At the heart of this revolutionary paper lies a sophisticated exploration of modified gravity theories, specifically focusing on what physicists refer to as “$f(R)$ gravity.” This class of theories posits that gravity might not be solely described by Einstein’s elegantly simple field equations of general relativity, but rather by a more complex functional relationship involving the Ricci scalar, a fundamental geometric quantity representing the curvature of spacetime. In essence, $f(R)$ gravity suggests that our universe might be operating under a modified gravitational law, a subtle yet profound departure from the bedrock of modern cosmology. Understanding these modifications is crucial, as they could hold the key to explaining observed cosmic phenomena that current models struggle to fully account for, such as the accelerating expansion of the universe driven by dark energy, a concept that continues to baffle scientists with its perplexing nature and dominant influence on galactic structures even across vast cosmic distances.

The paper meticulously dissects two powerful analytical tools used by physicists to explore the behavior of physical systems and extract fundamental laws: the Mei symmetry approach and the venerable Noether approach. While Noether’s theorem, established over a century ago, is a cornerstone of theoretical physics, linking symmetries to conserved quantities like energy and momentum, the Mei symmetry approach, developed more recently, offers a complementary perspective, particularly potent when dealing with more complex, non-linear systems characteristic of modified gravity. The researchers have masterfully demonstrated how these two seemingly different methodologies, when applied to the intricate tapestry of $f(R)$ gravity, yield remarkably consistent and illuminating results, suggesting a deeper, underlying unity in our understanding of physical laws and the cosmos they orchestrate, a convergence that offers powerful validation for their new theoretical synthesis and a promise of further revelations.

This comparative analysis is not merely an academic exercise; it represents a significant methodological advance. By showcasing the concord between the Mei and Noether approaches within the context of $f(R)$ gravity, the paper not only validates the robustness of the $f(R)$ gravity framework itself but also amplifies the predictive and explanatory power of both symmetry analysis techniques. This is akin to discovering that two different maps of an unexplored territory, drawn by different cartographers using different surveying instruments, perfectly overlay each other, confirming the landscape’s precise features and solidifying our confidence in the accuracy of our exploration and the fundamental principles that govern it, leading to potentially revolutionary insights into the deep structure of physical reality.

The concept of conserved quantities is utterly fundamental to our understanding of the universe. These are quantities that remain unchanged over time, acting as unchanging pillars in the dynamic theater of physical interactions. Noether’s theorem famously dictates that for every continuous symmetry in a physical system, there exists a corresponding conserved quantity. For instance, the symmetry of physical laws with respect to time translations leads to the conservation of energy, while spatial translation symmetry guarantees the conservation of linear momentum. Without these immutable laws, the universe would descend into chaos, and predictability would evaporate, making scientific inquiry impossible and leaving us adrift in a sea of unpredictable events and outcomes.

However, in the realm of exotic gravitational theories like $f(R)$ gravity, the standard symmetries and their associated conserved quantities can become far more intricate and subtle. General relativity, with its elegant geometric description of gravity, presents a certain set of symmetries that manifest in well-understood conserved quantities. But when the gravitational action is modified, as in $f(R)$ gravity, the landscape of symmetries shifts, demanding new methods to identify and understand the resulting conserved quantities, which might manifest in ways that challenge our everyday intuition about physical processes and fundamental constants.

The Mei symmetry approach, with its focus on differential equations and their symmetries, provides a powerful lens through which to examine these more complex scenarios. It allows physicists to identify hidden symmetries that might not be immediately apparent from the global structure of the theory. This is crucial in $f(R)$ gravity, where the functional dependence of the gravitational action on the Ricci scalar can introduce differential relationships that are central to the theory’s dynamics and its observable consequences across the vast expanse of the cosmos.

The synergy between the two approaches is the true revelation of this research. The authors demonstrate that the conserved quantities derived through the generalized Mei symmetries acting on the field equations of $f(R)$ gravity are directly analogous to, and in many cases identical to, the conserved quantities obtained through a careful application of Noether’s theorem to the modified Lagrangian of the theory. This convergence is a profound statement about the underlying consistency and structural integrity of modern gravitational physics, suggesting that the universe, even in its most exotic manifestations, adheres to remarkably coherent and interconnected fundamental principles.

This elegant reconciliation has significant implications for cosmology and astrophysics. $f(R)$ gravity is a leading candidate for explaining the accelerated expansion of the universe, a puzzling phenomenon attributed to dark energy. Dark energy, comprising roughly 70% of the universe’s total energy content, remains one of physics’ most significant mysteries. If $f(R)$ gravity indeed describes the universe’s expansion, then understanding its inherent symmetries and conserved quantities is paramount to accurately modeling cosmic evolution, the formation of large-scale structures, and the ultimate fate of the universe, providing a framework for testable predictions.

The potential applications extend to the study of black holes and other extreme gravitational environments. The singularities at the heart of black holes, where spacetime curvature becomes infinite according to general relativity, are theoretical puzzles. Modified gravity theories offer potential avenues for resolving these singularities, and the insights gained from understanding their symmetries and conserved quantities could provide crucial clues about the nature of gravity at its most extreme limits, perhaps revealing novel quantum gravity effects that govern the universe at its most fundamental scales of existence.

Furthermore, this research opens new avenues for experimental verification. By predicting specific behaviors and conserved quantities within $f(R)$ gravity, the theoretical framework provides concrete targets for observational astronomy. Future experiments, perhaps involving precise measurements of gravitational waves or detailed mapping of the cosmic microwave background, could potentially detect subtle deviations from general relativity that would support or refute these modified gravity models, offering direct empirical evidence to guide our understanding.

The work of Dabash, Emam, and Schöppner represents a significant leap forward in theoretical physics, providing a more unified and comprehensive understanding of gravity and its fundamental principles. It showcases the power of sophisticated mathematical tools to unravel the universe’s deepest secrets, moving us closer to a complete picture of cosmic reality. The elegance with which they bridge established theories with novel approaches is an inspiration to the scientific community and a testament to the enduring human quest for knowledge, promising a future filled with cosmic revelations and profound understanding of the forces that shape our universe and all its inhabitants.

The beauty of this research lies in its ability to bridge the abstract realms of theoretical physics with the tangible universe we observe, offering insights that might one day lead to technological advancements or at least a more profound appreciation for the intricate workings of our cosmic home. It’s a testament to the power of human intellect to probe the very fabric of existence, to find order in apparent complexity, and to reveal underlying harmonies that govern everything from the smallest subatomic particle to the largest celestial structure, a continuous process of discovery that fuels scientific progress.

In conclusion, this masterful work on symmetries and conserved quantities in $f(R)$ gravity is more than just an academic paper; it is a beacon of innovation, illuminating the path towards a more complete understanding of gravity and the universe. It has the potential to spark a new wave of research, inspire younger generations of scientists, and ultimately help us answer some of the most profound questions about our place in the cosmos and the fundamental laws that govern our existence, a quest for ultimate truth that drives scientific endeavor forward.

The profound implications of this research resonate beyond the immediate scientific community, hinting at a universe governed by laws more intricate and perhaps more beautiful than previously imagined. While the equations might seem daunting to the uninitiated, the underlying message is one of order, consistency, and deep interconnectedness within the cosmos, a message that should inspire awe and wonder in all who contemplate the vastness and complexity of existence and the remarkable intellectual journey humanity undertakes to comprehend it all.

Subject of Research: Understanding the fundamental laws governing gravity, particularly in the context of modified gravitational theories like $f(R)$ gravity, and exploring the relationships between symmetries and conserved quantities.

Article Title: Symmetry and conserved quantities in $f(R)$-gravity: Mei vs. Noether approaches.

Article References:
Dabash, T.F., Emam, M. & Schöppner, L. Symmetry and conserved quantities in $f(R)$-gravity: Mei vs. Noether approaches.
Eur. Phys. J. C 85, 1341 (2025). https://doi.org/10.1140/epjc/s10052-025-15067-z

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-15067-z

Keywords: $f(R)$ gravity, symmetry, conserved quantities, Noether theorem, Mei symmetry, general relativity, spacetime, cosmology, dark energy, theoretical physics.

The paper introduces a radical redefinition of curvature applied to arbitrary surfaces, particularly focusing on what are known as “d=2 pure simplicial complexes.” For the uninitiated, a simplicial complex is a mathematical structure built from basic units called simplices. In two dimensions, these are triangles, and a “pure” simplicial complex means it’s built solely out of these triangles, fitting together perfectly without gaps or overlaps. This discrete approach is crucial because as we delve into the quantum realm, the smooth, continuous spacetime of classical physics breaks down. Quantum mechanics thrives on discrete packets of energy and information, and this research suggests that spacetime itself might possess a similar underlying discreteness. By developing a method to quantify curvature within these discrete structures, the researchers are providing a potential framework for quantizing gravity, a quest that has eluded physicists for decades and remains one of the holy grails of modern theoretical physics.

At the heart of this novel approach lies a re-evaluation of how curvature is measured. In classical differential geometry, curvature is a property of continuous surfaces and is often described by concepts like the Gaussian curvature. However, when dealing with discrete structures, these continuous definitions become problematic. The researchers have devised a discrete analogue, a way to assign a “curvature value” to the vertices and faces of their simplicial complexes. This is not merely an abstract mathematical exercise; it’s a direct attempt to capture the geometric essence of gravity in a language compatible with quantum principles. The ability to define and manipulate curvature on these fundamental building blocks opens up the possibility of simulating gravitational phenomena at a microscopic level, offering a tangible way to explore the gravitational field in a quantum context.

The significance of this work cannot be overstated, especially when considering the persistent challenges in unifying general relativity and quantum mechanics. General relativity describes gravity as the curvature of spacetime caused by mass and energy, a beautifully elegant description that works exceptionally well on macroscopic scales. However, when we attempt to apply these principles to the extremely small scales of quantum particles, the theory breaks down, leading to infinities and paradoxes. This new discrete approach offers a potential loophole, a way to build a theory of gravity from the ground up, using discrete elements that are inherently quantum-friendly. It’s like switching from describing a flowing river to describing the individual water molecules that constitute it – a fundamental change in perspective that can reveal hidden dynamics.

The researchers meticulously detail their mathematical machinery for calculating this discrete curvature. They introduce specific formulas and definitions that allow them to quantify how much a given simplicial complex deviates from being flat, a direct analogue to curvature in continuous spaces. This involves analyzing the local arrangement of simplices around a vertex or a face, and how this arrangement “bends” the structure. This precise, quantitative approach is what elevates their work from speculative ideas to a concrete research program. It provides a rigorous foundation upon which further explorations into discrete quantum gravity can be built, allowing for calculations and predictions that can, in principle, be tested against observations.

One of the most exciting aspects of this research is its potential to shed light on phenomena where both gravity and quantum effects are expected to play a significant role. Think of the singularity at the heart of a black hole, where spacetime is thought to be infinitely curved according to classical general relativity, or the very first moments after the Big Bang, a period of immense energy density and incredibly small scales. In these extreme environments, a quantum theory of gravity is essential for a complete understanding. By providing a discrete geometrical framework, Chamseddine, Malaeb, and Najem offer a new lens through which to view these enigmatic cosmic events, potentially resolving long-standing paradoxes and unveiling new physical laws that govern these extreme regimes.

The paper’s focus on “d=2 pure simplicial complexes” is not arbitrary. These two-dimensional structures serve as a foundational testing ground for their discrete gravity concepts. While the ultimate goal is to extend this to higher dimensions and more complex structures, mastering the mathematics and physics in two dimensions is a crucial first step. It’s akin to learning to walk before you can run, or mastering basic arithmetic before tackling calculus. The elegance and consistency of their findings in this simplified setting provide strong evidence for the robustness of their proposed discrete curvature definition and its potential applicability to more complex, realistic scenarios in our universe.

The visual representation that accompanies the paper, an abstract yet evocative image, hints at the complexity and beauty of these discrete structures. It’s an artistic interpretation of the fundamental building blocks of spacetime, a tantalizing glimpse into a universe that might be stitched together at its deepest level. This visual dimension underscores the profound conceptual shift that discrete gravity represents, moving away from the smooth, continuous imagery of classical physics towards a more fragmented, pixelated, yet ultimately more fundamental reality. The image serves as a potent symbol for the paper’s revolutionary ideas, sparking curiosity and imagination in scientists and enthusiasts alike.

The authors’ meticulous mathematical framework for defining and calculating curvature on these discrete structures is a testament to their deep understanding of both geometry and theoretical physics. They have carefully navigated the challenges of translating continuous concepts into a discrete language, ensuring that their new definitions preserve essential physical properties. This rigorous approach is vital for building confidence in their findings and for enabling other researchers to build upon their work. Without this solid mathematical foundation, the ideas of discrete gravity would remain purely speculative, but this paper provides the concrete tools needed to explore it.

Furthermore, the choice of “pure” simplicial complexes is significant. It implies a certain mathematical tidiness and avoids complexities that could arise from incomplete or overlapping triangular structures. This focus on well-defined, fundamental units allows the researchers to isolate and study the effects of discrete geometry on gravity without introducing extraneous complications. It’s a strategy of simplifying the problem to its core elements, thereby gaining a clearer understanding of the fundamental physical principles at play, which is a hallmark of successful theoretical progress in physics.

The implications for future research are vast and exciting. This work could pave the way for developing entirely new numerical methods for simulating gravitational phenomena, particularly in regimes where classical approaches fail. Imagine being able to simulate the accretion disk around a black hole or the inflationary epoch of the early universe with unprecedented accuracy by directly modeling the discrete quantum nature of spacetime. The potential for new discoveries and a deeper understanding of the cosmos is immense, making this paper a potential catalyst for a new era in theoretical physics.

The paper’s direct engagement with “discrete gravity” positions it at the forefront of cutting-edge theoretical physics research. This field is gaining increasing traction as physicists grapple with the fundamental incompatibility between general relativity and quantum mechanics. By directly addressing gravity at a discrete level, the researchers are offering a genuinely novel pathway towards a unified theory. It’s a bold move that challenges established paradigms and opens up entirely new avenues of inquiry, driven by the fundamental question of what reality truly looks like at its most basic constituents.

The specific inclusion of “d=2 pure simplicial complexes” in their research is a strategic choice that allows for a manageable yet profound exploration of their discrete curvature concepts. This dimensionality is often a proving ground for new ideas in theoretical physics, offering a balance between simplicity and the ability to capture essential physical phenomena. Successfully applying their methods to these 2D structures provides a strong indication of their broader applicability and potential for scaling up to the 4D spacetime we inhabit, marking a crucial validation of their theoretical framework.

The very act of re-imagining curvature in a discrete, quantized manner could unlock secrets about the very nature of quantum entanglement and its relationship with spacetime geometry. Some theories suggest that the fabric of spacetime itself could emerge from quantum entanglement. If curvature, the fundamental aspect of gravity, can be understood in these discrete, quantum-friendly terms, it might offer a profound link between these two seemingly disparate phenomena, revealing a deeper, interconnected reality that we are only just beginning to perceive.

Ultimately, this research is more than just an academic exercise; it’s a visionary leap towards understanding the universe at its deepest, most fundamental level. By daring to redraw the geometric blueprints of spacetime, Chamseddine, Malaeb, and Najem have opened a door to a new quantum cosmos, one that might be more intricate, more granular, and ultimately more astonishing than we ever imagined. The journey to a complete theory of quantum gravity is long and arduous, but this paper represents a significant and exhilarating stride forward, promising to reshape our understanding of the universe and our place within it.

Subject of Research: Discrete Gravity and Curvature in Simplicial Complexes

Article Title: Curvature of an arbitrary surface for discrete gravity and for $d=2$ pure simplicial complexes

Article References:

Chamseddine, A.H., Malaeb, O. & Najem, S. Curvature of an arbitrary surface for discrete gravity and for \(d=2\) pure simplicial complexes.
Eur. Phys. J. C 85, 1274 (2025). https://doi.org/10.1140/epjc/s10052-025-15038-4

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-15038-4

Keywords: Discrete gravity, Simplicial complexes, Quantum gravity, Spacetime geometry, Curvature, Theoretical physics

The concept of modified rainbow gravity, a theoretical construct designed to reconcile quantum mechanics with general relativity at extremely high energies, introduces the idea that the gravitational field experienced by a particle is not a universal constant but rather contingent upon the particle’s own energy. This energy-dependent behavior of gravity, visualized by an analogy of a “rainbow” where different colors (energies) interact with gravity differently, opens up a vast new territory for theoretical exploration. The current study leverages this framework to examine how such exotic gravitational conditions would influence the internal structure and external appearance of compact objects. By introducing minimal geometric deformations, which deviate slightly from the idealized spherical symmetry often assumed in simpler models, and by considering anisotropy, a property where a material’s characteristics vary depending on the direction of measurement, the researchers have created a more realistic and nuanced picture of these astronomical powerhouses. This allows for a more detailed analysis of how these features, often overlooked in more simplified approaches, can profoundly influence the observable phenomena associated with these cosmic entities.

At the heart of this research lies the intricate dance between matter and gravity under conditions far more extreme than anything we can replicate on Earth. Compact objects, such as neutron stars and hypothetical strange stars, are known for their incredibly dense cores, where matter is squeezed to unimaginable densities. General relativity, our current best description of gravity, predicts the existence of black holes, objects so dense that nothing, not even light, can escape their gravitational pull. However, at the quantum level, our understanding of gravity breaks down. Modified rainbow gravity attempts to bridge this gap, and this study applies its tenets to investigate how slight deviations from symmetry, known as minimal geometric deformations, and directional dependencies in matter, termed anisotropy, would play out within these extreme environments. The implications of these deviations are far-reaching, potentially explaining subtle discrepancies in astronomical observations that current theories struggle to reconcile.

The research team posits that even the slightest deviations from perfect spherical symmetry in the structure of compact objects can have significant consequences when viewed through the lens of modified rainbow gravity. Imagine an object that is not a perfect sphere but slightly flattened or elongated. In the realm of rainbow gravity, the differential interaction of energy-dependent gravity with these subtle geometric imperfections can lead to observable effects that would not be present in a perfectly symmetric object. This introduces a layer of complexity that could unlock new avenues for detecting and characterizing these elusive celestial bodies. The authors meticulously explore how these minute geometric variances, when coupled with the energy-dependent nature of gravity, can lead to distinct signatures that differentiate them from purely spherically symmetric counterparts, offering a potent tool for observational astronomers.

Furthermore, the study delves into the critical role of anisotropy, a property inherent in many real-world materials where their characteristics, such as pressure or energy density, differ depending on the direction. In the context of compact objects, this means that the “stuff” inside these stars might behave differently if you probe it horizontally versus vertically. When this directional dependence is combined with the energy-dependent gravitational field proposed by rainbow gravity, the results become profoundly interesting. The researchers have mathematically modeled how this anisotropy, intertwined with the fabric of modified gravity, can lead to significant alterations in the object’s overall structure, stability, and even its observable emissions. This consideration moves beyond simplistic models and embraces the complex reality of matter under extreme pressure and gravitational stress.

The theoretical framework of modified rainbow gravity is particularly adept at addressing the extreme conditions found within compact objects. Unlike classical gravity, which treats all particles the same regardless of their energy, rainbow gravity suggests that very high-energy particles might experience gravity differently than low-energy ones. This is crucial when considering the extreme densities and energies present within neutron stars and other compact objects, where matter is pushed to its absolute limits. The researchers’ work highlights how this energy-dependent gravity, when combined with the aforementioned minimal geometric deformations and anisotropy, can lead to predictions that are significantly different from those derived from standard gravitational theories, offering a powerful new lens for astronomical investigation.

The implications of these theoretical findings are vast, potentially offering explanations for phenomena that have remained somewhat obscure within the confines of current astrophysical models. For instance, observed variations in the properties of neutron stars, or unexpected emissions from the vicinity of black holes, could find a more coherent explanation within this modified framework. By considering the subtle interplay of geometric imperfections and material anisotropy under the unique conditions of rainbow gravity, scientists may be able to refine their models and better predict the observable signatures of these cosmic giants. This could lead to more precise measurements and a deeper understanding of the fundamental forces at play in the universe’s most extreme environments.

The mathematical rigor employed in this study is essential for translating theoretical concepts into testable predictions. The research draws upon sophisticated differential geometry and tensor calculus to precisely describe the spacetime curvature and the behavior of matter under these modified gravitational conditions. The introduction of deformation parameters and anisotropy tensors allows for a quantitative analysis of how these factors influence the structure and dynamics of compact objects. This level of detail is critical for moving beyond qualitative descriptions and enabling astrophysicists to make concrete predictions that can be compared with observational data, thereby strengthening the scientific validation of the proposed theories.

One of the key advancements of this research is its ability to predict how these subtle effects might manifest themselves observably. While the deformations and anisotropy might be small, their cumulative impact within the intense gravitational environment of a compact object, especially when influenced by energy-dependent gravity, can lead to measurable differences in emitted radiation, gravitational wave signals, or even the mass-radius relationship of neutron stars. The researchers have, in essence, provided a roadmap for observational astronomers on what to look for and how to interpret unusual signals from these cosmic behemoths, paving the way for potential observational verification of their theoretical predictions.

The study also sheds light on the equation of state for matter within compact objects. The equation of state describes the relationship between pressure and density within a material. Under the extreme conditions of compact objects, and particularly under modified gravity with anisotropy, the standard equations of state may no longer be accurate. This research proposes that the inclusion of minimal geometric deformation and anisotropy within the modified rainbow gravity framework necessitates a re-evaluation of these equations of state, leading to a more accurate depiction of the internal physics of these objects. This refinement is crucial for understanding the stability and evolution of neutron stars and for predicting their ultimate fate, such as whether they will collapse into black holes or remain as stable configurations.

The potential of modified rainbow gravity to offer a more complete picture of the universe at its most extreme lies in its ability to incorporate factors that might be neglected in simpler models. The universe is rarely perfectly symmetrical, and matter exhibits directional properties. By acknowledging and mathematically modeling these realities within a framework that also accounts for the energy dependence of gravity, this research pushes the boundaries of our understanding. The profound implications extend to our understanding of fundamental physics, potentially offering clues about quantum gravity and the very nature of the vacuum.

The authors emphasize that their work is a theoretical exploration, but one with very tangible potential consequences for observational astrophysics. The models developed provide a framework for interpreting a wide range of astronomical data, from the precise mass and radius of neutron stars to the subtle signatures of gravitational waves emitted during stellar mergers. By looking for specific patterns and deviations predicted by their theory, astronomers can either confirm or refute the hypotheses put forth, driving forward our collective knowledge of the cosmos and its most enigmatic inhabitants, solidifying the scientific method’s iterative progress.

The journey into understanding compact objects is a perpetual quest, and this latest research represents a significant leap forward. By venturing into the complex terrain of modified rainbow gravity and incorporating the often-overlooked nuances of geometric deformation and anisotropy, the scientists have opened new avenues for research and interpretation. The universe, in its infinite complexity, continues to reveal its secrets, and this study offers a powerful new set of tools and insights for deciphering those deeply woven into the fabric of space, time, and matter under the most extreme conditions imaginable, offering a tantalizing glimpse into the unseen forces that govern our cosmos.

This rigorous theoretical investigation into the behavior of compact objects within the exotic realm of modified rainbow gravity, accounting for minute geometric imperfections and the directional dependence of matter properties, marks a crucial step in our quest to understand the universe’s most extreme phenomena. The researchers have meticulously crafted a theoretical framework that can potentially explain subtle astronomical anomalies and refine our understanding of fundamental physics. The beauty of this science lies in its ability to find profound implications in what might appear to be mere theoretical constructs, proving that even the smallest deviations can echo with cosmic significance, guiding our exploration of the celestial and the fundamental.

The potential for this research to be “viral” within the scientific community lies in its ability to offer fresh explanations for long-standing astrophysical puzzles and to provide concrete, testable predictions for observational astronomers. The elegance of the proposed framework, which seamlessly integrates complex theoretical concepts with practical observational targets, is highly compelling. Furthermore, the exploration of modified rainbow gravity itself is a topic of significant interest, representing a frontier in theoretical physics. This synergy of theoretical innovation and observational relevance is precisely what ignites excitement and drives progress in scientific discovery, creating a ripple effect that can inspire new research directions and foster collaboration across diverse fields of study, ultimately pushing the boundaries of human knowledge.

Subject of Research:
Impact of minimal geometric deformation and anisotropy on compact objects in modified rainbow gravity.

Article Title:
Impact of minimal geometric deformation and anisotropy on compact objects in modified rainbow gravity.

Article References:
Khatoon, M., Mahmood, I., Sohail, H. et al. Impact of minimal geometric deformation and anisotropy on compact objects in modified rainbow gravity. Eur. Phys. J. C 85, 1102 (2025). https://doi.org/10.1140/epjc/s10052-025-14741-6

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-14741-6

Keywords: Compact objects, modified gravity, rainbow gravity, anisotropy, geometric deformation