside the dipole configuration. The simulations performed in this study demonstrate that the inclusion of the quadrupole deformation parameter significantly modifies photon trajectory deflections compared to the standard Kerr solution. We further quantify the geometric dilution of the photon beam, finding a cross-section expansion ratio of approximately $4.7\times {10}^{13}$ for rays reaching Earth. This strong dilution imposes stringent constraints on the detectability of polarization-dependent signatures and time-delay echoes. Finally, characteristic illustrations are presented for trajectory distortions, bending-angle distributions, and intensity valleys produced by the combined gravitational and magnetic lensing effects. Full article

This paper investigates the validity of the long wavelength approximation in the calculation of two-photon decay of $2s_{1/2}$ level in hydrogen-like ions with nuclear charge $Z=1-100$ based on time-dependent second-order perturbation theory and angular momentum algebra. While the relativistic structure effects on the two-photon decay rates are highlighted in the literature, the role of slowing effects in the photon electric dipole operators are not discussed extensively. The rate is computed by the sum-over-states method, with bound-bound and bound-free electric dipole matrix elements obtained in the Babushkin and Coulomb gauges, which satisfy the Lorenz gauge condition, as well as their non-relativistic limits in the long-wavelength approximation (Length and Velocity forms, respectively). The present results explicitly show how this approximation breaks gauge invariance by overestimating the Babushkin values by ∼24%${\left(\alpha Z\right)}^2$ while underestimating the Coulomb rates by ∼$31\%{\left(\alpha Z\right)}^2$. Using analytical eigenfunctions of the Dirac equation, we found that the contributions of the negative continuum states to the rate scale are ∼$0.0134{\left(\alpha Z\right)}^4$ in the Babushkin gauge and ∼$1.46{\left(\alpha Z\right)}^4$ in the Coulomb gauge, making the latter gauge more susceptible to errors when attempting to achieve basis completeness in multiphoton calculations. The present results are useful in assessing the complexity requirements of radiative transition rates for atomic systems of interest. Full article

We present a detailed derivation of the quantum and quantum–thermal effective action for non-relativistic systems, starting from the single-particle case and extending to the Gross–Pitaevskii (GP) field theory for weakly interacting bosons. In the single-particle framework, we introduce the one-particle-irreducible (1PI) effective action formalism, taking explicitly into account the choice of the initial quantum state, its saddle-point plus Gaussian-fluctuation approximation, and its finite-temperature extension via Matsubara summation, yielding a clear physical interpretation in terms of zero-point and thermal contributions to the Helmholtz free energy. The formalism is then applied to the GP action, producing the 1PI effective potential at zero and finite temperature, including beyond-mean-field Lee–Huang–Yang and thermal corrections. We discuss the gapless and gapped Bogoliubov spectra, their relevance to equilibrium and non-equilibrium regimes, and the role of regularization. Applications include the inclusion of an external potential within the local density approximation, the derivation of finite-temperature Josephson equations, and the extension to D-dimensional systems, with particular attention to the zero-dimensional limit. This unified approach provides a transparent connection between microscopic quantum fluctuations and effective macroscopic equations of motion for Bose–Einstein condensates. Full article

Superheavy elements are an ideal testbed for studying relativistic, exchange, and correlation effects in scattering phenomena. In this work, we investigate electron scattering from copernicium $(Z=112)$ and oganesson $(Z=118)$ atoms. Both the relativistic Dirac and non-relativistic partial wave methods are employed to analyze the scattering dynamics, with the interaction between the projectile and target atom modeled within the framework of the optical potential approach. Our results demonstrate that relativistic, exchange, and correlation effects play a significant role in modifying the scattering cross-sections and scattering length, highlighting the influence of these interactions on the scattering processes from superheavy atomic systems. The work also attempts to identify common features of the scattering cross-section by comparing those of lighter elements in the same group. Full article

A general relativistic model of an astrophysical hypermassive extremely magnetized ultra-compact self-bound quark–gluon plasma (QGP: ALICE/LHC) object that is supported against its ultimate gravitational implosion by the simultaneous action of the vacuum polarization driven by nonlinear electrodynamics (NLED: ATLAS/LHC: light-by-light scattering)—the vacuum “awakening”—and the asymptotic freedom, a key feature of quantum chromodynamics (QCD), is presented. These QCD stars can be the final figures of the equilibrium of collapsing stellar cores permeated by magnetic fields with strengths well beyond the Schwinger threshold due to being self-bound, and for which post-supernova fallback material pushes the nascent remnant beyond its stability, forcing it to collapse into a hybrid hypermassive neutron star (HHMNS). Hypercritical accretion can drive its innermost core to spontaneously break away color confinement, powering a first-order hadron-to-quark phase transition to a sea of ever-freer quarks and gluons. This core is hydro-stabilized by the steady, endlessly compression-admitting asymptotic freedom state, possibly via gluon-mediated enduring exchange of color charge among bound states, e.g., the odderon: a glueball state of three gluons, or either quark-pairing (color superconductivity) or tetraquark/pentaquark states (LHCb Coll.). This fast—at the QGP speed of sound—but incremental quark–gluon deconfinement unbinds the HHMNS’s baryons so catastrophically that transforms it, turning it inside-out, into a neat self-bound QGP star. A solution to the nonlinear Tolman–Oppenheimer–Volkoff (TOV) equation is obtained—that clarifies the nonlinear effects of both NLED and QCD on the compact object’s structure—which clearly indicates the occurrence of hypermassive QGP/QCD stars with a wide mass spectrum ($0\lesssim {\mathrm{M}}_{\mathrm{Star}}^{\mathrm{QGP}}\lesssim$ 7 M_⊙ and beyond), for star radii ($0\lesssim R_{\mathrm{Star}}^{\mathrm{QGP}}\lesssim 24$ km and beyond) with B-fields (${10}^{14}\le {\mathrm{B}}_{\mathrm{Star}}^{\mathrm{QGP}}\le {10}^{16}$ G and beyond). This unexpected feature is described by a novel mass vs. radius relation derived within this scenario. Hence, endowed with these physical and astrophysical characteristics, such QCD stars can definitively emulate what the true (theoretical) black holes are supposed to gravitationally do in most astrophysical settings. This color quark star could be found through a search for its eternal “yo-yo” state gravitational-wave emission, or via lensing phenomena like a gravitational rainbow (quantum mechanics and gravity interaction), as in this scenario, it is expected that the light deflection angle—directly influenced by the larger effective mass/radius (${\mathrm{M}}_{\mathrm{Star}}^{\mathrm{QGP}}\left(B\right)$, ${\mathrm{R}}_{\mathrm{Star}}^{\mathrm{QGP}}\left(B\right)$) and magnetic field of the deflecting object—increases as the incidence angle decreases, in view of the lower values of the impact parameter. The gigantic—but not infinite—surface gravitational redshift, due to NLED photon acceleration, makes the object appear dark. Full article

Using a relativistic mean-field model calibrated to finite-nucleus observables and bulk properties of dense nuclear matter, we investigate hyperonic neutron-star matter within an SU(3) flavor symmetry scheme. To retain SU(6)-based couplings within SU(3) flavor symmetry, we introduce a quartic $\varphi$ self-interaction and $\varphi$-$\rho$ mixing. We demonstrate the roles of ${\alpha }_v$ ($F/(F+D)$ ratio), ${\theta }_v$ (mixing angle), and $z_v$ (singlet-to-octet coupling ratio) in SU(3)-invariant vector-meson couplings. It is found that $z_v$ predominantly controls the maximum mass of a neutron star, and $2M_{\odot }$ neutron stars can be supported for $z_v\le 0.15$. The ${\alpha }_v$ also helps sustain large masses, whereas ${\theta }_v$ has a smaller effect on neutron-star properties. This SU(3) framework reconciles nuclear and astrophysical constraints and offers a plausible resolution of the hyperon puzzle. Full article

Relativistic jets from active galactic nuclei (AGN) have been a topic of peak interest in the high-energy astrophysics community for their uniquely dynamic nature and incredible radiative power emanating from supermassive black holes and similarly accreting compact dense objects. An overall consensus on relativistic jet formation states that accelerated outflow at high Lorentz factors are generated by a complex relationship between the accretion disk of the system and the frame-dragging effects of the rotating massive central object. This paper will provide a basis for which circular polarization states, defined using a spin tetrad formalism, contribute to a description for the angular momentum flux in the jet emanating from the central engine. A representation of the Kerr spacetime is used in formulating the spin tetrad forms. A discussion on unresolved problems in jet formation and how we can use multi-method observations with polarimetry of AGN to direct future theoretical descriptions will also be given. Full article

We investigate the effect of general relativity on the Sitnikov problem. The Sitnikov problem is one of the simplest three-body problems, in which the two primary bodies (a binary system) have equal mass m and orbit their barycenter, while the third body is treated as a test particle under Newtonian gravity. The trajectory of the test particle is perpendicular to the orbital plane of the binary (along z-axis) and passes through the barycenter of the two primaries. To study the general relativistic contributions, we first derive the equations of motion for both the binary and the test particle based on the first post-Newtonian Einstein–Infeld–Hoffmann equation, and integrate these equations numerically. We examine the behavior of the test particle (third body) as a function of the orbital eccentricity of the central binary e, the dimensionless gravitational radius $\lambda$, which characterizes the strength of general relativistic effect, and the initial position of the test particle ${\overline{z}}_0$. Our numerical calculations reveal the following; as general relativistic effects $\lambda$ increase and the eccentricity e of the binary orbit grows, the distance $\overline{r}$ between the test particle and the primary star undergoes complicated oscillations over time. Consequently, the gravitational force acting on the test particle also varies in a complex manner. This leads to a resonance state between the position $\overline{z}$ of the test particle and the distance $\overline{r}$, causing the energy E of the test particle to become $E\ge 0$. This triggers the effective ejection of the test particle due to the gravitational slingshot effect. In this paper, we shall refer to this ejection mechanism of test particle as the “Sitnikov mechanism.” As a concrete phenomenon that becomes noticeable, the increase in general relativistic effects and the eccentricity of the binary orbit leads to the following: (a) ejection of test particles from the system in a shorter time, and (b) increasing escape velocity of the test particle from the system. As an astrophysical application, we point out that the high-velocity ejection of test particles induced by the Sitnikov mechanism could contribute to elucidating the formation processes of astrophysical jets and hyper-velocity stars. Full article

We present a comprehensive quantum field theoretical analysis of graviton self-energy and mass generation in 3+1 dimensional BTZ black hole spacetime, incorporating axion interactions within the framework of dark matter theory. Using a novel mathematical approach based on ultrahyperfunctions, generalizations of Schwartz tempered distributions to the complex plane, we derive exact quantum relativistic expressions for graviton and axion self-energies without requiring ad hoc regularization procedures. Our approach extends the Gupta–Feynman quantization framework to BTZ gravity while introducing a new constraint that eliminates unitarity violations inherent in previous formulations, thereby avoiding the need for ghost fields. Through systematic application of generalized Feynman parameters, we evaluate both bradyonic and tachyonic graviton modes, revealing distinct quantum correction patterns that depend critically on momentum, energy, and mass parameters. Key findings include (1) natural graviton mass generation through cosmological constant interactions, yielding $m^2=2\left|\mathsf{\Lambda }\right|/\kappa (1-\kappa )$; (2) qualitatively different quantum behaviors between bradyonic and tachyonic modes, with bradyonic corrections reaching amplitudes 6 times larger than their tachyonic counterparts; (3) the discovery of momentum-dependent quantum dissipation effects that provide natural ultraviolet regulation; and (4) the first explicit analytical expressions and graphical representations for 17 distinct graviton self-energy contributions. The ultrahyperfunction formalism proves essential for handling the non-renormalizable nature of the theory, providing mathematically rigorous treatment of highly singular integrals while maintaining Lorentz invariance. Our results suggest observable consequences in gravitational wave propagation through frequency-dependent dispersive effects and modifications to black hole thermodynamics, potentially bridging theoretical quantum gravity with experimental constraints. Full article