arXiv subjects

Debadri Bhattacharjee

Publications and source records attributed to Debadri Bhattacharjee.

16 recordsLinked to original sources

arXiv2026

Gravitational wave echoes as probes of the maximum mass of strange stars in quadratic curvature-matter coupled gravity

Gravitational wave astronomy provides an exemplary avenue to study exotic compact stars with utmost precision. Recent analyses of GW170817 have reported possible post-merger gravitational wave echoes with a significance of $4.2\sigma$ and a dominant frequency near $72$ Hz. Such echoes may originate from ultracompact remnants possessing photon spheres that partially trap gravitational perturbations. In general relativity, photon-sphere formation requires the stellar compactness to lie within one-third and four-ninths, which is challenging even for a realistic equations of state. Here, we explore this possibility in quadratic curvature gravity with non-minimal matter coupling, considering strange stars described by the MIT bag model equation of state. By solving the modified Tolman-Oppenheimer-Volkoff equations, we obtain the mass-radius relations and identify configurations capable of supporting photon spheres and GW echoes. In the proposed framework, the modified Buchdahl limit allows more compact stellar solutions, while photon-sphere constraints restrict the viable parameter space. We find that increasing the bag constant, decreases the maximum mass and echo time, shifting the echo frequency toward the kHz regime. The echo constraints yield more stringent maximum mass-radius limits than hydrostatic equilibrium, suggesting a revised maximum mass bounds for strange stars. These results highlight the potential of post-merger strange stars as GW echo sources and demonstrate the role of echoes as probes of modified gravity and high-frequency gravitational waves.

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arXiv2026

Influence of chemical potential to explain the maximum mass and tidal love number of strange stars

We investigate the influence of medium effects on strange quark matter and their consequences for the structural properties of compact stars. In this study, the bag constant, in the MIT bag model equation of state, is reformulated as a function of the chemical potential of quark. Imposing the Bodmer-Witten stability criterion, the parameter space is constrained by evaluating the energy per baryon. The Tolman-Oppenheimer-Volkoff equations are then solved to obtain the maximum mass-radius configurations. Our analysis shows that an increase in chemical potential leads to a reduction in the effective value of bag constant, resulting in a stiffer equation of state and correspondingly higher value of maximum stellar mass. Furthermore, we examine the chemical potential dependence of the tidal Love number and tidal deformability. The results demonstrate that, for the chosen set of parameters, the constraint from the GW170817 event, namely $\Lambda < 800$, is consistently satisfied. In this paper, we have tried to establish how chemical potential $(\mu)$ affects the maximum mass and tidal deformability of strange stars.

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arXiv2026

Investigating quark star properties through baryon number density $(n)$ within the framework of $f(Q)$ gravity

In this paper, we construct a viable strange star model in the framework of the equation of state, $p_r=\frac{1}{3}(\rho-4B)$, proposed in the MIT bag model, where $B$ is termed as the bag constant. Considering extreme Wood-Saxon-like parameterisation of baryon number density dependent Bag parameter $(B)$ in the framework of $f(Q)$ modified gravity. We have determined the possible range of baryon number density ($n$) for stable quark matter inside the star and calculated the corresponding range of $B$. By solving TOV equations, we obtain the possible maximum mass and radius considering the MIT bag model equation of state with baryon number density dependent $B$. All the physical parameters associated with the stars, such as $\rho,~p_r,~p_t$ and anisotropy parameter ($\Delta$), have been analysed in this model to establish the physical viability as well as acceptability of the model. Then, we study the stability of the model by analysing the causality conditions, energy conditions, generalised TOV equation, cracking condition of Herrera and the study of adiabatic index of the fluid. Within the parameter space used here to construct the model, we have predicted the radii of a few known compact stars, and it is found that the model is suitable in predicting the radii of stars where masses lie below the $2.46~M\odot$, and the predicted radii from the model are nearly equal to the values obtained from recent observations. It is significant to observe that up to $2.01~M\odot$, it may be treated as a Strange Star (SS). On the other hand, maximum mass above $2.01~M\odot$ and up to $2.46~M\odot$ may be treated as di-quark stars.

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arXiv2025

Thermodynamic invariance of the energy-momentum tensor under matter-Lagrangian choices and its astrophysical implications in $f(R,T)$ gravity

The correct choice for the matter Lagrangian $(\mathcal{L_{M}})$ in the framework of $f(R,T)$ theory of gravity, has been a fundamental yet often overlooked ambiguity. It has been a long-standing issue, whether to choose $\mathcal{L_{M}}=p$ or $-\rho$ as the proper definition of matter sector. In this work, we show that both choices lead to the same energy-momentum tensor, from thermodynamic point of view. However, for these two choices, the structure of the TOV equations are different. We construct and solve TOV equations using MIT bag model equation of state for $\mathcal{L_{M}}=p$ and $-\rho$, and study the impact of the choices for matter Lagrangian on the maximum mass limit as well as M-R plot of compact stars. It is interesting to note that allowed range of gravity-matter coupling coefficient $(\alpha_{c})$ is also different for $\mathcal{L_{M}}=p$ and $\mathcal{L_{M}}=-\rho$, i.e., $\alpha_{c}$ can not be taken arbitrarily. Notably, through $\mathcal{L_{M}}=p$, we achieve a maximum mass of $2.78~M_{\odot}$, whereas for $\mathcal{L_{M}}=-\rho$, we obtain a maximum mass of $2.41~M_{\odot}$. So, despite the same energy-momentum tensor for different choices of $\mathcal{L_{M}}$, the upper limit of maximum mass is significantly modified.

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arXiv2025

Exploring density dependent B as a suitable parameter in higher dimensional approach with a non-linear equation of state

In this investigation, we present a singularity free interior solution of the Einstein field equation for a class of anisotropic compact objects in dimensions $D\geq4$. In accordance with the concept of Vaidya and Tikekar, the geometry of the physical $(D-1)$-space of a star corresponding to $t=constant$ hypersurface is assumed to be of a $(D-1)$ spheroid. For the fulfilment of causality condition, a limit of the spheroidal parameter ($\lambda$) is noted depending on the values of amount of anisotropy ($\alpha$) and space-time dimensions ($D$). We note that by switching off the extra parameters ($\alpha$ and $D$), previously obtained limit of $\lambda$ can be generated. To validate our findings, we compare the results obtained from our model with observational data of PSR J1614-2230 (mass=$1.908^{+0.016}_{-0.016}M_{\odot}$, radius=$11.93^{+0.50}_{-0.50}km$). It is noted that the best fit equation of state corresponds to polynomial equation of state of the order of five. We use this finding to develop a density dependent MIT bag model which seems to be useful for the correct description of compact object in our model. The mass radius relation shows that our model mimics a wide range of recently observed pulsars in four and higher dimensions. Furthermore, we also found that our model exhibits stability according to Generalised TOV equation, Herrera cracking condition, and the adiabatic index.

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arXiv2025

Maximum mass limit of strange stars in quadratic curvature-matter coupled gravity

We explore the maximum mass limit of strange stars in quadratic curvature gravity with the non-minimal matter coupling. The characteristic parameters of the quadratic curvature coupling and the non-minimal matter coupling imply the contributions from higher-order curvature terms and the coupling between matter and geometry, respectively. We demonstrate, explicitly, that the conservation of energy-momentum tensor can be modified and in the case of negligible non-minimal matter coupling, the formalism of general relativity is recovered. By deriving the Tolman-Oppenheimer-Volkoff equations from the gravitational field equations and applying the MIT bag model equation of state, we obtain the corresponding mass-radius relationships for strange stars. Although the MIT bag model represents a simplified phenomenological equation of state, it remains an effective description of strange quark matter under the extreme conditions prevailing in neutron star/strange star interiors. Within the present framework, the adoption of this equation of state yields stellar radii that are in close agreement with those inferred from recent observations of compact stars as well as GW events. This consistency between theoretical predictions and observational results indicates that, despite its simplicity, the model captures essential features of dense matter and supports the reliability of the results reported in this work. Furthermore, we show that the maximum mass limit of strange stars can exceed the general relativistic counterpart. Specifically, we find that a maximum mass up to 3.11 solar mass is achievable which suggests that the lighter companion of GW190814 could plausibly be a strange star.

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arXiv2025

Maximum mass of singularity-free anisotropic compact stars in Rastall theory of gravity

The current model explores spherically symmetric anisotropic compact stars within the Rastall theory of gravity. By employing the Krori and Barua metric ansatz (K.D. Krori and J. Barua, J. Phys. A: Math. Gen. 8 (1975) 508), we derive a set of tractable, singularity-free relativistic solutions to the Einstein field equations. Using a best-fit equation for the numerical solution of the TOV equation, we determine the maximum mass and corresponding radius in this model. Our findings reveal that an increase in the Rastall parameter $(\xi)$ leads to a higher maximum mass, indicating a stiffer nature of the equation of state. For $\xi$ values ranging from 0.01 to 0.09, we calculate the maximum mass to be between $2.24M_{\odot}$ and $2.36M_{\odot}$, with corresponding radii from 9.48 to 10.15 km. Furthermore, our model's predictions for the radii of recently observed pulsars are consistent with observational data. The model satisfies essential criteria for causality, energy conditions, and stability, confirming its viability and physical acceptability as a stellar structure.

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arXiv2025

Exploring gravastar-like structures with strongly interacting quark matter shell in the framework of $f(Q)$ gravity under conformal symmetry

In this work, we investigate gravastar-like structures in static and spherically symmetric space-time within the framework of $f(Q)$ gravity coupled with conformal symmetry. We have modified the conventional gravastar model by introducing a strongly interacting quark matter shell which maintains the apex of causal limit through the EoS, $p=\rho-2B_{g}$, where, $B_{g}$ is the bag constant. Non-singular and non-vanishing solutions for the interior and shell regions are obtained, respectively. We have used the Israel junction condition to evaluate the mass of the thin shell for different choices of characteristic radii. Interestingly, the mass of the shell is independent of the matter distribution in the shell region. We found that for radii 9.009, 10.009 and 11.009, the mass increases as $1.80,~1.95$ and $2.28~M_{\odot}$. The physical features, such as, proper length, energy and entropy of the shell region are studied within the parameter space. Surface redshift calculations were used to validate the proposed model.

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arXiv2025

Influence of density-dependent bag function $B(n)$ on strange stars for non-zero strange quark mass ($m_s\neq0$) in $f(R,T)$ gravity consistent with observational validation

In this work, a new class of solution of the Einstein field equation for an isotropic strange star using the modified Mak-Harko type density profile along with the equation of state as proposed in the MIT bag model and considering finite mass of the strange quark ($m_s$) is presented in the framework of $f(R,T)$ gravity with $f(R,T)=R+2\zeta T$, where, $\zeta$ is the coupling parameter. To incorporate the quark matter hypothesis with a physically viable stellar framework, a baryon number density ($n$) dependent bag function $B(n)$ is analysed, using exponential type parametrisation. The energy per baryon ($E_B$) has been investigated to restrict $B(n)$ and corresponding $n$ within a stable window, specifically satisfying the condition $E_B\leq 930.4~MeV$, which corresponds to the binding energy of $\isotope[56]{Fe}$. We note a lower limit of $n$ below which $E_B>930.4~MeV$ as $E_B$ increases with the decrease of $n$. This value, however, depends on $m_s$. Additionally, $n$ has a maximum value of $0.36~fm^{-3}$ irrespective of $m_s$ depending on the range of bag function. All the essential characteristics are satisfactorily fulfilled within the stellar interior for the selected set of parameter space. In this model, the maximum mass and radius are found by solving the TOV equations numerically which yields $M=2.03~M_{\odot}$ with a radius of $11.49~km$ for $m_s=0~MeV$ and $n=0.36~fm^{-3}$ and $\zeta=-0.1$. It is also noted that the maximum mass and the corresponding radius are the function of $m_s$, $\zeta$ and $n$. The proposed model has been shown to comply with the required energy conditions and satisfies the criterion for dynamical stability, thereby confirming its physical plausibility as a physically consistent stellar model within the parameter space used.

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arXiv2025

Estimating the mass of the thin shell of gravastars in generalised cylindrically symmetric space-time within the framework of Rastall theory of gravity

This study investigates the gravastars in the framemwork of Rastall theory of gravity in generalised cylindrically symmetric space-time. Following the Mazur-Mottola hypothesis (P. O. Mazur and E. Mottola, Universe {\bf 9}, 88 (2023)), gravastars are classified as one of the most unique and exotic kind of compact objects, presenting themselves as a plausible alternative to black holes. In this study, we build upon the Mazur-Mottola framework of Gravitational Bose-Einstein Condensate (GBEC) stars by generalising it to a cylindrically symmetric spacetime within the framework of Rastall gravity to present a novel approach for estimating the mass limit of the thin shell of isotropic gravastars. We have ensured singularity-free solutions for the interior de-Sitter core, non-vanishing solutions for the thin shell and flat vacuum solution of the exterior region, within this parameter space. Under the framework of Rastall gravity and cylindrically symmetric spacetime, the Lanczos equations at the hypersurface junction $(r=R)$ undergo significant modifications, leading to a revised form of the Darmois-Israel junction conditions. These modified junction conditions are utilised to investigate the influence of the Rastall parameter $(\xi)$ on the mass of the thin shell and key characteristics of gravastars, including the shell's proper length, energy, and entropy. Additionally, we propose a novel method for estimating the mass of the thin shell using the concept of surface redshift $(Z_{s})$. By adhering to the Buchdahl upper limit, $Z_{s}<2$ for isotropic configuration, we have determined the mass bounds of the thin shell for various characteristic radii and values of the Rastall parameter $(\xi)$.

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arXiv2025

The role of finite value of strange quark mass $(m_{s}\neq0)$ and baryon number density $(n)$ on the stability and maximum mass of strange stars

This study describes the impact of non-zero value of strange quark mass $(m_{s})$ and number density of baryons $(n)$ on the structure, stability and maximum mass of strange stars. We derive an exact relativistic solution of the Einstein field equation using the Tolman-IV metric potential and modified MIT bag model EoS, $p_{r}=\frac{1}{3}(\rho-4B')$, where $B'$ is a function of bag constant $B$, $m_{s}$ and baryon number density $(n)$. Following CERN's findings, transition of phase from hadronic matter to Quark-Gluon Plasma (QGP) may occur at high densities in presence of favourable conditions. The standard MIT bag model, with a constant $B$, fails to explain such transition properly. Introducing a finite $m_{s}$ and Wood-Saxon parametrisation for $B$, dependent on baryon number density $(n)$, provides a more realistic EoS to address such phase transition. Both $m_{s}$ and $n$ constrain the EoS, making it softer as $m_{s}$ increases. Solutions to the TOV equations reveal that for massless strange quarks, maximum mass is 2.01 $M_{\odot}$ and corresponding radius is 10.96 Km when $n=0.66~fm^{-3}$. These values decrease to 1.99 $M_{\odot}$ and 1.96 $M_{\odot}$, with corresponding radii of 10.88 Km and 10.69 Km for $m_{s}=50$ and $100~MeV$ respectively having same $n$ value. It is interesting to note that a corelation exists between $n$ and $m_{s}$. The hadronic to quark matter transition occurs at higher values of $n$, when $m_{s}$ increases such as $n\geq0.484,~0.489$ and $0.51~fm^{-3}$ for $m_{s}=50$ and $100~MeV$ respectively. Beyond these values, the energy per baryon $(\mathcal{E_{B}})$ drops below $930.4~MeV$, indicating a complete transition to quark matter. For physical analysis, we have considered $n~(=0.578~fm^{-3})$ which lies in the stable region with $B(n)=70~MeV/fm^{3}$. The model provides a viable description of strange stars, satisfying all necessary physical requirements.

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arXiv2024

Interacting quark matter and $f(Q)$ gravity: A new paradigm in exploring the properties of quark stars

Perturbative Quantum Chromodynamics corrections and the colour superconductivity indicate that strongly interacting matter can manifest unique physical behaviours under extreme conditions. Motivated by this notion, we investigate the interior structure and properties of quark stars composed of interacting quark matter, which provides a comprehensive avenue to explore the strong interaction effects, within the framework of $f(Q)$ gravity. A unified equation of state is formulated to describe various phases of quark matter, including up-down quark matter $(2SC)$, strange quark matter $(2SC+s)$, and the Colour-Flavor Locked $(CFL)$ phase. By employing a systematic reparametrisation and rescaling, the number of degrees of freedom in the equation of state is significantly reduced. Utilising the Buchdahl-I metric ansatz and a linear $f(Q)$ functional form, $f(Q)=\alpha_{0}+\alpha_{1}Q$, we derive the exact solutions of the Einstein field equations in presence of the unified interacting quark matter equation of state. For the $2SC$ phase, we examine the properties of quark stars composed of up-down quark matter. For the $(2SC+s)$and $CFL$ phases, we incorporate the effects of a finite strange quark mass $(m_{s}\neq0)$. The Tolman-Oppenheimer-Volkoff equations are numerically solved to determine the maximum mass-radius relations for each phase. Our results indicate that the model satisfies key physical criteria, including causality, energy conditions, and stability requirements, ensuring the viability of the configurations. Furthermore, the predicted radii for certain compact star candidates align well with observational data. The study highlights that quark stars composed of interacting quark matter within the $f(Q)$ gravity framework provide a robust and physically consistent stellar model across all considered phases.

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arXiv2024

Hybrid compact stars with finite strange quark mass and dark energy: implications for astrophysical observations

In this work, a detailed investigation of compact stars composed of deconfined quark matter with finite strange quark mass ($m_s \neq 0$) admixed with dark energy is presented. The quark sector is modeled using the MIT bag model equation of state, while the dark energy component obeys a linear equation of state, $p^{de} = \omega \rho^{de}$ with $\omega$ in the range $-1\leq\omega\leq-frac{1}{3}$. The stellar configuration is explored within the Finch-Skea ansatz for the $g_{rr}$ metric potential. A coupling between quark matter and dark energy is introduced through $\rho^{de} =\beta \rho^Q$, where $\beta$ represents the dark energy coupling parameter. Causality restricts $\beta$ within $0<\beta<-\frac{1}{3\omega}$. The structural features of such compact stars are analysed by varying $\beta$ in this range. Solving the Tolman-Oppenheimer-Volkoff equations yields a maximum mass of $2.012~M_{\odot}$ with a radius of about 11 km. For a fixed $\omega$, both mass and radius decrease as $\beta$ increases. The model satisfies causality, energy and stability conditions, ensuring physical acceptability. Finally, the framework is applied to estimate radii of compact star candidates identified as strange quark stars with dark energy, showing good agreement with observational data.

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arXiv2024

Charged analogues of singularity-free anisotropic compact stars under linear $f(Q)$-action

This study simulates the characteristics of spherically symmetric, anisotropic compact stellar bodies with electrical charge within the framework of the $f(Q)$ theory of gravity. Employing the Krori-Barua metric ansatz (K.D. Krori, J. Barua, J. Phys. A: Math. Gen. 8 (1975) 508) along with a linear form of $f(Q)$ model, {\it viz.}, $f(Q)=\alpha_{0}+\alpha_{1}Q$, we obtain a tractable set of exact relativistic solutions of the field equations. A specific form of charge $(q=q_{0}r^{3})$ is considered here for the present analysis. It is noted that the model is valid up to the value of charge intensity $q_{0}\leq0.0009~Km^{-2}$. Beyond this value, the model does not permit physically viable results. We have obtained the best fit equation of state in the model, which is incorporated to solve the TOV equations numerically to determine the mass-radius relation within the parameter space used here. With increasing charge intensity $(q_{0})$ from 0.0002 to 0.0009, the maximum mass ranges from $2.84-2.92~M_{\odot}$, and the corresponding radii range from $12.00-12.20~Km$. Moreover, the predicted radii of some recently observed pulsars and GW 190814 show that our model also complies with the estimated radii based on the observational results. Our model is found to satisfy all the characteristic features, such as behaviour of matter variables, causality condition, energy constraints and stability criteria, which are pertinent in the context of a stable stellar configuration to emerge as a viable and physically acceptable stellar model in the framework of $f(Q)$ gravity.

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arXiv2024

Impact of non-zero strange quark mass $(m_{s}\neq0)$ in $f(R,T)$ gravity admitting observational results of strange stars

In this article we propose a new class of isotropic strange star using Buchdahl-I metric ansatz in the context of MIT bag model equation of state considering of non-zero strange quark mass $(m_{s})$ in the framework of modified $f(R,T)$ theory of gravity. The barotropic form of MIT bag model equation of state and a specific class of $f(R,T)$ model, {\it viz.}, $f(R,T)=R+2\alpha_{c}T$ where $\alpha_{c}$ is termed as the gravity-matter coupling constant, produces a tractable set of solutions of Einstein field equations. From the allowed numerical values of the coupling constant $(\alpha_{c})$, we have considered a range of $\alpha_{c}$ from -2.0 to 2.0. Maximum mass and radius in this model is found by numerically solving the TOV equations and we note that within the stability window imposed by energy per baryon, for an arbitrary choice of bag constant $B=70~MeV/fm^{3}$, $m_{s}$ and $\alpha_{c}$ act as a constraining factor. Interestingly, the increment of $m_{s}$ and $\alpha_{c}$ results in a softer equation of state which leads to the decrease in the maximum mass and radius while negative values of $\alpha_{c}$ leads to a stiffer equation of state thereby increasing the maximum mass and radius in the present model. For physical application, we consider EXO 1745-248 and study the effects of $m_{s}$ and $\alpha_{c}$ on its radius. Using the formalism, we have analysed the characteristic properties of EXO 1745-248. Apart from that, we have predicted the radii of a wide range of strange star candidates in the context of $f(R,T)$ gravity and the obtained results agree well with the observed results. We note that the proposed model satisfies all the necessary energy conditions and stability criteria to emerge as a viable stellar configuration.

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arXiv2024

Charged gravastar model in Rastall theory of gravity

Gravastars are considered as one of the prime exotic type compact objects which may be found at the end state of gravitational collapse of massive stars with a view to resolve the complexities that are pertinent in case of a black hole \cite{Mazur}-\cite{Mazur2}. In this paper, we analyse the role of charge on the possible formation of isotropic spherically symmetric gravastar configuration in the framework of Rastall gravity. Gravastar contains three distinct layers {\it viz.} i) Interior region, ii) Thin shell and iii) Exterior region. The interior region is characterised by the equation of state $p=-\rho$ that defines the repulsive outward pressure in radial direction at all points on the thin shell. The thin shell, contains ultra-relativistic stiff fluid which is denoted by the equation of state $p=\rho$ following Zel'dovich's criteria \cite{Zeldovich,Zeldovich1} for cold baryonic universe, can withstand the repulsive pressure exerted by the interior region. The exterior region is the vacuum space-time represented by the Reissner-Nordstr$\ddot{o}$m solution. In view of the above specifications, we construct and analyse a charged gravastar model in Rastall theory of gravity which represents several salient features. The basic physical attributes, {\it viz.} proper length, energy, entropy and equation of state parameter of the shell are investigated. In this model, it is interesting to note that for large value of the radius of hyper-surface (R) the EoS parameter of the thin shell corresponds to dark energy EoS with $\mathcal{W}(R)\rightarrow-1$. However, for small value of $R$ the EoS parameter $\mathcal{W}(R)\rightarrow0$, defines a dust shell. The stability of the model is ensured through the study of gravitational surface redshift and maximisation of shell entropy within the framework of Rastall theory of gravity.

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