Spacetime Geometry Research Articles

Numerical results on quantum energy inequalities in integrable models at the two-particle level

In this article, we study the impact of self-interaction and multiparticle states on sustaining negative energies in relativistic quantum systems. For physically reasonable models, one usually requires bounds on both magnitude and duration of the accumulation of negative energy, typically given in form of a quantum energy inequality (QEI). Such bounds have applications in semiclassical gravity where they exclude exotic spacetime geometries and imply the formation of singularities. The essence of this article is a novel numerical method for determining optimal QEI bounds at the one- or two-particle level, extending previous work focused on the one-particle case and overcoming a new type of technical challenge associated with the two-particle scenario. Our method is tailored for integrable models in quantum field theory constructed via the S-matrix boostrap. Applying the method to a representative model, the sinh-Gordon model, we confirm self-interaction as the source of negative energy, with stronger interactions leading to more pronounced negativities. Moreover, we establish the validity of QEIs and the averaged weak energy condition (AWEC) at the one- and two-particle level. Lastly, we identify a constrained one-parameter class of nonminimal stress tensor expressions satisfying QEIs at both levels, with more stringent constraints emerging from the QEI bounds at the two-particle level. Published by the American Physical Society 2024

More holographic M5 branes in AdS7 × S4

We study classical M5 brane solutions in the probe limit in the AdS7×S4 spacetime geometry with worldvolume 3-form flux. These solutions describe the holography of codimension-4 defects in the 6d boundary dual N=(0,2) supersymmetric gauge theories. Starting from some half-BPS solutions which follow stricter BPS conditions, we find a general 116-BPS solution. We show how some of the giant-like M5 brane solutions here may be related to the codimension-2 surface operators in the 4d gauge theory.

Causal Structure in Spin Foams

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry.

Study of boson stars with wormhole

In this paper, we study the mixed system of boson stars (BSs) with wormholes at their center. The boson star is obtained by employing a complex scalar field without self-interaction or a complex scalar field with quartic self-interaction and the wormhole is obtained by employing a phantom field. Utilizing the numerical method, we successfully obtain both symmetric and asymmetric solutions within the two asymptotically flat regions. The key focus of our study involves the systematic exploration of variations in results by varying the throat parameter η0, and the parameter c, representing the quartic term in potential. In the ground state, we find the mass M and Noether charge Q versus the scalar field frequencies ω are multi-valued curves when the η0 is small or the self-interaction is strong, the multi-valued curves will turn into single-valued curves as η0 or c increases. Furthermore, we observe that asymmetric solutions can transition into symmetric solutions at specific scalar field frequencies ω for certain settings of η0 and c. In addition, when it comes to the excited state, the properties of symmetric solutions remain akin to those in the ground state, while asymmetrical results display different characteristics from the ground state. We also present the wormhole spacetime geometry to investigate the properties of this model.

Modified f(Q,C) gravity dark energy models with observational constraints

We investigate an isotropic and homogeneous flat dark energy model in [Formula: see text] gravity theory that is linear in non-metricity Q and quadratic in boundary term C as [Formula: see text], where [Formula: see text] is a model parameter. We have solved the field equations in flat Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime geometry and considered a relation in the form of Hubble function in total energy density parameters [Formula: see text], [Formula: see text], and Hubble constant [Formula: see text]. We have compared our results with two observational datasets [Formula: see text] and Pantheon SNe Ia datasets by using MCMC analysis and have obtained the best fit present values of parameters. We have used these best fit values throughout in result analysis and discussion. We have found the equation of state (EoS) parameter as [Formula: see text] over [Formula: see text]. We have also investigated the Om diagnostic function and present age of the universe for these two datasets.

A study on matter accretion onto charged black hole solution in metric-affine gravity

This study deals with astrophysical accretion onto the charged black hole solution, which is sourced by the dilation, spin, and shear charge of matter in metric affine gravity. The metric affine gravity defines the link between torsion and nonmetricity in space–time geometry. In the current analysis, we study the accretion process of various perfect fluids that are accreting near the charged black hole in the framework of metric affine gravity. Within the domain of accretion, multiple fluids have been examined depending on the value of f1. The ultra-stiff, ultra-relativistic, and sub-relativistic fluids are considered in the discussion of accretion. In the framework of equations of state, we consider isothermal fluids for this investigation. Further, we explore the effect of polytropic test fluid on accretion disks, and it is presented in phase diagrams. Some important aspects of the accretion process are investigated. Analyzing the accretion rate close to a charged black hole solution, typical behavior is created and discussed graphically.

Spacetime geometry from Dirac spinor theory

Spacetime geometry from Dirac spinor theory

Rotating curved spacetime signatures from a giant quantum vortex.

Gravity simulators1 are laboratory systems in which small excitations such as sound2 or surface waves3,4 behave as fields propagating on a curved spacetime geometry. The analogy between gravity and fluids requires vanishing viscosity2-4, a feature naturally realized in superfluids such as liquid helium or cold atomic clouds5-8. Such systems have been successful in verifying key predictions of quantum field theory in curved spacetime7-11. In particular, quantum simulations of rotating curved spacetimes indicative of astrophysical black holes require the realization of an extensive vortex flow12 in superfluid systems. Here we demonstrate that, despite the inherent instability of multiply quantized vortices13,14, a stationary giant quantum vortex can be stabilized in superfluid 4He. Its compact core carries thousands of circulation quanta, prevailing over current limitations in other physical systems such as magnons5, atomic clouds6,7 and polaritons15,16. We introduce a minimally invasive way to characterize the vortex flow17,18 by exploiting the interaction of micrometre-scale waves on the superfluid interface with the background velocity field. Intricate wave-vortex interactions, including the detection of bound states and distinctive analogue black hole ringdown signatures, have been observed. These results open new avenues to explore quantum-to-classical vortex transitions and use superfluid helium as a finite-temperature quantum field theory simulator for rotating curved spacetimes19.

Quantum matter and gravitation: photons in a waveguide

The conditions required by quantum matter to modify space-time geometry are explored within the framework of the general theory of relativity. The required characteristics for space-time modification in solid state structures, are met in either (a) massive photon Bose–Einstein condensate in a waveguide, or (b) the massive photons in superconductor’s bulk, or (c) the Bose–Einstein condensate of acoustic phonons, or (d) a metal–insulator-topological insulator heterostructure.

Observation of vortex-string chiral modes in metamaterials

As hypothetical topological defects in the geometry of spacetime, vortex strings could have played many roles in cosmology, and their distinct features can provide observable clues about the early universe’s evolution. A key feature of vortex strings is that they can interact with Weyl fermionic modes and support massless chiral-anomaly states along strings. To date, despite many attempts to detect vortex strings in astrophysics or to emulate them in artificially created systems, observation of these vortex-string chiral modes remains experimentally elusive. Here we report experimental observations of vortex-string chiral modes using a metamaterial system. This is implemented by inhomogeneous perturbation of Yang-monopole phononic metamaterials. The measured linear dispersion and modal profiles confirm the existence of topological modes bound to and propagating along the string with the chiral anomaly. Our work provides a platform for studying diverse cosmic topological defects in astrophysics and offers applications as topological fibres in communication techniques.

Gromoll–Meyer's actions and the geometry of (exotic) spacetimes

Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a different smooth structure assumption to some classical known model could produce different physical meanings. Motivated by the works [27,2], [3,18], in this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll–Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers.

Particle production from non-minimal coupling in a symmetry breaking potential transporting vacuum energy

We propose an inflationary scenario where the inflaton field is non-minimally coupled to spacetime curvature and inflation is driven by a vacuum energy symmetry breaking potential without specifying a priori whether the inflaton field is small or large. As we incorporate vacuum energy into our analysis, we further explore the implications of a non-zero potential offset within inflationary dynamics. We propose that vacuum energy can transform into particles as a result of the transition triggered by spontaneous symmetry breaking. This entails a vacuum energy cancellation that yields an effective cosmological constant during inflation by virtue of a quasi-de Sitter evolution and shows that vacuum energy contribution can manifest as geometric particles produced by inflaton fluctuations, with particular emphasis on super-Hubble modes. We conjecture these particles as quasi-particles arising from interaction between the inflaton and spacetime geometry, enhanced by non-minimal coupling. Specifically, we propose that dark matter arises from a pure geometric quasi-particle contribution, quantifying the corresponding dark matter candidate ranges of mass. In this scenario, we further find that a zero potential offset leads to a bare cosmological constant at the end of inflation, while a negative offset would require an additional kinetic (or potential) contribution in order to be fully-canceled. In this regard, we conclude that the scenario of large-field inflation is preferred since it necessitates a more appropriate selection of the offset. Our conclusion is reinforced as small-field inflation would lead to a significant screening of the Newtonian gravitational constant as inflation ends.

An exact new solution of the Schrödinger equation with a zero potential energy analogous to Fick’s equation of diffusion

This paper presents a novel and exact solution of the Schrödinger equation with zero potential energy, based on the analogy with Fick’s equation of diffusion. The author derived the wavefunction of a particle in a vacuum as an error function of the rotational phase angle, which corresponds to the geometry of a flat space. This solution reduces to the sinusoidal form of the wavefunction commonly used in quantum mechanics. The author also explored the implications of this solution for the connection between quantum physics and gas mechanics, and the possibility of using error functions and general transforms to model past, present, and future events in physics. The author used computer simulations to compare the error function solution and the sinusoidal solution in terms of response time, accuracy, and fit to the geometry of a flat space. The results showed that the error function solution was superior to the sinusoidal solution in all aspects, and that it had a stronger link to the gas mechanics, useful to Quantum ASTROPHYSICS. The results also suggested that the error function solution could be used to model past, present, and future events in physics, using error functions and general transforms. This paper is a preliminary analysis of the deeper physics underlying the error function solution of the Schrödinger equation, based on the author’s previous publications on point physics generalizing to Hod-PDP mechanism, field tensor modeling, string-metrics, and information-time event matrix formulations. The paper recommends that future research should extend the error function solution to space time geometry higher dimensions, non-zero potentials, and more diverse experiments. The paper also recommends that future research should explore the applications of error functions and general transforms within physics and other mathematical physical general related fields of sciences.

Spacetime geometry from canonical spherical gravity

Spacetime geometry from canonical spherical gravity

Spontaneous collapse models lead to the emergence of classicality of the Universe

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can one then describe the emergence of the classical, well-defined geometry that we observe? Considering that the decoherence-driven quantum-to-classical transition relies on external physical entities, this process cannot account for the emergence of the classical behaviour of the Universe. Here, we show how models of spontaneous collapse of the wavefunction can offer a viable mechanism for explaining such an emergence. We apply it to a simple General Relativity dynamical model for gravity and a perfect fluid. We show that, by starting from a general quantum superposition of different geometries, the collapse dynamics leads to a single geometry, thus providing a possible mechanism for the quantum-to-classical transition of the Universe. Similarly, when applying our dynamics to the physically-equivalent Parametrised Unimodular gravity model, we obtain a collapse on the basis of the cosmological constant, where eventually one precise value is selected, thus providing also a viable explanation for the cosmological constant problem. Our formalism can be easily applied to other quantum cosmological models where we can choose a well-defined clock variable.

Black hole formation in gravitational collapse and their astrophysical implications

In this study, we have explored the process of black hole (BH) formation occurring in the collapse of a self-gravitating configuration using an innovative approach. The exact solution of the Einstein field equations is obtained in a model-independent way by considering a parametrization of the expansion scalar (Θ) in the background of spherically symmetric space-time geometry governed by the FLRW metric. Smooth matching of the interior solution with the Schwarzschild exterior metric across the boundary hypersurface of the star, together with the condition that the mass function m(t, r) is equal to Schwarzschild mass M, is used to obtain all the physical and geometrical parameters in terms of the stellar mass. The four known massive stars namely R136a3, Melnick, R136c, and R136b with their known astrophysical data (mass, radius, and present age) are used to study the physics of the model both numerically and graphically. We demonstrate that the formation of the apparent horizon occurs earlier than the singular state that is, the collapse of massive stars in our model results in the eventual formation of black holes as their final state. We have conducted an analysis indicating that the lifespans of massive stars are closely related to their respective masses. Our findings demonstrate that more massive stars exhibit considerably shorter lifespans in comparison to their lighter counterparts. Thus, the presented model corresponds to the evolutionary stages of astrophysical stellar objects and theoretically predicts their possible lifespan. We have also shown that our model satisfies the energy conditions and stability requirements via Herrera’s cracking method.

Spacetime geometry of acoustics and electromagnetism

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The resulting extensions are geometrically complete and phase-invariant (i.e., dual-symmetric) formulations that span all five grades of spacetime, with dynamical potentials and measurable fields spanning complementary grades that are related by a spacetime vector derivative (i.e., the quantum Dirac operator). These complete representations correct the equations of motion, energy–momentum tensors, forces experienced by probes, Lagrangian densities, and allowed gauge freedoms, while making manifest the deep structural connections to relativistic quantum field theories. Finally, we discuss the implications of these corrections to experimental tests.

Influence phase of a dS observer. Part I. Scalar exchange

Inspired by real-time computations in AdS black holes, we propose a method to obtain the influence phase of a cosmological observer by calculating the on-shell action on a doubled spacetime geometry. The influence phase is the effective action for an open system: for a dS static patch observer coupled to a scalar field it incorporates the radiation reaction due to the bulk fields and their dS Hawking radiation. For a general extended source in dS, we describe how to account for finite size effects. In the long-time limit, we get a Markovian open quantum system susceptible to cosmological fluctuations, whereas the short-time limit reproduces the worldline theory of flat-space radiation reaction. We also present a fully covariantised form for the cubic corrections to the radiation reaction in even spacetime dimensions, including Hubble contributions, and find an intriguing recursive structure across dimensions.

Femtoscopy with Lévy Sources from SPS through RHIC to LHC

Femtoscopy is a unique tool to investigate the space-time geometry of the matter created in ultra-relativistic collisions. If the probability density distribution of hadron emission is parametrized, then the dependence of its parameters on particle momentum, collision energy, and collision geometry can be given. In recent years, several measurements came to light that indicated the adequacy of assuming a Lévy-stable shape for the mentioned distribution. In parallel, several new phenomenological developments appeared, aiding the interpretation of the experimental results or providing tools for the measurements. In this paper, we discuss important aspects of femtoscopy with Lévy sources in light of some of these advances, including phenomenological and experimental ones.

Charged Particles Orbiting Charged Black-Bounce Black Holes

The detailed and comprehensive analysis of radiation processes in accretion disks consisting of electrically charged particles around black holes may provide powerful information about the spacetime geometry of the central black hole. We investigate the circular orbits of electrically charged particles around an electrically charged black-bounce Reissner–Nordström (RN) black hole, known as an RN Simpson–Visser (SV) black hole. We also study the profiles of the innermost stable circular orbits (ISCOs), energy, and angular momentum of the particles in their ISCOs, as well as the efficiency of energy release processes in the accretion disk in the Novikov–Thorne model. Finally, we calculate and study the effects of the black-bounce parameter as well as the black-hole charge on the intensity of the radiation of ultrarelativistic charged particles orbiting the charged RN SV black hole along circular orbits and falling into the black hole. It is observed that the black-bounce parameter essentially decreases the ISCO radius, and consequently the energy extraction and intensity of electromagnetic radiation.