Background Spacetime Research Articles

The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation

In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.

Gravitational lensing in a spacetime with cosmic string within the Eddington-inspired Born–Infeld gravity

This study explores the deflection angle of photon rays or light-like geodesics within the framework of Eddington-inspired Born–Infeld (EiBI) gravity background space-time, taking into account the influence of cosmic strings. The primary focus lies in deriving the effective potential of the system applicable to both null and time-like geodesics, as well as determining the angle of deflection for light-like geodesics. Our analysis shows that the presence of cosmic strings induces modifications in these physical quantities, leading to shifts in their respective values.

Micro-cosmos model of a nucleon

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro-cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton’s radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro-cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics.

The optical features of noncommutative charged 4D-AdS-Einstein–Gauss–Bonnet black hole: shadow and deflection angle

In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a 4D-AdS-Einstein–Gauss–Bonnet black hole. This solution, which finds its inspiration in noncommutative geometry, had previously been established in our previous work. The radius of the shadow was determined using the Hamilton-Jacobi method and the Carter separation. Our results revealed that the presence of noncommutativity in the background of spacetime impacts the variation of the shadow radius. More specifically, we have demonstrated that an increase in the parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} induces a decrease in the radius of the shadow. In a similar way, analogous observations have been made by studying the variation of the electric charge Q. The noncommutative parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} and the electric charge Q have been constrained regarding the EHT observation data of the M87* and Sgr A* black holes. Furthermore, the angle of deflection, which is the outcome of lensing by the black hole, has been derived following the Ishihara et al. approach for a receiver and source positioned at finite distances from the black hole in an asymptotically non-flat spacetime. The impact of the noncommutative parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} and the charge Q of the black hole are hence analyzed, and our results depict that these parameters have a significant influence on the angle at which light is deflected by the gravitational field of the black hole.

Klein–Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality

We use two correlated metric functions and transform/deform the pointlike global monopole (PGM) spacetime metric into a quasi-PGM (QPGM) spacetime one. We study Klein–Gordon (KG) particles (manifestly introduced by the non-minimal coupling form of the operator D˜μ=Dμ+Fμ , with Fμ ∈R , and D μ = ∂ μ − ie A μ ) in such QPGM spacetime background. We show that the KG-particles in the QPGM spacetime are isospectral and invariant with KG-particles in the PGM spacetime, provided that the two metric functions are correlated. The Wu-Yang magnetic monopole (WYMM) is also included in the process. We report the effects of both monopoles PGM/QPGM and WYMM on the spectroscopic structure of two models, KG-oscillators and KG-Coulomb particles in such spacetime background. Moreover, we discuss KG-Coulomb particles and shifted KG-oscillators in a PGM spacetime and a WYMM, where such models are manifestly introduced by some Lorentz scalar interaction potentials S(r). The current study is not only of fundamental observability nature but also of pedagogical interest in quantum gravity.

Study of scalar particles through the Klein–Gordon equation under rainbow gravity effects in Bonnor–Melvin-Lambda space-time

In our investigation, we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity, considering the Bonnor–Melvin-Lambda (BML) space-time background. The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constant Λ and the topological parameter α of the geometry. The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated, utilizing two sets of rainbow functions: (i) f(χ)=(eβχ−1)βχ , h(χ) = 1 and (ii) f(χ) = 1, h(χ)=1+βχ2 . Here 0<χ=∣E∣Ep≤1 with E representing the particle’s energy, E p is the Planck’s energy, and β is the rainbow parameter. We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results. Afterwards, we study the quantum dynamics of quantum oscillator fields within this BML space-time, employing the Klein–Gordon oscillator. Here also, we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields. Notably, we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant. Furthermore, we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.

Boyer–Lindquist Space-Times and Beyond: Metamaterial Analogues for Arbitrary Space-Times

Analogue space-times (and in particular metamaterial analogue space-times) have a long varied and rather complex history. Much of the previous related work to this field has focused on spherically symmetric models; however, axial symmetry is much more relevant for mimicking astrophysically interesting systems that are typically subject to rotation. Now it is well known that physically reasonable stationary axisymmetric space-times can, under very mild technical conditions, be put into Boyer–Lindquist form. Unfortunately, a metric presented in Boyer–Lindquist form is not well adapted to the “quasi-Cartesian” metamaterial analysis that we developed in our previous articles on “bespoke analogue space-times”. In the current article, we shall first focus specifically on various space-time metrics presented in Boyer–Lindquist form, and subsequently determine a suitable set of equivalent metamaterial susceptibility tensors in a laboratory setting. We shall then turn to analyzing generic space-times, not even necessarily stationary, again determining a suitable set of equivalent metamaterial susceptibility tensors. Perhaps surprisingly, we find that the well-known ADM formalism proves to be not particularly useful, and that it is instead the dual “threaded” (Kaluza–Klein–inspired) formalism that provides much more tractable results. While the background laboratory metric is (for mathematical simplicity and physical plausibility) always taken to be Riemann flat, we will allow for arbitrary curvilinear coordinate systems on the flat background space-time. Finally, for completeness, we shall reconsider spherically symmetric space-times, but now in general spherical polar coordinates rather than quasi-Cartesian coordinates. In summary, this article provides a set of general-purpose calculational tools that can readily be adapted for mimicking various interesting (curved) space-times by using nontrivial susceptibility tensors in general (background-flat) laboratory settings.

Gravitational self force from scattering amplitudes in curved space

We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with mass m orbiting in the background spacetime induced by a heavy gravitational source with mass M. Observables are organized as an expansion in m/M to all orders in G — the gravitational self-force expansion. An essential component of our analysis is the backreaction of the heavy source which we capture by including the associated light degrees of freedom. As illustration we consider a Schwarzschild background and verify geodesic motion as well as the first-order self-force correction to two-body scattering through \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}$$\\end{document}(G3). Amplitudes in curved space offer several advantages, and further developments along these lines may advance the computation of gravitational-wave signals for extreme-mass-ratio inspirals.

Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole

In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.

Gravitational Landau levels and the chiral anomaly

A popular physical picture of the mechanism behind the four-dimensional chiral anomaly is provided by the massless Dirac equation in the presence of constant electric and magnetic background fields. The magnetic field creates highly degenerate Landau levels, the lowest of which is gapless. Any parallel component of the electric field drives a spectral flow in the gapless mode that causes particles to emerge from, or disappear into, the Dirac sea. Seeking a similar picture for the gravitational contribution to the chiral anomaly, we consider the massless Dirac equation in a background spacetime that creates gravitational Landau levels. We find that in this case the resulting spectral flow, with its explicit particle production, accounts for only a small part of the anomalous creation of chiral charge. The balance is provided by the vacuum expectation charge arising from the spectral asymmetry.

Relativistic spin-0 Duffin–Kemmer–Petiau equation in Bonnor–Melvin–Lambda solution

In this paper, we conduct a comprehensive exploration of the relativistic quantum dynamics of spin-0 scalar particles, as described by the Duffin–Kemmer–Petiau (DKP) equation, within the framework of a magnetic space-time. Our focus is on the Bonnor–Melvin–Lambda (BML) solution, a four-dimensional magnetic universe characterized by a magnetic field that varies with axial distance. To initiate this investigation, we derive the radial equation using a suitable wave function ansatz and subsequently employ special functions to solve it. Furthermore, we extend our analysis to include Duffin–Kemmer–Petiau oscillator fields within the same BML space-time background. We derive the corresponding radial equation and solve it using special functions. Significantly, our results show that the geometry’s topology and the cosmological constant (both are related to the magnetic field strength) influence the eigenvalue solution of spin-0 DKP fields and DKP-oscillator fields, leading to substantial modifications in the overall outcomes.

Spacetime metric from quantum-gravity corrected Feynman propagators

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length [Formula: see text]. These corrections cause the length element [Formula: see text] to be replaced with [Formula: see text] within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length [Formula: see text]. We perform this analysis in the case of the background spacetime [Formula: see text] in the Euclidean sector.

Colliding null matter with a specific stress tensor

The accretion disks around black holes consist of infalling matter boosted almost to the speed of light making collisions with opposite counterpart. This is the rough picture occurring near black holes or other strongly gravitating centers that produce observed phenomena such as astrophysical jets. A toy model that can be considered imitating such a process is colliding null sources in general relativity. We present such a simple model projected into the plane of null coordinates that takes into account only neutral sources. We show that even at such a simplified model, uncharged and non-rotating, it is possible to obtain jet-like ejections albeit they lie below the horizon. In the present study the spacetime consists of either one of (i) a cloud of strings, (ii) a global monopole, (iii) a particular model of bumblebee gravity, all described by a similar class of stress-energy tensor. There are gravitational waves accompanying the null sources and naturally collision of gravitational waves is also taken into account. After the collision, the spacetime contains both null and non-null sources, followed by trailing gravitational radiations. Locally the interaction region of the colliding null-sources and gravitational waves is isometric to the static background spacetime.

Island formula from Wald-like entropy with backreaction

We propose a Lorentzian derivation of the generalized entropy associated with the island formula for black holes as a Wald-like entropy without reference to the exterior non-gravitating region or field-theoretic von Neumann entropy of Hawking radiation in a fixed curved spacetime background. We illustrate this idea by studying two-dimensional black holes in the Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model in which Hawking radiation is represented by conformal scalars. With some prescriptions assumed, we show that the generalized entropy for the island formula can be reproduced as the Wald-like entropy of the two-dimensional dilaton-gravity theories upon the inclusion of the backreaction from Hawking radiation described by conformal anomaly. We give a discussion on how a similar idea can be applied to higher-dimensional black holes. It is emphasized that the generalized entropy is obtained in a fully gravitational fashion, yet it yields the same Page curve as that of the half-gravitational set-up. We argue that the results in this paper exacerbate the issues raised in the work of massive islands and inconsistency of islands in theories of long-range gravity.

Quasinormal mode spectrum of the AdS black hole with the Robin boundary condition

We study the quasinormal mode (QNM) spectrum of an asymptotically AdS black hole with the Robin boundary condition at infinity. We consider the Schwarzshild-AdS4 with the flat event horizon as the background spacetime and study its scalar field perturbation. Denoting leading coefficients of slow- and fast-decay modes of the scalar field at infinity as φ 1 and φ 2, respectively, we assume a linear relation between them as ϕ2=cot(θ/2)ϕ1 , where θ is a constant called the Robin parameter and periodic under θ∼θ+2π . In a certain range of the Robin parameter, there is an instability driven by the boundary condition. We also find the holonomy in the QNM spectrum under the parametric cycle of the boundary condition: θ=0→2π . After the one-cycle, nth overtone of the QNM moves to (n−1) th overtone. The fundamental tone of the QNM is swept out to the infinity in the complex plane.

Cosmology from the vacuum

We argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the Universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. In particular, while inflation may explain the origin of perturbations in the cosmology picture, the perturbations can be deduced from the dual picture without any knowledge of the inflationary potential.

Self-dual fields on self-dual backgrounds and the double copy

We explore the double copy for self-dual gauge and gravitational fields on self-dual background spacetimes. We consider backgrounds associated with solutions of the second Plebanski equation and describe results with different gauge-fixing conditions. Finally we discuss the kinematic and w-algebras and the double copy, identifying modified Poisson structures and kinematic structure constants in the presence of the self-dual background. The self-dual plane wave and Eguchi-Hanson spacetimes are studied as examples and their respective w-algebras derived. Published by the American Physical Society 2024

Reissner–Nordström black holes in quintic quasi-topological gravity

This paper investigates charged black holes within the framework of quintic quasi-topological gravity, focusing on their thermodynamics, conserved quantities, and stability. We construct numerical solutions and explore their thermodynamic properties, supplemented by the study of analytically solvable special cases. By verifying the first law of thermodynamics, we validate our approach and compare our findings to those of Einstein gravity. The physical properties of the solutions are examined across anti-de Sitter, de Sitter, and flat spacetime backgrounds. Our analysis reveals that anti-de Sitter solutions demonstrate thermal stability, while de Sitter and flat solutions lack this property. Finally, we discuss the implications of our results and propose potential avenues for future research in this field.

Research on the Tunneling Radiation of Bosons from the Kerr-Sen-like Black Hole by Einstein-Bumblebee Gravitational Theory

Lorentz-breaking theory not only affects the curved space-time background, but also modifies the dynamic equations of bosons and fermions in curved space-time to some extent. Therefore, we need to make appropriate corrections for the quantum tunneling radiation of bosons and fermions in different black hole spacetimes. New expressions of black hole Hawking temperature and other physical quantities modified by Lorentz-breaking theory and their physical meanings are obtained. In this paper, according to the Kerr-Sen-like (KSL) black hole spacetime metric obtained from Einstein-Bumblebee gravitational theory, by introducing the correction term of the aether-like field vector into the scalar field action and the d'Alembert operator in curved spacetime, and applying the variational principle in curved spacetime, the Lorentzbreaking correction term in the spacetime metric and the new form of the dynamic equation of the bosons with zero spin in KSL spacetime are studied. By correctly selecting the aether-like field vector corresponding to the KSL spacetime metric and solving the modified bosons dynamic equation, the modified quantum tunneling rate is obtained. On this basis, the Hawking temperature and Bekenstein- Hawking entropy of the black hole with Lorentz-breaking correction term are studied. The effects of Lorentz-breaking theory on the distribution of positive and negative energy levels of bosons and the maximum crossing of energy levels are also studied, and then the conditions of quantum non-thermal radiation in the black hole space-time is studied. At the end of this paper, the physical significance of a series of results obtained in this paper is discussed in depth. The results show that the modified form of the bosons dynamic equation in curved spacetime, taking into account Lorentz-breaking theory, is shown in equation (26) and equation (27). The new expressions of the quantum tunneling rate, Bekenstein-Hawking entropy, Hawking temperature and quantum non-thermal radiation energy range of KSL black hole are obtained by applying equation (26) to KSL black hole space-time. These results are useful for studying the quantum tunneling radiation characteristics of black holes. It should be noted that the above research results are obtained under the WKB theory and the semiclassical case. If the effects of different powers of Planck are to be considered, the above research methods and related results need to be used for further modified research by using beyond the semi-classical theory.

The Unruh Vacuum and the “In-Vacuum” in Reissner-Nordström Spacetime

The Unruh vacuum is widely used as a quantum state to describe black hole evaporation since, near the horizon, it reproduces the physical state of a quantum field, the so-called “in-vacuum”, in the case where a black hole is formed by gravitational collapse. We examine the relation between these two quantum states in the background spacetime of a Reissner–Nordström black hole (both extremal and not), highlighting the similarities and striking differences.