arXiv subjects

Vitalii Vertogradov

Publications and source records attributed to Vitalii Vertogradov.

At least 19 recordsLinked to original sources

arXiv2026

Effective Matter Conversion in Gravitational Collapse and the Dynamical Formation of Regular Black Holes

We study inverse source reconstruction in generalized Vaidya spacetimes. A prescribed density fixes the mass and tangential pressure, while a two-sector decomposition determines a dimensionless radial balance function. We distinguish this function from a time-directed conversion rate and identify the additional null-flux information required for a covariant exchange vector. Positivity restricts the allowed target pressures: a de Sitter core cannot be represented by nonnegative sectors with nonnegative tangential equations of state. An explicit finite-density profile admits a positive vacuum-like completion, finite curvature invariants, and inner and outer trapping horizons above a calculable threshold. Its total source satisfies the null, weak, and dominant energy conditions during monotonic accretion, while the timelike convergence condition fails in the core. We check polytropic, bag-model-inspired, and condensate-inspired profiles and the corresponding cosmological reconstruction. Finally, we compute the stationary endpoint's shadow and compare its exterior deformation with published Sagittarius A* measurements. The construction establishes local curvature regularity and marginal-sphere formation, without claiming a microscopic formation mechanism, perturbative stability, or geodesic completeness.

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arXiv2026

Black hole and wormhole branches in gravitational decoupling

Minimal Geometric Deformation (MGD) applied to a static Schwarzschild black hole seed generates a single decoupler function $h(r)$, obtained by solving the $θ$-sector field equations together with an equation of state. Once $h(r)$ is fixed, the resulting one-parameter family is controlled by the coupling strength $k$ through $F(r;k)=1+k\,h(r)$. We show that, whenever the deformation develops a simple outermost root that crosses the seed horizon, the same fixed decoupler leads to two mutually exclusive branches associated with different global completions: on one side of the critical coupling the deformed metric preserves the seed horizon as a black hole, whereas on the other side the root $r_*>2M$ lies in the exterior and cannot be interpreted as an interior modification of the black hole geometry. We prove that this root forces a loss of Lorentzian signature on the interval $(2M,r_*)$, so that no smooth extension of the exterior metric through the seed horizon $r=2M$ exists once $r_*$ lies outside it. Within the static, spherically symmetric class considered here, the corresponding smooth Lorentzian completion is a two-ended wormhole obtained by excising $(2M,r_*)$ and doubling the region $r\geq r_*$ across the minimal sphere $\mathcal T=\{r=r_*\}$. No topology change of any single spacetime is claimed or required: $k>k_c$ and $k<k_c$ simply correspond to two different, non-diffeomorphic manifolds, and Lemma~1 below shows that the metric itself dictates which of the two is the admissible completion for a given $k$. We compute the second homology group of both completions explicitly, $H_2(Σ_{\rm BH},\mathcal H)=0$ for the black hole exterior relative to its horizon and $H_2(Σ_{\rm WH})\cong\mathbb Z$ for the completed wormhole manifold, giving a discrete invariant that distinguishes the two branches.

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arXiv2026

Optical-area minimum method for static spherical black hole shadows

We formulate a global optical-area method for shadows of static, spherically symmetric black holes. For the metric $ds^{2}=-A(r)dt^{2}+B(r)dr^{2}+C(r)dΩ^{2}$, spherical sections of the optical geometry have area $\mathcal{A}_{\rm opt}=4πC/A$. A null ray with impact parameter $b$ can cross a spherical section only if $b^{2}\leq C/A$. The capture threshold is fixed by the infimum of $C/A$ on the connected interval between the observer and the black hole horizon. When attained at an interior point, the infimum gives $b_{\rm sh}^{2}=\min(C/A)$, while a static observer outside the controlling minimum, on the inward-sky branch, measures $\sin^{2}α_{\rm sh}=\mathcal{A}_{*}/ \mathcal{A}_{\rm opt}(r_{\rm o})$. The usual photon-sphere equation follows when the minimum occurs at a smooth interior point. Exponential instability additionally requires the minimum to be nondegenerate. The local optical-radius and photon-sphere formulas are established results. Our contribution is to organize them into an observer-to-horizon global selection rule that compares all stationary candidates and relevant endpoint limits. The radial function $B(r)$ does not affect the shadow angle, although it enters the coordinate-time instability rate, whose numerical value also depends on the normalization of the static time coordinate. We derive compact first- and second-order formulas for deformed metrics, demonstrate candidate comparison with a synthetic two-minimum profile, and apply the construction to Reissner--Nordström, Bardeen, charged dilaton, and Kottler black holes. An explicit transformation of the charged-dilaton example from a nonareal to an areal radial coordinate verifies radial-coordinate invariance, while the Kottler example probes a nonasymptotically flat static region.

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arXiv2026

Shadow of the generalized Vaidya black hole

In this paper, we investigate the shadow of the generalized Vaidya black hole described by the Husain solution. Assuming a barotropic equation of state for the additional matter sector, we first identify the self-similar class admitting a homothetic Killing vector and transform the geometry to a conformally static form. This allows us to derive the effective potential for null geodesics in the conformally static representative, determine the corresponding homothetic photon surface, and then transform the result back to the original generalized Vaidya coordinates. We show that, within the weak-energy-condition branches, the parameter $α$ controlling the equation of state determines whether the shadow is enlarged or reduced relative to the Vaidya case: the branch $0\leqα<1/2$ increases the photon-sphere and shadow radii, whereas the branch $1/2<α\leq 1$ decreases them. We then turn to the genuinely time-dependent Husain metric and derive quasistatic slow-evolution equations for the instantaneous photon surface and critical impact parameter. In particular, we show that the growth or contraction of the shadow is governed by the local effective influx in the photon region rather than by the signs of $\dot M$ and $\dot N$ separately. For the charge-like branch, this yields a transparent criterion for when accretion enlarges the shadow and when rapid charge growth instead causes it to shrink.

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arXiv2026

Regular Black Hole Formation and Gamma-Ray Burst from Matter Conversion

During the gravitational collapse of a massive star into a regular black hole, a new form of matter must be produced in order to prevent the formation of a central singularity. Since such matter is not present in the initial stellar configuration, it must emerge dynamically during the collapse. This formation process is expected to be accompanied by a strong release of energy in the form of electromagnetic radiation, which may be observable. Here we investigate the gravitational collapse of baryonic matter into Dymnikova-Hayward-Bardeen regular black holes. We estimate the radiation density and the corresponding bolometric luminosity generated by the formation of the matter sector responsible for singularity avoidance. We show that such processes provide a possible mechanism for gamma-ray bursts. Moreover, compatibility with gamma-ray burst requires small regularization effects. As a result, the corresponding regular black holes differ weakly from the Schwarzschild black hole.

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arXiv2026

Universal Bounds on Horizons, Photon Spheres, and Shadows: The Role of Energy Conditions in Spherically Symmetric Black Holes

In this work, we derive rigorous and universal bounds on the geometric characteristics of black holes in asymptotically flat spacetimes under assumptions that weak energy condition is satisfied. We prove that the event horizon radius, the photon sphere , and the shadow ones take their maximal values in the Schwarzschild black hole case. Any additional matter distribution satisfying the weak energy condition necessarily decreases these radii relative to their Schwarzschild counterparts. Thus, the Schwarzschild solution provides an absolute upper bound on observable size characteristics of static, spherically symmetric black holes. We further analyze configurations possessing two distinct horizons and investigate their extremal regime, in which the inner and outer horizons merge. For extremal black holes, we establish both lower and upper bounds on the extremal horizon location. These bounds depend on the asymptotic structure of the lapse function, in particular on the presence or absence of a $1/r^2$ term in its asymptotic expansion. We derive explicit conditions on the lapse function determining when the extremal Reissner-Nordstrom radius provides a lower bound and when it instead serves as an upper bound. In addition, we prove that in asymptotically flat spacetimes the pressure at the outer event horizon is always either positive or equal to zero. As a consequence, the strong energy condition can not be violated outside the black hole, even in models of regular black holes where it may be violated in the interior region to avoid singularity formation.

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arXiv2026

Exact Dynamical Regular Black Holes from Generalized Polytropic Matter

We present a class of exact, dynamical, and fully analytic solutions describing regular black holes formed via the gravitational collapse of matter obeying a generalized polytropic equation of state. Starting from a Vaidya-type geometry with a radially dependent mass function, we demonstrate that regularization of the Kiselev solutions can be achieved through a physically motivated modification of the energy density profile. This procedure leads to nonsingular spacetimes with a de~Sitter core and finite curvature invariants at the center. We show that the resulting matter content is naturally described by a generalized polytropic equation of state of the form $P=αρ-ζρ^γ$, where the polytropic index $γ$ is uniquely determined by the regularization scheme. Within this framework, we obtain exact dynamical generalizations of several well-known regular black hole solutions, including the Hayward and Bardeen spacetimes, as particular cases corresponding to specific values of the polytropic parameters. Remarkably, the requirement that the equation of state remains coordinate independent imposes a universal constraint relating the regularization scale to the mass function, which in turn guarantees the existence of a regular de~Sitter core with a curvature scale independent of the black hole mass. Our results provide a unified analytic description of Hayward-like and Bardeen-like black holes emerging from gravitational collapse, offering a consistent effective-matter interpretation rooted in generalized polytropic matter.

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arXiv2025

Interplay of Null Energy Condition Violations and Thermodynamics in Kiselev Black Hole Evaporation

The evaporation of black holes with two horizons presents a rich thermodynamic landscape that departs fundamentally from the Schwarzschild paradigm. In this work, we analyze the Hawking temperature dynamics of the Kiselev black hole under varying mass $M$ and anisotropic fluid parameter $N$, explicitly connecting temperature behavior to phase transitions and violations of the null energy condition (NEC). We find that the temperature does not necessarily diverge during evaporation; instead, it typically falls to zero as the black hole evaporates. This cooling behavior is preceded, in certain parameter regimes, by a phase transition marked by a peak in temperature and a divergence in heat capacity. Crucially, the presence and nature of these phase transitions are dictated by the spacetime regions where the NEC is violated: global NEC violation leads to horizon merger and temperature suppression, while partial or absent violation can restore the standard evaporation picture. Our results establish a direct correspondence between thermodynamic stability, horizon dynamics, and energy condition structure in anisotropic black hole spacetimes.

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arXiv2025

Analytical approach for calculating shadow of dynamical black hole

We develop a compact and transparent framework for photon dynamics and shadow formation in slowly evolving, spherically symmetric spacetimes. Starting from the Eddington-Finkelstein action, we derive a force-decomposed radial equation in which the radial acceleration splits into an induced term sourced by mass variation, a centrifugal term, and a purely general-relativistic correction. A key result is a gauge-invariant energy-flux relation, $d(E^2)/dv=-Λ/r$, with $Λ\equiv \varepsilon\,\dot M\,\dot v^2$, which controls how time dependence modifies the canonical energy of null geodesics. In the adiabatic regime we obtain an explicit first-order shift of the photon-sphere radius, $r_{ph}(v)=r_0-a_i/(a_g'+a_c')$, and connect it to the observable shadow through the evolving critical impact parameter, $b_{\rm crit}(v)=\sqrt{r_{ph}(v)^2/f(r_{ph}(v))}$. For Vaidya spacetimes this predicts that accretion ($\dot M>0$) expands the photon sphere and increases the shadow angle, whereas mass loss has the opposite effect. Our formulation refines classic force-balance ideas to dynamical settings, provides a constructive link to time-dependent photon surfaces, and yields simple, observer-ready expressions for the evolution of the shadow. The framework offers a baseline for confronting time-variable horizon-scale imaging with dynamical inflow/outflow models.

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arXiv2025

Energy Extraction and Evolution of Regular Black Holes: The Case of Bardeen Spacetime

This paper examines regular black holes, in particular the Bardeen spacetime where singularities are replaced by non-singular cores. It explores the energy extraction through the charged Penrose process and shows that magnetic charge evaporation can drive a regular black hole towards a singularity. Two evaporation models are proposed, dealing with charge loss and combined charge evaporation with mass accretion, providing insights into the evolution and stability of regular black holes.

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arXiv2025

Regular Black Hole Models in the Transition from Baryonic Matter to Quark Matter

In this paper, we investigate gravitational collapse scenarios involving baryonic matter transitioning into quark-gluon plasma under extreme astrophysical conditions, focusing on their implications for the formation of regular black holes. Standard gravitational collapse models inevitably predict central singularities, highlighting the limitations of classical general relativity in extreme density regimes. By introducing a physically motivated, inhomogeneous transition rate between baryonic and quark matter, we demonstrate analytically and numerically that it is possible to construct regular black hole solutions featuring a nonsingular de Sitter-like core. We further analyze the observable consequences of these models, particularly emphasizing modifications to the black hole shadow radius, which provide direct observational constraints accessible through Event Horizon Telescope (EHT) measurements.

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arXiv2025

Formation of regular black hole from baryonic matter

We present a family of exact, singularity-free solutions describing the collapse of baryonic matter characterized by a barotropic equation of state whose coefficient $α(r,v)$ varies in both radius and time. By matching these interior solutions to the Husain exterior metric, we obtain a self-consistent, dynamical spacetime representing a regular black hole. Although the pressure profile of our models grows with radius and eventually violates the dominant energy condition beyond a critical surface-necessitating an external junction to ensure a globally well-defined spacetime-the interior solution remains non-singular throughout the collapse. We further analyze the optical properties of these regular black holes and find that both the photon sphere radius and the corresponding shadow radius increase monotonically as the local equation of state parameter $α$ is raised. Moreover, the matching interface between the interior and exterior metrics naturally suggests a phase transition in the collapsing fluid, which can postpone the formation of an apparent horizon. Taken together, our results not only highlight novel physical features of horizon formation in regular collapse models but also identify characteristic shadow signatures that could be tested by future observations.

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arXiv2025

Dynamical Black Holes: Apparent Horizon Versus Energy Conditions

Dynamical black holes have an apparent horizon as one of their characteristics. The later might be null, time-like, or space-like surfaces that define the evolution of a black hole. Our study examines how an apparent horizon's behavior is influenced by the null energy condition in spherically-symmetric spacetime. If the location of an apparent horizon and the NEC horizon coincide, it is proven to be null surface. The outer apparent horizon may appear time-like despite the growth of the black hole mass, which must be astrophysical important because the shadow of a black hole always decreases. We show that if NEC is satisfied everywhere in spacetime, then the dynamical black hole asymptotically tends to Vaidya black hole. Our research demonstrates that evaporation of a regular black hole consistently results in a horizonless object with a regular center, which opens the possibility of elucidating the information loss paradox.

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arXiv2025

Barotropic Equation of State and Nonlinear Electrodynamics in Dynamical Black Hole Spacetimes

Models of black holes that differ from idealized vacuum and electrovacuum solutions of Einstein's equations often contain parameters whose physical interpretation is unclear. However, to propose a black hole model for experimental verification, we must clearly understand which parameters describe the black hole and what physical constraints can be imposed on each parameter. When considering dynamical black holes with a barotropic equation of state, an additional integration constant arises, the nature of which remains unclear except for a few specific values of the equation of state coefficient. Nevertheless, when examining solutions such as Husain or Kiselev, we can observe remarkable effects related to black hole evaporation, which are associated with the violation of null energy conditions. However, the main issue lies in the fact that while violations of energy conditions may occur in nature, the ambiguity in the values of parameters describing black holes makes it difficult to determine whether such violations result from natural physical processes or are purely mathematical artifacts that should be excluded from consideration. Moreover, energy conditions play a crucial role in the evolution of a black hole shadow - a characteristic that can potentially be observed experimentally. In this article, we elucidate the parameter arising in Husain's and Kiselev's solutions using nonlinear electrodynamics. We demonstrate that for physically relevant equations of state, the additional parameter represents a combination of electric and magnetic charges.

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arXiv2025

Gravitational Collapse and Formation of Regular Black Holes: Dymnikova, Hayward, and Beyond

The gravitational collapse of a star can lead to the formation of a regular black hole. However, a key factor in this process is the transition of ordinary baryonic matter into a substance that forms the de Sitter core. However, the formation of de Sitter core during gravitational collapse remains an open question, particularly since ordinary baryonic matter does not naturally transition into the exotic matter required to form a de Sitter core. In this paper, we investigate the gravitational collapse of baryonic matter and its potential to form well-known regular black hole solutions, such as those proposed by Dymnikova and Hayward. We model the collapse process as a transition of baryonic matter into a new type of matter, accompanied by the release of energy in the form of electromagnetic radiation. Using a generalized dynamical framework, we derive the energy density of the emitted radiation as a function of both the properties of the initial baryonic matter and the resulting exotic matter. Our findings demonstrate that the gravitational collapse can lead to the formation of various types of regular black holes, providing insights into the physical mechanisms underlying their creation. The detectable radiation signature offers a potential observational test for distinguishing between different black hole models.

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arXiv2025

Regular Black Hole from gravitational collapse of dust and radiation

A black hole is the end state of the gravitational collapse of massive stars. However, a typical black hole contains a singularity and to avoid singularity formation we have to violate a strong energy condition that states that gravity must attract. The nature of the matter that prevents the singularity formation is still unknown. In this paper, we offer a simple model of gravitational collapse of dust and radiation. In the simplest case, such a model leads to a singular black hole. However, if we assume an energy exchange between dust and radiation, which increases towards the center of the collapsing cloud, then it becomes possible to construct a model of a regular black hole. We identify the conditions under which a regular center is possible and also give an explicit example of how such an interaction leads to a regular center.

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arXiv2024

Exact Regular Black Hole Solutions with de Sitter Cores and Hagedorn Fluid

In this paper, we present three exact solutions to the Einstein field equations, each illustrating different black hole models. The first solution introduces a black hole with a variable equation of state, $P = k(r)ρ$, which can represent both singular and regular black holes depending on the parameters $M_0$ and $w_0$. The second solution features a black hole with Hagedorn fluid, relevant to the late stages of black hole formation, and reveals similarities to the first solution by also describing both singular and regular black holes in a specific case. Furthermore, we investigate the shadows cast by these black hole solutions to constrain their parameters. Recognizing that real astrophysical black holes are dynamic, we developed a third, dynamical solution that addresses gravitational collapse and suggests the potential formation of naked singularities. This indicates that a black hole can transition from regular to singular and back to regular during its evolution.

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arXiv2024

On Geodesic motion of particles with zero energy in Kerr and rotating dirty black holes

In this work, we explore the properties of timelike geodesic for particles with zero energy. We found some similarities between geodesic motion in Schwarzschild black hole and timelike geodesics for particles with zero energy. We show, that general relativistic corrections might disappear for negative energies. The existence of circular orbits for zero-energy particles might lead to an unbound center of mass energy of two colliding particles. However, in this work, we explicitly show that closed orbits are absent for zero energy particles in generic axially symmetric black holes. We also investigate timelike motion in generic axially symmetric black holes.

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