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Yaghoub Heydarzade

Publications and source records attributed to Yaghoub Heydarzade.

At least 19 recordsLinked to original sources
arXiv2026

Can the Universe Change Signature When Gravity is Dynamical?

Can a universe undergo a regular Euclidean-Lorentzian signature transition when the gravitational coupling itself is dynamical? We address this question in scalar-tensor gravity with nonminimal coupling $F(ϕ)R$. Although the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) sector can be mapped to the Einstein frame for $F>0$ and a nondegenerate scalar redefinition, not all transition properties are frame independent. For a finite, positive, and sufficiently regular conformal factor, the existence and transverse character of the type change are preserved, whereas the extrinsic geometry is not. We therefore use the Einstein frame as a solution-generating representation and impose total geodesy in the physical Jordan frame. We construct two exactly integrable classes of solutions. In the oscillator-ghost-oscillator branch, the scalar field is stationary at the transition and Jordan-frame total geodesy follows under suitable regularity assumptions on the conformal factor. In the critical exponential-potential branch, the scalar is generically nonstationary and total geodesy instead requires \begin{equation*} H_E\big|_Σ= \frac12 \left( \frac{d\ln F}{dψ} \right)_Σ\dotψ_Σ. \end{equation*} We also distinguish this condition from the stronger smoothness requirements of a Kossowski-Kriele-type transverse metric. Finally, while the canonical Einstein-frame scalar does not allow effective phantom evolution, the dynamical nonminimal coupling can generate a locally superaccelerating Jordan-frame regime near the transition when $\left(\frac{d\ln F}{dψ}\right)_Σ>0$ for the chosen oscillator branch. Thus signature change persists beyond Einstein gravity, with regularity and effective cosmological behavior remaining intrinsically frame sensitive.

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arXiv2026

Dynamical and Observational Analysis of Generalized Nash's Theory of Gravity

We investigate cosmic evolution in generalized Nash's theory of gravity involving the quadratic Ricci invariant $χ=R_{μν}R^{μν}$. The analysis is divided into two complementary branches. First, we study the power-law family $f(R,χ)=R^α+βχ$ as a reduced autonomous system in a flat FLRW background. Because the adopted variables become singular at the Einstein--Hilbert limit $α=1$, the phase-space analysis is restricted to $α\neq1$, with $α=2$ used as a representative quadratic benchmark. This benchmark contains radiation-like boundary configurations, restricted scaling saddles, and de Sitter-like accelerating endpoints (a stable node away from $α=2$ and non-hyperbolic at the benchmark itself), but not a complete regular radiation-to-matter-to-de Sitter sequence. Second, we constrain the regular observational branch $f_{\rm obs}(R,χ)=R-2Λ+βχ$, which reduces exactly to flat $Λ$CDM when $β\to0$. The Hubble rate is obtained from the reduced $Λ$CDM-connected background branch, integrated over $0\le z\le10$ and matched at higher redshift to a standard radiation+matter+$Λ$ background. Using SNe~Ia, BAO, and Planck~2018 compressed CMB distance priors, we find an expansion history very close to $Λ$CDM, with the quadratic correction tightly constrained around the nested standard-model limit. The resulting bound on $β$ should be interpreted as a background-level constraint within this reduced prescription, not as a perturbation-level viability test of the full higher-derivative theory.

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arXiv2026

FLRW-Cosmology in Scalar-Vector-Tensor Theories of Gravity

We generalize our previous theorem for FLRW spacetimes within the framework of generic metric gravity theories. In earlier work, we proved that, in the absence of matter fields, the field equations of any metric gravity theory constructed from the curvature tensor and its covariant derivatives reduce in FLRW spacetime to the Einstein equations with an effective perfect-fluid source. In the present work, we extend this result to a broad class of scalar-vector-tensor theories in which the gravitational action contains arbitrary scalar and vector fields together with their covariant derivatives at any order. We prove that, under the symmetry conditions imposed by FLRW geometry, the metric field equations necessarily take the Einstein form with an effective perfect-fluid source, supplemented by the corresponding scalar and vector field equations. This result shows that FLRW metrics belong to the class of universal metrics: the tensorial structure of the gravitational field equations is solely fixed by the symmetry of the FLRW spacetime and is independent of the specific form of the gravitation theory, while the resulting cosmological dynamics remains theory dependent. We illustrate our theorem using recently proposed Einstein-scalar and Einstein-Proca theories.

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arXiv2026

Signature Change in $f(R, T_ϕ)$ Theory

We investigate a simple $f(R, T_ϕ)$ gravity model coupled to a scalar field and demonstrate that the theory admits classical degenerate metric solutions, analogous to those known in general relativity. In particular, we identify a class of solutions that exhibits a smooth transition from a Euclidean to a Lorentzian domain, thus yielding a classical dynamical realization of signature change.

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arXiv2026

Quantum Cosmology in $f(R, T)$ Theory with Schutz's Perfect Fluid

The $f(R, T)$ theory of gravity extends general relativity (GR) by allowing the gravitational Lagrangian to depend on both the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. The resulting matter-geometry coupling introduces additional dynamical effects that may account for the late-time acceleration of the universe without invoking dark energy. In the present work, we focus instead on the early-time regime and investigate the corresponding quantum cosmological dynamics. We analyze a Friedmann--Lemaitre--Robertson--Walker (FLRW) universe within the $f(R, T)$ framework, employing Schutz's perfect fluid formalism to extract a time parameter emerging from the matter sector itself. This approach is particularly well motivated in $f(R, T)$ gravity, where the coupling between geometry and the energy-momentum tensor's trace makes matter an active participant in the dynamics of spacetime and the evolution of cosmic time. The gravitational Hamiltonian, canonical momenta, and potential are derived, leading to the corresponding Schrödinger--Wheeler--DeWitt (SWDW) equation. The wave function of the universe is obtained for specific forms of $f(R, T)$, and the results are compared with previous studies in $f(R)$ and $f(R, T)$ models, highlighting the role of matter-geometry coupling in the emergence of quantum cosmological dynamics.

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arXiv2025

Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories

We demonstrate that the non-vacuum field equations of Cotton gravity and Conformal Killing gravity admit a generalized class of Vaidya-type solutions. In particular, beyond the standard induced term associated with the matter source, the generalized metric incorporates two additional correction terms of purely geometric origin, arising from the unique structure of these theories. This extended solution generalizes the classical Vaidya spacetime in General Relativity and offers new insights into the dynamics of radiating spacetimes within the framework of these third-rank gravity theories.

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arXiv2025

Dynamical Wormhole Solutions in $f(R, T)$ Gravity

A class of $f(R, T)$ theories extends the Einstein-Hilbert action by incorporating a general function of $R$ and $T$, the Ricci scalar and the trace of the ordinary energy-momentum tensor $T_{μν}$, respectively, thereby introducing a specific modification to the Einstein's field equations based on matter fields. Given that this modification is intrinsically tied to an energy-momentum tensor $T_{μν}$ that a priori respects energy conditions, we explore the potential of $f(R, T)$ theories admitting wormhole configurations satisfying energy conditions, unlike General Relativity, which typically necessitates exotic matter sources. Consequently, we investigate the existence of dynamical wormhole geometries that either uphold energy conditions or minimize their violations within the framework of trace of energy-momentum squared gravity. To ensure the generality of our study, we consider two distinct equations of state for the matter content and systematically classify possible solutions based on constraints related to the wormhole's throat size, the coupling parameter of the theory, and the equation of state parameters.

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arXiv2025

Thermodynamics of FLRW universe in Quadratic Gravity

In this paper, we investigate the thermodynamic aspects of quadratic gravity in a $D$-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. First, we derive the field equations and the effective energy-momentum tensor for quadratic gravity. Then, using these equations, we obtain the generalized Misner-Sharp energy within the framework of this model. We consider the thermodynamic behavior of the apparent horizon and derive the equations of state related to the pressure, temperature, and radius of the apparent horizon. Using the thermodynamic pressure, we obtain the critical points corresponding to phase transitions. We determine the critical temperature and critical radius in terms of model parameters, including the quadratic coupling and the cosmological constant. We also examine key thermodynamic quantities, such as Wald entropy, specific heat at constant pressure, enthalpy, Gibbs free energy. By examining the behavior of these quantities, we can gain insight into the thermodynamic stability of the quadratic gravity model. In particular, we find that quadratic terms change the stability conditions and can lead to new thermodynamic behaviors compared to general relativity.

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arXiv2025

Generalized Misner-Sharp energy in $f(R,\mathcal{G})$ gravity

In this work, we explore the formulation of the Misner-Sharp energy within the framework of $f(R, \mathcal{G})$ gravity, a modified theory incorporating the Ricci scalar $R$ and the Gauss-Bonnet scalar $\mathcal{G}$. By extending the quasilocal energy definition to both static spherically symmetric spacetime and the dynamic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive explicit expressions for the generalized Misner-Sharp energy using two complementary approaches: the integration method and the conserved charge method based on the Kodama vector. Our analysis shows that the Misner-Sharp energy expression in $f(R, \mathcal{G})$ gravity reduces to standard $f(R)$ gravity results when the Gauss-Bonnet term is absent, revealing how curvature modifications influence the geometric structure and dynamics of cosmic evolution. Furthermore, we investigate the thermodynamic properties at the apparent horizon associated with the FLRW background, and we find a connection to non-equilibrium thermodynamics unique to $f(R, \mathcal{G})$ gravity. These findings underscore the subtle and fundamental role of curvature corrections in determining the energy distribution and thermodynamic behavior of gravitational systems.

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arXiv2025

Non-Vacuum Solutions in Cotton Theory

Cotton theory (CT) introduces a higher derivative extension of General Relativity (GR) characterized by third-rank field equations. Recently, key distinctions between CT and GR concerning wave and vacuum solutions have been highlighted in [1, 2]. In this study, two particular non-vacuum solutions of CT are investigated within its Codazzi formulation. The motivation is to reveal how this theory might account for or adapt to the effects of non-vacuum sources, and whether it can provide new insights into the behavior of both singular and regular black holes in astrophysical contexts. It is shown that CT generalizes the Kiselev and Dymnikova solutions in GR. Some aspects of the generalized solutions, in particular concerning singularities, thermodynamics, and geodesics, are addressed in comparison to GR.

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arXiv2024

Wave Metrics in the Cotton and Conformal Killing Gravity Theories

We study wave metrics in the context of Cotton Gravity and Conformal Killing Gravity. First, we consider pp-wave metrics with flat and non-flat wave surfaces and show that they are exact solutions to the field equations of these theories. More explicitly, the field equations reduce to an inhomogeneous Laplace and Helmholtz differential equations, depending on the curvature of the two-dimensional geometry of the wave surfaces. An interesting point here is that the ones with non-flat wave surfaces are not present in classical GR, which manifests a crucial distinction between these theories and GR. Moreover, we investigate Kerr-Schild-Kundt metrics in the context of these theories and show that, from among these metrics, only the AdS wave metrics solve the field equations of these theories. However, AdS spherical and dS hyperbolic wave metrics do not solve the field equations of these theories, which is in contrast to the classical GR. In the case of AdS wave metrics, the field equations of these theories reduce to an inhomogeneous Klein-Gordon equation. We give all the necessary and sufficient conditions for the metric function $V$ to solve these field equations.

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arXiv2024

Dynamical Photon Spheres in Charged Black Holes and Naked Singularities

To understand the nature of a black hole shadow in dynamical spacetimes, we construct an analytical model of a dynamical photon sphere in the context of the Bonnor-Vaidya spacetime. Comparing the resulting photon sphere radius with the one in Vaidya spacetime, we find that the charge always decreases the radius of the photon sphere. We also prove that a naked singularity in Bonnor-Vaidya spacetime, unlike the static Reissner-Nordstrom naked singularity, may cast a shadow, and as a result, it cannot be distinguished from a black hole through its shadow.

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arXiv2024

Geometric Perfect Fluids and Dark Side of the Universe

Recently we showed that in FLRW cosmology, the contribution from higher curvature terms in any generic metric gravity theory to the energy-momentum tensor is of the perfect fluid form. Such a geometric perfect fluid can be interpreted as a fluid remaining from the beginning of the universe where the string theory is thought to be effective. Just a short time after the beginning of the Universe, it is known that the Einstein-Hilbert action is assumed to be modified by adding all possible curvature invariants. We propose that the observed late-time accelerating expansion of the Universe can be solely driven by this geometric fluid. To support our claim, we specifically study the quadratic gravity field equations in $D$-dimensions. We show that the field equations of this theory for the FLRW metric possess a geometric perfect fluid source containing two critical parameters $σ_1$ and $σ_2$. To analyze this theory concerning its parameter space $(σ_1, σ_2)$, we obtain the general second-order nonlinear differential equation governing the late-time dynamics of the deceleration parameter $q$. Hence using some present-day cosmological data as our initial conditions, our findings for the $σ_2=0$ case are as follows: $ (i)$ In order to have a positive energy density for the geometric fluid $ρ_g$, the parameter $σ_1$ must be negative for all dimensions up to $D = 11$, $(ii)$ For a suitable choice of $σ_1$, the deceleration parameter experiences signature changes in the past and future, and in the meantime it lies within a negative range which means that the current observed accelerated expansion phase of the Universe can be driven solely by the curvature of the spacetime, $(iii)$ $q$ experiences a signature change and as the dimension $D$ of spacetime increases, this signature change happens at earlier and later times, in the past and future, respectively.

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arXiv2023

Hairy Kiselev Black Hole Solutions

In the realm of astrophysics, black holes exist within nonvacuum cosmological backgrounds, making it crucial to investigate how these backgrounds influence the properties of black holes. In this work, we first introduce a novel static spherically-symmetric exact solution of Einstein field equations representing a surrounded hairy black hole. This solution represents a generalization of the hairy Schwarzschild solution recently derived using the extended gravitational decoupling method. Then, we discuss how the new induced modification terms attributed to the primary hairs and various background fields affect the geodesic motion in comparison to the conventional Schwarzschild case. Although these modifications may appear insignificant in most cases, we identify specific conditions where they can be comparable to the Schwarzschild case for some particular background fields.

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arXiv2023

Dynamical Wormhole Solutions in Rastall Theory

Wormhole configurations in Einstein's general theory of relativity (GR) require exotic matter sources violating the weak energy condition (WEC). Rastall's theory is a generalization of GR in its matter source considering a nonconserved energy-momentum (EM) tensor. Hence, on one hand, the nature of this generalization of the matter source of field equations and, on the other hand, the possibility of respecting energy conditions for dynamical wormholes in contrast to static ones motivates us to study the possibility of the existence of wormhole configurations respecting energy conditions or minimizing the violations of them in Rastall's modified theory. We derive general analytical solutions considering a constant redshift function and a particular equation of state for energy density and pressure profiles. We show that because of the modification in the EM source of the field equations, there exist solutions respecting the WEC in the vicinity of the wormhole's throat for specified values of the parameters. Some particular solutions are discussed in detail.

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arXiv2021

Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings

The Kerr-Schild-Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the "universality theorem" to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of Modified Horndeski theories with Maxwell's field. We obtain exact solutions of these theories representing the $pp$-waves and AdS-plane waves in arbitrary $D$ dimensions.

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arXiv2021

On the initial singularity in Kantowski-Sachs spacetime

The emergent universe scenario is a proposal for resolving the Big Bang singularity problem in the standard Friedmann-Lemaitre-Robertson-Walker cosmology. In the context of this scenario, the Universe originates from a nonsingular static state. In the present work, considering the realization of the emergent universe scenario, we address the possibility of having a nonsingular Kantowski-Sachs type static state. Considering four and five dimensional models (with and without brane), it is shown that both the existence and stability of a nonsingular state depend on the dimensions of the spacetime and the nature of the fluid supporting the geometry.

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