Israel Junction Conditions Research Articles

Charged gravastar model in noncommutative geometry under [formula omitted] gravity

In this article, we study the properties of charged gravastars in torsion-based f(T) gravity in the presence of noncommutative geometry. We have taken the interior from noncommutative motivated space–time, noting that why, from a physical point of view, such a choice is justified, then we have taken the thin shell as stiff matter and taken three different exterior metrics (Reissner–Nordstrom (R–N), Bardeen and Ayon-Beato–Garcia (ABG) metric) to construct the gravastar model. We have studied the physical properties like proper length, entropy, energy, and EoS for these models, and we have also used Israel junction conditions to study the effective pressure, energy density, and potential of the thin shell. Finally, we comment on the stability of such a thin shell and the deflection angle caused by such a thin shell, which could, in principle, be tested by future radio telescopes like the Event Horizon Telescope (EHT).

Gravastar Model in Krori–Barua Metric Under f(Q)$f(\mathcal {Q})$ Gravity

AbstractIn this paper, the characteristics of a gravastar in gravity, which is upheld by Krori–Barua (KB) metric are explored. The authors have used KB metric for the interior and shell regions of the gravastar. The field equations are deduced by using KB metric. In the outside regions of the gravastar, two regular black hole metrics are taken. Additionally, the Israel junction condition to calculate the potential difference across the thin shell concerning different types of regular black holes, such as Bardeen and Hayward is applied. The physical properties like proper length, entropy, energy, equation of state, and stability are also discussed.

Einstein-Gauss-Bonnet dark matter halo: negative masses, rotation curves and the origin of dark matter effects

This work presents a novel approach to address the longstanding challenge posed by the rotation curves of galaxies and the associated missing mass problem. Utilizing the four-dimensional modified gravity framework of Einstein-Gauss-Bonnet (EGB), we develop a new model that integrates the concept of dark matter featuring negative mass due to the Gauss-Bonnet term. Our methodology involves using the action of EGB with boundary terms to derive the Israel junction condition, allowing the formulation of a model featuring a spherical dark halo. The mass expression of this dark halo exhibits a remarkable proportionality to the radius r at large distances, forming the basis for subsequent analyses. The model’s implications extend to the dynamics of the early Universe, where we introduce a dynamic scalar field classified as Chameleon. Posting this scalar field as the origin of dark matter effects, we establish a crucial link between the coupling constant α and the scalar field through Z2 symmetry breaking via the effective potential. This connection enables a subtle description of velocity, reminiscent of Modified Newtonian Dynamics (MOND), providing insights into the gravitational interplay and dark matter dynamics. A pivotal aspect of our study involves a particular comparison of the model’s predictions with observational data sourced from SPARC datasets. The alignment of our theoretical outcomes with empirical evidence underscores the model’s efficiency and its potential contribution to our understanding of galactic rotation dynamics.

Membrane models as a means of propulsion in general relativity: super-luminal warp-drive that satisfies the weak energy condition

Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner—as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of the brane may be set individually by choice of model parameters. The Weak Energy Condition (WEC) is shown to be satisfied everywhere in both models. Although the branes in these toy models are not compact, it is demonstrated that super-luminal warp-drive is possible that satisfies the WEC. Additionally, the nature of these models provides framework for speculation on a mechanism for transition from sub-luminal to super-luminal warp. It is shown that the difference in extrinsic curvature across a thin membrane can yield a positive contribution to the Landau–Raychaudhuri equation, thus providing a means to evade some super-luminal warp-drive no-go theorems. Neither quantum effects nor stability of the models is considered.

Analytic approximations for the primordial power spectrum with Israel junction conditions

This work compares cosmological matching conditions used in approximating generic pre-inflationary phases of the Universe. We show that the joining conditions for primordial scalar perturbations assumed by Contaldi [] are inconsistent with the physically motivated Israel junction conditions; however, performing general relativistic matching with the aforementioned constraints results in unrealistic primordial power spectra. Eliminating the need for ambiguous matching, we look at an alternative semianalytic model for producing the primordial power spectrum allowing for finite duration cosmological phase transitions. Published by the American Physical Society 2024

Study of charged gravastar model in [formula omitted] gravity

In recent days gravastar has been a very lucrative alternative to black holes, as it does not suffer from the singularity problem as well and it is based on sound physical grounds. Modified Symmetric teleparallel equivalent of gravity also has seen quite a few successes in recent years both in cosmology as well as in astrophysical objects like black holes and wormholes. In this paper, we have considered the charged gravastar in f(Q) formulation and have solved it fully analytically and found various physical characteristics like energy density, entropy and EoS for the gravastar. We have used the Israel junction condition to make some phenomenological predictions regarding the potential of the thin shell around the gravastar. We have also studied the deflection of the angle caused by the gravastar. Finally, we conclude by noting how future radio telescopes could detect the gravastar shadow and how can one distinguish it from the black hole event horizon.

Study of gravastars in 4D Einstein-Gauss-Bonnet gravity

In the present work, we investigate the configuration of gravastar in the framework of Einstein-Gauss-Bonnet (EGB) gravity. A gravastar is conceptually an alternative model for black holes, which has three distinct layers with different equations of state. Under these specifications, we find out a set of exact and singularity free solutions of the gravastar in EGB gravity. The interior and exterior layers are matched by considering the Israel and Darmois junction conditions. The mass of the thin intermediate shell is formulated and various physical aspects of gravastar, specifically, energy of the shell, entropy inside the shell, intermediate thin shell and proper length of the shell is examined. It is noted that the Gauss-Bonnet term strongly affects the physical properties of gravastar in EGB gravity.

Non-exotic static spherically symmetric thin-shell wormhole solution in f (Q, T ) gravity* *MT supported by the University Grants Commission (UGC), New Delhi, India, for awarding National Fellowship for Scheduled Caste Students (UGC-Ref. No. 201610123801). SG supported by the Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi, for junior research fellowship (File No. 09/1026(13105)/2022-EMR-I). PKS supported

In this study, we conduct an analysis of traversable wormhole solutions within the framework of linear gravity, ensuring that all energy conditions hold for the entire spacetime. The solutions presented in this paper are derived through a comprehensive analytical examination of the parameter space associated with the wormhole model. This involves considering the exponents governing the redshift and shape functions, as well as the radius of the wormhole throat (), the redshift function value at the throat (), and the model parameters (α and β). Moreover, we establish bounds on these free parameters, which guarantee the satisfaction of the energy conditions throughout spacetime and also provide two solutions. Furthermore, we use the Israel junction condition to observe the stability of a thin-shell around the wormhole. Finally, we calculate the null energy condition criteria as well as the potential for the thin-shell and how it varies with the chosen shape function.

Einstein-Chern-Simons equations on the 3-brane world

In this article it is studied the 3-brane world in the context of five-dimensional Einstein-Chern-Simons gravity. We started by considering Israel's junction condition for AdS-Chern-Simons gravity. Using the S-expansion procedure, we mapped the AdS-Chern-Simons junction conditions to Einstein-Chern-Simons gravity, allowing us to derive effective four-dimensional Einstein-Chern-Simons field equations.

Stabilizing spherical energy shells with angular momentum in gravitational backgrounds

Spherical energy shells in General Relativity tend to collapse due to gravitational effects and/or due to tension effects. Shell stabilization may be achieved by modifying the gravitational properties of the background spacetime. Thus, gravastars consist of stiff matter shells with an interior deSitter space and an exterior Schwarzshild spacetime whose attractive gravity balances the interior repulsive gravity of the interior deSitter spacetime leading to a stable stiff matter shell. Similar stabilization effects may be achieved by considering rotating shells. Here we study the stability of slowly rotating fluid shells. We show that the angular velocity of the shell has stabilizing properties analogous to the repulsive deSitter gravity of the interior of a gravastar. We thus use the Israel junction conditions [W. Israel, Nuovo Cim. B 44S10 (1966) 1, Erratum: Nuovo Cim. B 48 (1967) 463; N. Deruelle, M. Sasaki and Y. Sendouda, Prog. Theor. Phys. 119 (2008) 237, arXiv:0711.1150 [gr-qc]] and the fluid equation of state of the rotating shell to construct the dynamical equations that determine the evolution of the rotating shell radius. These dynamical equations depend on the parameters of the background spacetime and on the angular velocity of the shell. Assuming a rotating interior and a Schwarzschild exterior spacetime we show that the angular velocity of the shell has interesting stabilizing properties on the evolution of its radius R. Thus, rotating matter (or vacuum) shells can imitate black holes while avoiding the presence of a singularity and without the presence of an interior deSitter space.

Generalized Darmois–Israel Junction Conditions

We present a general method to derive the appropriate Darmois–Israel junction conditions for gravitational theories with higher-order derivative terms by integrating the bulk equations of motion across the singular hypersurface. In higher-derivative theories, the field equations can contain terms which are more singular than the Dirac delta distribution. To handle them appropriately, we formulate a regularization procedure based on representing the delta function as the limit of a sequence of classical functions. This procedure involves imposing suitable constraints on the extrinsic curvature such that the field equations are compatible with the singular source being a delta distribution. As explicit examples of our approach, we demonstrate in detail how to obtain the generalized junction conditions for quadratic gravity, F(R) theories, a 4D low-energy effective action in string theory, and action terms that are Euler densities. Our results are novel, and refine the accuracy of previously claimed results in F(R) theories and quadratic gravity. In particular, when the coupling constants of quadratic gravity are those for the Gauss–Bonnet case, our junction conditions reduce to the known ones for the latter obtained independently by boundary variation of a surface term in the action. Finally, we briefly discuss a couple of applications to thin-shell wormholes and stellar models.

Quasi-homologous evolution of relativistic charged objects within [formula omitted] gravity

This paper attempts to explore the evolution of relativistic charged (dissipating or non-dissipating) cosmic objects evolving in quasi-homologous (QH) regime and satisfying the condition of zero complexity factor (CF), under the framework of f(G,T) gravitational theory. For a specific version of f(G,T) theory, various exact solutions for time-dependent charged fluid configurations endowed with spherical symmetry satisfying the above-stated conditions are presented. We will see that few of the provided solutions characterize the evolution of non-static fluid configurations, whose center (r=0) is enclosed by a void. However, some of the modified solutions exhibit shells and fulfill the Israel junction conditions, while others exhibit voids (i.e., they omit the appearance of shells) and fulfill the Darmois matching conditions on both hypersurfaces. Some future applications regarding the presented models in the field of cosmology and relativistic astrophysics are also mentioned.

A Peek Outside Our Universe

According to general relativity (GR), a universe with a cosmological constant Λ, like ours, is trapped inside an event horizon, r<3/Λ. What is outside? We show, using Israel (1967) junction conditions, that there could be a different universe outside. Our universe looks like a black hole for an outside observer. Outgoing radial null geodesics cannot escape our universe, but incoming photons can enter and leave an imprint on our CMB sky. We present a picture of such a fossil record from the analysis of CMB maps that agrees with the black hole universe predictions but challenges our understanding of the origin of the primordial universe.

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Although the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac $\delta$-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities $[\kappa]$ and $[\cal J]$ of the surface gravity $\kappa$ and angular momentum density $\cal J$. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of $[\kappa]$ and $[\cal J]$. Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal $\boldsymbol n$ to the surface is allowed to tend continuously to a null vector. The relation to Israel's original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating `black hole' exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrab\`es-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

An effective three-dimensional de Sitter cosmology in string theory

Motivated by the lack of consensus on whether or not de Sitter (dS) lies in the Swampland, we use a recently developed braneworld construction and known Anti-de Sitter (AdS) vacua to compute an explicit effective dS cosmology in three dimensions. We consider a non-perturbative AdS4 vacuum decaying to another lower AdS4 vacuum via bubble-nucleation. We also consider the more speculative case where a dS4 decay to a Minkowski4. The Israel junction conditions are solved across the bubble and we obtain the Friedmann equations from which the cosmological constants can be read off, in the respective cases. The cosmological constants are computed in a flux background yielding small positive values admitting a dS cosmology. However, we find that an energetically viable model in the AdS to AdS case requires more fine-tuning.

Thin shell collapse in Kiselev geometry

We present some new aspects of Kiselev black hole and then study the null and timelike thin shell collapse in this space-time. For the latter, we show that Kiselev black hole can be matched to de Sitter core with a thin timelike dust shell to produce a non-singular space-time. It is argued that for timelike hypersurface, the equation of state parameter must be non-negative. Using Barrabès–Israel junction conditions, the equation of motion of the shell is obtained. The stability of stationary solutions of the shell is discussed and some appropriate ranges for the parameters of shell and Kiselev geometry are found for which a stable stationary black hole is constructed.

Boson stars and solitons confined in a Minkowski box

We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen U(1) gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the box surface layer determine the stress tensor that the box must have to confine the scalar hair. Some of these horizonless hairy solutions exist for any value of the scalar field charge and not only above the natural critical charges of the theory (namely, the critical charges for the onset of the near-horizon and superradiant instabilities of the Reissner-Nordström black hole). However, the ground state solutions have a non-trivial intricate phase diagram with a main and a secondary family of solitons (some with a Chandrasekhar mass limit but others without) and there are a third and a fourth critical scalar field charges where the soliton spectra changes radically. Most of these intricate properties are not captured by a higher order perturbative analysis of the problem where we simply back-react a normal mode of the system.

Erratum: Dispersion of gravitational waves in cold spherical interstellar medium

The study published in IJMPD 27(4):1850040, 2018 provided a numerical result for the frequency-shift of GWs due to dispersion in interstellar medium. In order to adjust the metric functions of the originally improperly matched ‘background’ spacetime in Sec. 2.1, the authors have adopted Darmois–Israel junction conditions. In Sec. 4.1 the code used in the original paper erroneously computed the magnitude of frequency-shift for the transient event GW150914 due to a missing conversion factor. In both cases where numerical errors and potential contradictions have been identified and eliminated, adjustments were undertaken in order to maintain consistency with closely-related earlier studies.

Stable, thin wall, negative mass bubbles in de Sitter space-time

Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found \cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of {\it stable}, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific mass distribution, separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel junction conditions at the wall. For the case of an interior corresponding simply to de Sitter space-time with a different cosmological constant from the outside space-time, separated by a thin wall with energy density that is independent of the radius, we find static but unstable solutions which satisfy the dominant energy condition everywhere. The bubbles can collapse through spherically symmetric configurations to the exact, singular, negative mass Schwarzschild-de Sitter solution. Interestingly, this provides a counter-example of the cosmic censorship hypothesis. Alternatively, the junction conditions can be used to give rise to an interior mass distribution that depends on the potential for the radius of the wall. We show that for no choice of the potential, for positive energy density on the wall that is independent of the radius, can we get a solution that is non-singular at the origin. However, if we allow the energy density on the wall to depend on the radius of the bubble, we can find {\it stable}, static, non-singular solutions of negative mass which everywhere satisfy the dominant energy condition.

Revisiting the Israel junction conditions in Einstein–Cartan gravity

The Israel junction conditions of a thin shell in the context of Einstein–Cartan gravity are revisited. It is shown that with a choice of the torsion discontinuity taken to be orthogonal to the hypersurface and consistent with the antisymmetric properties of torsion tensor and contorsion tensor, the generalized asymmetric surface energy–momentum tensor turns out to be tangent to the hypersurface while the resulting generalized Israel junction conditions are modified. The main differences to previous works are mentioned.