De Sitter Interior Research Articles

Charged gravastars with conformal motion in the Finslerian space-time

In this article, we investigate the charged gravastar under conformal motion with the background of Finsler geometry. Mazur and Mottola pioneered the concept of the gravastar (gravitational vacuum star) for the first time. This vacuum object consists of three distinct regions, that is, (i) interior de Sitter region, (ii) thin shell consisting of ultrarelativistic stiff, and (iii) exterior vacuum Schwarzschild region. The nature of these regions can be analyzed by considering different equations of state parameters. We have studied various physical features of the gravastar, such as length, energy, entropy, stability, and the adiabatic index, both graphically and analytically within the Finslerian framework. Also, we have obtained the exact and non-singular solution for the gravastar model.

Global monopoles in the extended Gauss-Bonnet gravity

We discuss self-gravitating global O(3) monopole solutions associated with the spontaneous breaking of O(3) down to a global O(2) in an extended Gauss-Bonnet theory of gravity in ($3+1$) dimensions, in the presence of a nontrivial scalar field $\mathrm{\ensuremath{\Phi}}$ that couples to the Gauss-Bonnet higher curvature combination with a coupling parameter $\ensuremath{\alpha}$. We obtain a range of values for $\ensuremath{\alpha}<0$ (in our notation and conventions), which are such that a global (Israel type) matching is possible of the space-time exterior to the monopole core $\ensuremath{\delta}$ with a de Sitter interior, guaranteeing the positivity of the Arnowitt-Deser-Misner (ADM) mass of the monopole, which, together with a positive core radius $\ensuremath{\delta}>0$, are both dynamically determined as a result of this matching. It should be stressed that in the general relativity (GR) limit, where $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, and $\mathrm{\ensuremath{\Phi}}\ensuremath{\rightarrow}\text{constant}$, such a matching yields a negative ADM monopole mass, which might be related to the stability issues the [Barriola-Vilenkin (BV)] global monopole of GR faces. Thus, our global monopole solution, which shares many features with the BV monopole, such as an asymptotic-space-time deficit angle, of potential phenomenological/cosmological interest, but has, par contrast, a positive ADM mass, has a chance of being a stable configuration, although a detailed stability analysis is pending.

Gravitational Condensate Stars: An Alternative to Black Holes

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein’s equations is obtained, characterized by an interior de Sitter region of p=−ρ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order kBℓMc/ℏ, instead of the Bekenstein–Hawking entropy, SBH=4πkBGM2/ℏc. Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox.

Classification of Circular Equatorial Orbits around Regular Rotating Black Holes and Solitons with the de Sitter/ Phantom Interiors

We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by Ttt=Trr. Solutions of this class describe regular rotating black holes and spinning solitons replacing naked singularities. All these objects have the interior de Sitter equatorial disk, and can have two kinds of interiors determined by the energy conditions. One of them contains an additional interior de Sitter vacuum S-surface with the de Sitter disk as a bridge, whose internal cavities are filled with a phantom fluid. We study in detail the innermost equatorial circular orbits and show that in the field of spinning solitons, the innermost orbits exist within ergoregions related to phantom regions. We show also that around spinning solitons there can exist four corotating light rings and around a regular black hole, one corotating light ring, which is stable for a certain class of black holes. For all objects there exists one counterrotating light ring.

Slowly rotating gravastars

We solve Einstein's equations for slowly rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. We determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at $p=\ensuremath{-}\ensuremath{\rho}$, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed.

Regular electrically charged objects in Nonlinear Electrodynamics coupled to Gravity

We present a brief review of the basic properties of regular electrically charged black holes and electromagnetic solitons, predicted by analysis of regular solutions to dynamical equations of Nonlinear Electrodynamics minimally coupled to Gravity (NED-GR). The fundamental generic feature of regular NED-GR objects is the de Sitter vacuum interiors and the relation of their masses to spacetime symmetry breaking from the de Sitter group. Regular spinning NED-GR objects have interior de Sitter vacuum disk with the properties of a perfect conductor and ideal diamagnetic. The disk is confined by the ring with the superconducting current which provides the non-dissipative source of the electromagnetic fields and of the intrinsic magnetic momentum.

Stable bounded excursion gravastars with regular black holes

This paper explores the possible existence of stable regions of bounded excursion gravastars in the background of regular black holes (Bardeen and Bardeen-de Sitter black holes). For this purpose, we match internal de Sitter geometry with an external regular black hole through an intermediate shell with an equation of state. The matter surface located at the shell greatly affects the dynamical configuration of the shell. We consider stiff and dust fluids to discuss the outcomes of the developed structures. We then determine the critical values of physical parameters at which the shell neither collapses nor expands for both cases with different choices of external and internal geometries. It is found that there does not exist any possible region of stable bounded excursion gravastar for the interior flat and exterior regular geometries. However, the stable bounded excursion gravastar is obtained for the interior de Sitter and exterior regular black holes with a suitable choice of physical parameters for both stiff and dust shells. We conclude that the possibility of the existence of both bounded excursion gravastars as well as black holes cannot be excluded in the dynamical model.

Charged gravastars in f(R,T,RμνTμν) gravity

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

Image of the Electron Suggested by Nonlinear Electrodynamics Coupled to Gravity

We present a systematic review of the basic features that were adopted for different electron models and show, in a brief overview, that, for electromagnetic spinning solitons in nonlinear electrodynamics minimally coupled to gravity (NED-GR), all of these features follow directly from NED-GR dynamical equations as model-independent generic features. Regular spherically symmetric solutions of NED-GR equations that describe electrically charged objects have obligatory de Sitter center due to the algebraic structure of stress–energy tensors for electromagnetic fields. By the Gürses-Gürsey formalism, which includes the Newman–Janis algorithm, they are transformed to axially symmetric solutions that describe regular spinning objects asymptotically Kerr–Newman for a distant observer, with the gyromagnetic ratio g=2. Their masses are determined by the electromagnetic density, related to the interior de Sitter vacuum and to the breaking of spacetime symmetry from the de Sitter group. De Sitter center transforms to the de Sitter vacuum disk, which has properties of a perfect conductor and ideal diamagnetic. The ring singularity of the Kerr–Newman geometry is replaced with the superconducting current, which serves as the non-dissipative source for exterior fields and source of the intrinsic magnetic momentum for any electrically charged spinning NED-GR object. Electromagnetic spinning soliton with the electron parameters can shed some light on appearance of a minimal length scale in the annihilation reaction e+e−→γγ(γ).

Stability and Dynamics of Regular Thin-Shell Gravastars

This paper explores the stable and dynamical configuration of thin-shell gravastars developed from the matching of exterior (Hayward and Hayward anti-de Sitter black holes) and interior (de Sitter) spacetimes. These spacetimes are connected at a thin-shell by considering Visser cut and paste technique. The matter surface energy density and pressure are formulated from the Lanczos equations. We consider the shaded regions to discuss the stability of gravastars by using radial perturbation at the equilibrium shell radius. We then observe thin-shell dynamics with massless as well as massive scalar field through equations of motion and Klein-Gordon equations. The respective scalar thin-shell represents collapse and expansion of the developed structure with the shell radius, velocity and effective potential. We conclude that stable regions of gravastar shell decrease and dynamical configuration (collapse and expansion) increase with cosmological constant.

Explicit isometric embeddings of black holes geometry with non-singular matter distribution

The work is devoted to the construction of explicit embeddings for the metrics of the black holes, formed by nonsingular matter distribution. One of the possible examples of such type of solutions is regular black holes. Using the existing classification of minimal symmetric embeddings of the Schwarzschild metric as a base, we construct embeddings for regular black holes with de Sitter interior. Another simple example is black hole, formed by collapsing homogeneous spherically symmetric cloud of dustlike matter. We discuss embeddings for two variants of such black holes -the one with the eternally existing horizon, when dust ball never leaves the interior of the horizon, and another variant with the dynamically forming horizon.

Existence and stability of static spherical fluid shells in a Schwarzschild-Rindler–anti–de Sitter metric

We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin ^2 \theta d\phi ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\frac{\Lambda}{3}r^2$. This is an alternative to the well known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In the SRAdS spacetime the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three shell fluid equations of state: vacuum shell ($p=-\sigma$), stiff matter shell ($p=\sigma$) and dust shell ($p=0$) where $p$ is the shell pressure and $\sigma$ is the shell surface density. We also identify the metric parameter conditions that need to be satisfied for shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence sf stable spherical scalar field domain walls in the SRAdS spacetime.

The Higgs Mechanism and Spacetime Symmetry

In this review, we summarize the results of the analysis of the inherent relation between the Higgs mechanism and spacetime symmetry provided by generic incorporation of the de Sitter vacuum as a false vacuum with the equation of state p=−ρ. This relation has been verified by the application for the interpretation of the experimental results on the negative mass squares for neutrinos, and of the appearance of the minimal length in the annihilation reaction e+e−→γγ(γ). An additional verification is expected for the dark matter candidates with the interior de Sitter vacuum of the GUT scale, whose predicted observational signatures include the induced proton decay in the matter of an underground detector, such as IceCUBE.

Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

We outline the basic properties of regular black holes, their remnants and self-gravitating solitons G-lumps with the de Sitter and phantom interiors, which can be considered as heavy dark matter (DM) candidates generically related to a dark energy (DE). They are specified by the condition T t t = T r r and described by regular solutions of the Kerr-Shild class. Solutions for spinning objects can be obtained from spherical solutions by the Newman-Janis algorithm. Basic feature of all spinning objects is the existence of the equatorial de Sitter vacuum disk in their deep interiors. Energy conditions distinguish two types of their interiors, preserving or violating the weak energy condition dependently on violation or satisfaction of the energy dominance condition for original spherical solutions. For the 2-nd type the weak energy condition is violated and the interior contains the phantom energy confined by an additional de Sitter vacuum surface. For spinning solitons G-lumps a phantom energy is not screened by horizons and influences their observational signatures, providing a source of information about the scale and properties of a phantom energy. Regular BH remnants and G-lumps can form graviatoms binding electrically charged particles. Their observational signature is the electromagnetic radiation with the frequencies depending on the energy scale of the interior de Sitter vacuum within the range available for observations. A nontrivial observational signature of all DM candidates with de Sitter interiors predicted by analysis of dynamical equations is the induced proton decay in an underground detector like IceCUBE, due to non-conservation of baryon and lepton numbers in their GUT scale false vacuum interiors.

Stability of gravastars with exterior regular black holes

This paper examines the stability of thin-shell gravastars in the context of regular spacetimes (Bardeen and Bardeen-de Sitter black holes). We apply cut and paste approach to construct gravastars through the matching of interior non-singular de Sitter geometry with exterior regular black hole. This model contains three regions, i.e., interior, thin-shell and exterior. The interior and exterior regions are connected at thin-shell. We investigate physical viability of the developed model by the energy conditions and explore its stability by using radial perturbation about the equilibrium shell radius. It is found that thin-shell gravastars show large stable regions for the Bardeen-de Sitter black hole as compared to the Bardeen black hole. It is concluded that stable regions exist near the formation of expected event horizon.

Universes Inside a Black Hole with the de Sitter Interior

We outline the basic ideas and analyze the possibilities of the quantum birth of universes inside regular black holes with the de Sitter interior replacing a singularity. We compare different cases and show that the most plausible case is the birth of a flat universe from an initial quantum fluctuation with a small admixture of radiation and strings with the negative deficit angle, which provides the existence of a potential barrier needed for quantum tunneling.

Classification and basic properties of circular orbits around regular black holes and solitons with the de Sitter center

We present the detailed analysis of the circular orbits in the regular geometry with the de Sitter center which describes the regular black holes, their extreme states and the gravitational solitons (G-lumps)—non-singular non-dissipative objects without event horizons replacing naked singularities. We present general classification of the time-like and isotropic geodesics and find the existence of the special class of the isotropic geodesics which correspond to the stable circular orbits of photons whose wavelength is much less than a characteristic scale of geometry. The stable isotropic and time-like geodesics exist in the deep interiors of the gravitational solitons replacing the naked singularities. They are specified by the critical values that depend on the basic parameters including those characterizing the interior de Sitter vacuum, and can serve as the diagnostic tool for the spacetime structure of interiors of the regular black holes and solitons.

Origin of the magnetic momentum for regular electrically charged objects described by nonlinear electrodynamics coupled to gravity

Dynamical equations of nonlinear electrodynamics minimally coupled to gravity (NED–GR), admit the class of regular solutions, asymptotically Kerr–Newman for a distant observer, which describe regular electrically charged rotating black holes and spinning electromagnetic solitons with the angular momentum [Formula: see text] and the gyromagnetic ratio [Formula: see text]. Their basic generic feature is the existence of the interior de Sitter equatorial disk of the radius [Formula: see text] with the equation-of-state [Formula: see text] in the co-rotating frame, with the properties of a perfect conductor and ideal diamagnetic, and with the superconducting ring current along the edge of the disk, which replaces the ring singularity of the Kerr–Newman geometry and provides the nondissipative source of electromagnetic fields and the origin of an intrinsic magnetic momentum for an electrically charged regular object described by NED–GR. Generic features of the electromagnetic soliton with the parameters of the electron, [Formula: see text], suggest that the intrinsic origin of the electron magnetic momentum can be a superconducting ring current evaluated as [Formula: see text] A.

Stable gravastars: Guilfoyle’s electrically charged solutions

Compelling alternatives to black holes, namely, gravitational vacuum stars (gravastars), which are multilayered compact objects, have been proposed to avoid a number of theoretical problems associated with event horizons and singularities. In this work, we construct a spherically symmetric thin-shell charged gravastar model where the vacuum phase transition between the de Sitter interior and the external Reissner–Nordström spacetime (RN) are matched at a junction surface, by using the cut-and-paste procedure. Gravastar solutions are found among the Guilfoyle exact solutions where the gravitational potential W2 and the electric potential field ϕ obey a particular relation in a simple form a(b−ϵϕ)2 + b1, where a, b and b1 are arbitrary constants. The simplest ansatz of Guilfoyle’s solution is implemented by the following assumption: that the total energy density is constant, where Q(r) is the electric charge up to a certain radius r. We show that, for certain ranges of the parameters, we can avoid the horizon formation, which allows us to study the linearized spherically symmetric radial perturbations around static equilibrium solutions. To lend our solution theoretical support, we also analyze the physical and geometrical properties of gravastar configurations.

Thinking Non Locally: The Atemporal Roots of Particle Physics

Developing an approach defined in previous papers a correspondence between elementary particles and elements of a particular set of directed graphs said glyphs is made explicit. These can, in turn, be put in correspondence with a particular set of biquaternions. Charge conjugation and weak isospin inversion then become both topological (on glyphs) and algebraic (on biquaternions) symmetries. The formalism describes leptons and quarks, the latter successfully combined into mesons and baryons. The introduction is possible of both a de Sitter interior spacetime of particles and the usual external Minkowski spacetime. The biquaternions can be related to creation and annihilation operators of the corresponding fermionic fields in Quantum Field Theory (QFT). The base states of QFT and their mutual interactions are thus constrained by their common emergence from logically antecedent structures. This result appears relevant for the understanding of the elementary particles spectrum.