Search Results (32)

One extension of general relativity, known as $\mathrm{f}\left(\mathrm{R}\right)$ gravity, where $\mathrm{R}$ denotes the Ricci scalar, is regarded as a promising candidate for addressing the anomalies observed in conventional general relativity. In this work, we apply the field equations of $\mathrm{f}\left(\mathrm{R}\right)$ gravity to a spacetime with spherical symmetry with distinct metric potentials, i.e., $g_{tt}\ne g_{rr}$. By solving the resulting nonlinear differential equations, we derive a novel black hole solution without imposing constraints on the Ricci scalar or on the specific form of $\mathrm{f}\left(\mathrm{R}\right)$ gravity. This solution does not reduce to the Schwarzschild solution of Einstein’s general relativity. This solution is notable because it includes a gravitational mass and extra terms that make the singularities in the curvature stronger than those in black holes from Einstein’s general relativity. We analyze these black holes within the framework of thermodynamics and demonstrate their consistency with standard thermodynamic quantities. Furthermore, we investigate the stability by examining odd-type perturbation modes and show that the resulting black hole is stable. Finally, we derive the coefficients of the two scalar fields and demonstrate that the black hole obtained in this study is free from ghosts. Full article

In this work, we explore a class of spherically symmetric black hole (BH) solutions within the framework of modified gravity, focusing on a non-ghost-free $f(R,G)$ theory coupled to a scalar field. We present a novel black hole geometry that arises as a deformation of the Schwarzschild solution and analyze its physical and thermodynamic properties. Our results show that the model satisfies stability conditions, with the Ricci scalar R, as well as its first and second derivatives, remaining positive throughout the spacetime. The solution admits multiple horizons and exhibits strong curvature singularities compared to those in general relativity. Furthermore, it supports a non-trivial scalar field potential. A comprehensive thermodynamic analysis is performed, including evaluations of the entropy, temperature, heat capacity, and quasi-local energy. We find that the black hole exhibits thermodynamic stability within certain ranges of model parameters. In addition, we investigate geodesic deviation and derive the conditions necessary for stability within the $f(R,G)$ gravitational framework. Full article

Recent observations suggest that General Relativity (GR) faces challenges in fully explaining phenomena in regimes of strong gravitational fields. A promising alternative is the $f\left(R\right)$ theory of gravity, where R denotes the Ricci scalar. This modified theory aims to address the limitations observed in standard GR. In this study, we derive a black hole (BH) solution without introducing nonlinear electromagnetic fields or imposing specific constraints on R or the functional form of $f\left(R\right)$ gravity. The BH solution obtained here is different from the classical Schwarzschild solution in GR and, under certain conditions, reduces to the Schwarzschild (A)dS solution. This BH is characterized by the gravitational mass of the system and an additional parameter, which distinguishes it from GR BHs, particularly in the asymptotic regime. We show that the curvature invariants of this solution remain well defined at both small and large values of r. Furthermore, we analyze their thermodynamic properties, demonstrating consistency with established principles such as Hawking radiation, entropy, and quasi-local energy. This analysis supports their viability as alternative models to classical GR BHs. Full article

Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously following Weyl’s idea of unifying gravity and electromagnetism. In fact, vacuum Schwarzschild solutions differ from the ones in a constant curvature scenario in $f\left(R\right)$ theories, with the appearance of a coefficient in the term that is linear in r and a corrected “cosmological constant”. Non-vacuum Schwarzschild solutions formally have the same solutions as in the previous case, with the exception being the physical interpretation of a cosmological constant as the source of the matter Lagrangian and not a simple reparameterization of the $f\left(R\right)$ description. Reissner–Nordstrøm solutions cannot be found in a vacuum, only in the presence of matter fields, with the result that the solutions also differ from the constant curvature scenario in $f\left(R\right)$ theories by the term being linear in r, the corrected/dressed charge, and the cosmological constant. These results have bearings on future numerical simulations for black holes and gravitational waves in next-generation wavelet templates. Full article

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models $f\left(R\right)=R+\alpha R^2$ and $f\left(R\right)=R+2\gamma \sqrt{R+8\Lambda }$ under the $f\left(R\right)$ theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter–RN spacetime) with $\Lambda =-1$. It is shown that when the BHs’ horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking–Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs. Full article

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG)—more specifically, $f(R,T_{\mu \nu }{T}^{\mu \nu })$ gravity, where R represents the Ricci scalar and $T_{\mu \nu }$ denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe’s early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory’s explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory. Full article

This article explores wormhole solutions within the framework of Finsler geometry and the modified gravity theory. Modifications in gravitational theories, such as $f(\mathcal{R},\mathcal{T})$ gravity, propose alternatives that potentially avoid the exotic requirements. We derive the field equations from examining the conditions for Finslerian wormhole existence and investigate geometrical and material characteristics of static wormholes using a polynomial shape function in Finslerian space–time. Furthermore, we address energy condition violations for different Finsler parameters graphically. We conclude that the proposed models, which assume a constant redshift function, satisfy the necessary geometric constraints and energy condition violations indicating the presence of exotic matter at the wormhole throat. We also discuss the anisotropy factors of the wormhole models. The results are validated through analytical solutions and 3-D visualizations, contributing to the broader understanding of wormholes in Finsler-modified gravity contexts. Full article

We consider a dynamic scenario for characterizing the late Universe evolution, aiming to mitigate the Hubble tension. Specifically, we consider a metric $f\left(R\right)$ gravity in the Jordan frame which is implemented to the dynamics of a flat isotropic Universe. This cosmological model incorporates a matter creation process, due to the time variation of the cosmological gravitational field. We model particle creation by representing the isotropic Universe (specifically, a given fiducial volume) as an open thermodynamic system. The resulting dynamical model involves four unknowns: the Hubble parameter, the non-minimally coupled scalar field, its potential, and the energy density of the matter component. We impose suitable conditions to derive a closed system for these functions of the redshift. In this model, the vacuum energy density of the present Universe is determined by the scalar field potential, in line with the modified gravity scenario. Hence, we construct a viable model, determining the form of the $f\left(R\right)$ theory a posteriori and appropriately constraining the phenomenological parameters of the matter creation process to eliminate tachyon modes. Finally, by analyzing the allowed parameter space, we demonstrate that the Planck evolution of the Hubble parameter can be reconciled with the late Universe dynamics, thus alleviating the Hubble tension. Full article

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function $F(R,{\square }^{-1}R)$, where R denotes the Ricci curvature scalar and the operator ${\square }^{-1}$ introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of $f(R,{\square }^{-1}R)$ gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*. Full article

In recent years, the rapid development of exoplanet research has provided us with an opportunity to better understand planetary systems in the universe and to search for signs of life. In order to further investigate the prevalence of habitable exoplanets and to validate planetary formation theories, as well as to comprehend planetary evolution, we have utilized confirmed exoplanet data obtained from the NASA Exoplanet Archive database, including data released by telescopes such as Kepler and TESS. By analyzing these data, we have selected a sample of planets around F, G, K, and M-type stars within a radius range of 1 to 20 $R_{\oplus }$ and with orbital periods ranging from 0.4 days to 400 days. Using the IDEM method based on these data, we calculated the overall formation rate, which is estimated to be 2.02%. Then, we use these data to analyze the relationship among planet formation rates, stellar metallicity, and stellar gravitational acceleration ($logg$). We firstly find that the formation rate of giant planets is higher around metal-rich stellars, but it inhibits the formation of gas giants when $logg$ > 4.5, yet the stellar metallicity seems to have no effect on the formation rate of smaller planets. Secondly, the host stellar gravitational acceleration affects the relationship between planet formation rate and orbital period. Thirdly, there is a robust power-law relationship between the orbital period of smaller planets and their formation rate. Finally, we find that, for a given orbital period, there is a positive correlation between the planet formation rate and the $logg$. Full article

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories with minimal and non-minimal couplings, we review how inflation can be realized in terms of several string-motivated models of inflation, which involve Gauss–Bonnet couplings of the scalar field, higher-order derivatives of the scalar field, and some subclasses of viable Horndeski theories. We also present and analyze inflation in the context of Chern–Simons theories of gravity, including various subcases and generalizations of string-corrected modified gravities, which also contain Chern–Simons correction terms, with the scalar field being identified with the invisible axion, which is the most viable to date dark matter candidate. We also provide a detailed account of vacuum $f\left(R\right)$ gravity inflation, and also inflation in $f(R,\varphi )$ and kinetic-corrected $f(R,\varphi )$ theories of gravity. At the end of the review, we discuss the technique for calculating the overall effect of modified gravity on the waveform of the standard general relativistic gravitational wave form. Full article

In this work, we explore the formalism of the irreversible thermodynamics of open systems and the possibility of gravitationally generated particle production in modified gravity. More specifically, we consider the scalar–tensor representation of $f(R,T)$ gravity, in which the matter energy–momentum tensor is not conserved due to a nonminimal curvature–matter coupling. In the context of the irreversible thermodynamics of open systems, this non-conservation of the energy–momentum tensor can be interpreted as an irreversible flow of energy from the gravitational sector to the matter sector, which, in general, could result in particle creation. We obtain and discuss the expressions for the particle creation rate, the creation pressure, and the entropy and temperature evolutions. Applied together with the modified field equations of scalar–tensor $f(R,T)$ gravity, the thermodynamics of open systems lead to a generalization of the $\mathrm{\Lambda }$CDM cosmological paradigm, in which the particle creation rate and pressure are considered effectively as components of the cosmological fluid energy–momentum tensor. Thus, generally, modified theories of gravity in which these two quantities do not vanish provide a macroscopic phenomenological description of particle production in the cosmological fluid filling the Universe and also lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Full article

We consider the theory of quantum gravity in which gravity emerges as a result of the symmetry-breaking transition in the quantum vacuum. The gravitational tetrads, which play the role of the order parameter in this transition, are represented by the bilinear combinations of the fermionic fields. In this quantum gravity scenario the interval $ds$ in the emergent general relativity is dimensionless. Several other approaches to quantum gravity, including the model of superplastic vacuum and $BF$ theories of gravity support this suggestion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action S, cosmological constant $\mathrm{\Lambda }$, scalar curvature R, scalar field $\mathrm{\Phi }$, wave function $\psi$, etc. The composite fermion approach to quantum gravity suggests that the Planck constant ℏ can be the parameter of the Minkowski metric. Here, we extend this suggestion by introducing two Planck constants, bar ℏ and slash $/h$, which are the parameters of the correspondingly time component and space component of the Minkowski metric, $g_{\mathrm{Mink}}^{\mu \nu }=\mathrm{diag}(-{\hslash }^2,/h^2,/h^2,/h^2)$. The parameters bar ℏ and slash $/h$ are invariant only under $SO\left(3\right)$ transformations, and, thus, they are not diffeomorphism invariant. As a result they have non-zero dimensions—the dimension of time for ℏ and dimension of length for $/h$. Then, according to the Weinberg criterion, these parameters are not fundamental and may vary. In particular, they may depend on the Hubble parameter in the expanding Universe. They also change sign at the topological domain walls resulting from the symmetry breaking. Full article

General Relativity is an extremely successful theory, at least for weak gravitational fields; however, it breaks down at very high energies, such as in correspondence to the initial singularity. Quantum Gravity is expected to provide more physical insights in relation to this open question. Indeed, one alternative scenario to the Big Bang, that manages to completely avoid the singularity, is offered by Loop Quantum Cosmology (LQC), which predicts that the Universe undergoes a collapse to an expansion through a bounce. In this work, we use metric $f\left(R\right)$ gravity to reproduce the modified Friedmann equations which have been obtained in the context of modified loop quantum cosmologies. To achieve this, we apply an order reduction method to the $f\left(R\right)$ field equations, and obtain covariant effective actions that lead to a bounce, for specific models of modified LQC, considering a massless scalar field. Full article

An investigation has been carried out on a reconfigured form of the Einstein-Hilbert action, denoted by $f(R,T^{\varphi })$, where $T^{\varphi }$ represents the energy-momentum tensor trace of the scalar field under consideration. The study has focused on how the structural behavior of the scalar field changes based on the potential’s shape, which has led to the development of a new set of Friedmann equations. In the context of modified theories, researchers have extensively explored the range of gravitational wave polarization modes associated with relevant fields. In addition to the two transverse-traceless tensor modes that are typically observed in general relativity, two additional scalar modes have been identified: a massive longitudinal mode and a massless transverse mode, also known as the breathing mode. Full article