Schwarzschild Spacetime Research Articles

Generalized Schwarzschild Spacetimes with a Linear Term and a Cosmological Constant

Particular Kottler spacetimes are analytically investigated. The investigated spacetimes are spherically symmetric nonrotating spacetimes endowed with a Schwarzschild solid-angle element. SchwarzschildNairiai spacetimes, Schwarzschild spacetimes with a linear term, and Schwarzschild spacetimes with a linear term and a cosmological constant are studied. The infinite-redshift surfaces are analytically written. To this aim, the parameter spaces of the models are analytically investigated, and the conditions for which the analytical radii are reconducted to the physical horizons are used to set and to constrain the parameter spaces. The coordinate-singularity-avoiding coordinate extensions are newly written. Schwarzschild spacetimes with a linear term and a cosmological constant termare analytically studied, and the new singularity-avoiding coordinate extensions are detailed. The new roles of the linear term and of the cosmological constant term in characterizing the Schwarzschild radius are traced. The generalized Schwarzschild–deSitter case and generalized Schwarzschild–anti-deSitter case are characterized in a different manner. The weak field limit is newly recalled. The embeddings are newly provided. The quantum implementation is newly envisaged. The geometrical objects are newly calculated. As a result, for the Einstein field equations, the presence of quintessence is newly excluded. The Birkhoff theorem is newly proven to be obeyed.

Loosely trapped surface for slowly rotating black hole

Abstract We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order.

Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime

AbstractWe study the formation of singularities of smooth solutions to the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime. The system is in the spherically symmetric form, and its coefficients and nonhomogeneous terms contain a parameter reflecting the mass of the black hole, which makes it highly nonlinear and complicated. To overcome the influence of the mass parameter of black hole, we introduce a pair of suitable auxiliary variables related to it and derive their characteristic decompositions to establish the estimates of the smooth solution. We show that, for a kind of initial data, the smooth solution develops singularity in finite time and the mass‐energy density itself approaches infinity at the blowup point.

Non-Markovian dynamics control of an open quantum system in a Schwarzschild space–time

By considering two qubits respectively coupled with two independent reservoirs and ignoring the interaction between them, two different cases are studied in two models: only one qubit accelerates and hovers near the event horizon or both two qubits accelerate and hover near the event horizon. The first model is given by referring to the damping Jaynes–Cummings model with a reservoir described by Lorentzian spectral density. And the second model is a pure dephasing model with a reservoir described by Ohmic spectral density. We investigate the impact of acceleration and Hawking temperature on the non-Markovianity and the quantum speed limit time of a two-qubit open quantum system. Through the numerical calculation, it is found that for these two models, by reducing the acceleration of qubits and the Hawking temperature outside the event horizon, the non-Markovianity of the dynamic process of the quantum system in the Schwarzschild space–time can be enhanced until it approaches the non-Markovianity when both qubits are in the inertial frame. However, we find that in the first model, the evolution speed of quantum state can be accelerated with decreasing acceleration and Hawking temperature. While in the second model, the quantum state evolution speed can be accelerated with increasing acceleration and Hawking temperature. For both models, the evolution speed of the quantum state of the system in the Markovian dynamics can still be accelerated.

Accretion tori around rotating neutron stars I. Structure, shape, and size

We present a full general relativistic analytic solution for a radiation-pressure-supported equilibrium fluid torus orbiting a rotating neutron star (NS). We applied previously developed analytical methods that include the effects of both the NS's angular momentum and quadrupole moment in the Hartle-Thorne geometry. The structure, size, and shape of the torus are explored, with a particular focus on the critically thick solution -- the cusp tori. For the astrophysically relevant range of NS parameters, we examined how our findings differ from those obtained for the Schwarzschild space-time. The solutions for rotating stars display signatures of an interplay between relativistic and Newtonian effects where the impact of the NS angular momentum and quadrupole moment are almost counterbalanced at a given radius. Nevertheless, the space-time parameters still strongly influence the size of tori, which can be shown in a coordinate-independent way. Finally, we discuss the importance of the size of the central NS which determines whether or not a surrounding torus exists. We provide a set of tools in a Wolfram Mathematica code, which establishes a basis for further investigation of the impact of the NSs’ super-dense matter equation of state on the spectral and temporal behaviour of accretion tori.

Braneworld black bounce to transversable wormhole

We provide a way for embedding a 4-dimensional geometry corresponding to the Simpson-Visser (SV) spacetime — which is capable of representing a traversable wormhole, a one-way wormhole, or a regular black hole — into a Randall-Sundrum setup. To achieve this, we linearly deform the bulk geometry and the bulk matter distribution concerning a coupling constant. These deformations induce a transition from a 5D vacuum AdS state to an anisotropic matter distribution. The latter results in the induced geometry on the brane transitioning from a singular Schwarzschild spacetime to a regularized SV spacetime. Since there are no sources or matter fields on the brane, we can assert that the induced SV geometry on the brane arises from the influence of geometrical and matter deformations in the bulk. Thus, the central singularity is suppressed. We determine the cases where the energy conditions are either satisfied or violated. Our spacetime is asymptotically radial AdS, which is intriguing given the absence of a global AdS box that would prevent instability under larger wavelength perturbations. Therefore, it is no longer appropriate to claim that instability exists for very small perturbations near the AdS horizon. Thus, we propose that the stability of the solution can be analyzed by examining the speed of sound due to the presence of matter fields in the energy momentum tensor.

Orbital Precession in Janis–Newman–Winicour Spacetime

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data.

Casimir wormholes with GUP correction in the Loop Quantum Cosmology

In this paper, we obtain novel traversable, static, and spherically symmetric wormhole solutions, derived from the effective energy density and isotropic pressure resulting from the Casimir effect, corrected by the Generalized Uncertainty Principle (GUP) within the framework of Loop Quantum Cosmology (LQC). The goal is to explore the interplay between competing quantum gravity effects and quantum vacuum phenomena in the emergence of non-trivial spacetime structures. We examine features such as traversability, embedding diagrams, energy conditions, curvature, and stability of the obtained solutions. Additionally, we analyze the junction conditions required to integrate the wormhole spacetime with an external Schwarzschild spacetime and calculate the amount of exotic matter needed to maintain the wormhole. Finally, we evaluate the conditions under which this latter remains visible or is hidden by the event horizon associated with the Schwarzschild spacetime.

Impact of chaplygin-like equation of state on Joule–Thomson expansion and tidal forces of AdS black holes

This study examines a recently hypothesized black hole. We study the Joule–Thomson coefficient, the inversion temperature and also the isenthalpic curves in the Ti−Pi plane. The Joule–Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in AdS black holes surrounded by Chaplygin dark fluid. In T−P plane, the inversion temperature curves and isenthalpic curves are obtained with different parameters. Next, we explore the radial time-like geodesics that leads us to explore the tidal force effects for a radially in-falling particle in such black hole spacetime. We also numerically solve the geodesic deviation equation for two nearby radial geodesics for a freely falling particle. Our analysis shows that contrary to the Schwarzschild spacetime, the tidal forces do not become zero at spatial infinity due to the lack of asymptotic flatness because of the presence of a non-zero cosmological constant. The geodesic separation profile shows an oscillating trend and depends on the dynamic spacetime parameters q,B and Λ.

Second-order perturbations of the Schwarzschild spacetime: Practical, covariant, and gauge-invariant formalisms

Second-order perturbations of the Schwarzschild spacetime: Practical, covariant, and gauge-invariant formalisms

Particle motion around luminous neutron stars: Effects of deviation from Schwarzschild spacetime

Particle motion around luminous neutron stars: Effects of deviation from Schwarzschild spacetime

Distribution of distance-based quantum resources outside a radiating Schwarzschild black hole

Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.

Interior volume of the charged BTZ black holes

In Schwarzschild spacetime, Reinhart (1973) has shown the hypersurface rss=3M/2 (the subscript stands for “steady-state”) to be the maximal hypersurface. This steady-state radius rss plays a crucial role in defining and evaluating the interior volume of a black hole. In this article, we investigate various methods to compute the maximal interior volume of a charged BTZ black hole. We find that the presence of charge Q in a black hole introduces a “log” term in the metric as a result of which, an analytical solution for the volume does not exist. So we first compute the volume of the black hole for the limiting case when the charge Q is very small (i.e., Q≪1: Q is a dimensionless parameter in (2+1) dimensions) and then carry out a numerical analysis to solve for the volume for more generic values of the charge. We find that the volume grows monotonically with the advance time v. We further investigate the functional behavior of the entropy of a massless scalar field living on the maximal hypersurface of a near-extremal black hole. We show that this volume entropy exhibits a very different functional form from the horizon entropy.

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The C3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^3$$\\end{document} approach is an invariant formalism that utilizes the eigenvalues of the Riemann curvature tensor to match spacetimes across a specific matching surface. We apply this approach to match an anisotropic fluid with an exterior vacuum solution, including the case in which discontinuities appear on the matching surface. As a particular example, a class of analytic solutions, which describe the gravitational field of realistic neutron stars, is matched to the exterior Schwarzschild spacetime.

Quantum coherence and quantum Fisher information of Dirac particles in curved spacetime under decoherence

Previous studies have shown that the decoherence of environments generally negatively influences the quantum correlations in the Schwarzschild black hole. In our paper, we find that the decoherence of the generalized amplitude damping (GAD) channel has both positive and negative effects on the quantum coherence of Dirac fields, which means that the decoherence of environments can not only reduce the quantum coherence but also increase the quantum coherence in Schwarzschild spacetime. This result banishes the widespread belief that the decoherence of the environment can only destroy the quantum coherence in curved spacetime. Furthermore, another novel phenomenon has been observed for the first time: with increasing Hawking temperature T, the QFI of physically inaccessible modes rapidly decays from infinity to 0, which may provide a way to detect whether the particles enter the physically inaccessible region or not. This result may provide a new perspective for exploring and analyzing black holes.

Schwarzschild spacetime in fractal dimensions: Deflection of light, supermassive black holes and temperature effects

In this paper, we construct a Schwarzschild metric in the fractal dimension based on fractal calculus, and we study the deflection of light near the sun. It was observed that the new fractal spherically symmetric spacetime metric may describe supermassive black holes, which have been detected through various astronomical observations such as SDSS. We have discussed the deflection of light by the gravitational field of the sun. It was observed that the total deflection of light is affected by the fractal dimension. To estimate the numerical value of the fractal dimension, we have used the 2004[Formula: see text]analysis of almost 2 million VLBI observations of 541 radio sources made by 87 VLBI sites, which estimates the factor [Formula: see text] based on PNN formalism. It was observed that the fractal dimension is roughly less than unity. However, our analysis showed that large bending gravity gives fractal dimensions lower than unity to some extent. We also gave a naïve idea about the emission thermal Unruh process in fractal dimension. It was observed that both the temperature and the entropy of black holes are affected by the fractal dimension, and that for low numerical values, the entropy of the black hole is enhanced.

Uniqueness of the static vacuum asymptotically flat spacetimes with massive particle spheres

In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for static vacuum asymptotically flat spacetimes, which focus on scenarios featuring event horizons or photon spheres. Similarly to the uniqueness theorems concerning photon spheres or event horizons, only a single massive particle sphere is sufficient to obtain a unique solution. However, in contrast to previous theorems, our result leads to the existence of an entire spacetime foliation sliced by a set of massive particle spheres spanning various energies. Published by the American Physical Society 2024

Scalar field solutions and energy bounds for modeling spatial oscillations in Schwarzschild black holes based on the Regge–Wheeler equation

This text discusses the behavior of solutions and the energy stability within Schwarzschild spacetimes, with a particular emphasis on the behavior of massless scalar fields under the influence of a non-rotating and spherically symmetric black hole. The stability of solutions in the proximity of the event horizon of black holes in general relativity remains an open question, especially given the difficulties introduced by minor perturbations that may resemble Kerr solutions. To address this, this work explores a simplified model, including massless scalar fields, to better understand perturbation behaviors around black holes under the Schwarzschild approach. We depart from Richard Price’s work in connection with how scalar, electromagnetic, and gravitational fields behave. The tortoise coordinate transformation is considered to set the stage for numerical solutions to the wave equations. Afterward, we explore energy estimates, which are used to gauge stability and wave behavior over time. Our analysis reveals that the time evolution of the energy does not exceed twice its initial value. Further and under the assumption of initial conditions in L2−spaces, we obtain an exponential decreasing behavior in the energy time evolution. A question to continue exploring is how perturbations in L2 in the initial conditions that introduce Kerr solutions as a second-order effect in the linearized equations perturb this obtained exponential decay.

Embedding diagrams in stationary spacetimes

We find the spatial and dynamic embedding diagrams in stationary black hole spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared through their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes, and compare them with the dynamic embedding diagram of Schwarzschild spacetime.

Ray tracing through absorbing dielectric media in the Schwarzschild spacetime

Abstract General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the Drude model. When absorption is included the eikonal becomes complex, with the imaginary part related to the absorption along a ray between emission and observation points. We extend results from the literature to include dispersion in the index of refraction. The complex Hamiltonian splits into a real part that describes the equations of motion and a constraint equation that governs the momentum loss in the system. We work in coordinates which are fully real, with a real metric in physical spacetime. We assume the dust and plasma distributions of the Drude matter to coincide and vary as a power-law $1/r^h$. We find that transmission requires $h>1$, otherwise exponential absorption occurs along ray paths. We use ray-tracing through strongly absorbing matter near the surface of the compact star, as well as specializing to a point-lens in the weak-field limit with weakly absorbing matter to generate potentially observable light curves for distant observers. In the appropriate limits, our theory reproduces results from the literature.