Einstein's General Relativity Research Articles

Equilibrium and Stability of the Solar System Rely on a Human-Like Program of Substance and Information Transfer

This study bridges the realms of astronomy and life science, illuminating the intricate interplay between celestial phenomena and terrestrial biology. While humans may perceive the palpable effects of seasons, climate, geographical location, and the movements of the Sun and moon, other phenomena such as changes in Earth's magnetic field and seismic activity are often sensed by animals but elude human perception. However, with disciplined and sustained training, humans possess the potential to harness the rich array of sensors and sensory systems within the body, thereby unlocking the ability to discern and validate the cosmic influences documented by ancient civilizations. In instances where traditional astronomical inquiries, such as the maintenance of galactic equilibrium, present enigmatic puzzles, insights from cutting-edge life science research may offer promising leads. Newly unveiled mechanisms such as the "Function Enhancement Program of Five-Organs through Umbilical Access" and the rhythmic orchestration of the "Rotating Presidency of Twelve-Organs" elucidate the intricate operations of visceral organs within the human body. Indirect evidence suggests a correlation between these biological processes and the transfer of gaseous substances among celestial bodies, including Mercury, Venus, the Sun, and Jupiter, hinting at a temporal synchronicity that may contribute to the equilibrium and stability of the solar system. Confirmation of substance and information transfer processes could unlock new avenues of inquiry in astronomy, shedding light on vexing conundrums such as dark energy and matter, binary pulsars, gravitational waves, inflation fields, and alternative theories to Einstein's General Relativity. Thus, by bridging the disciplines of astronomy and life science, this study offers fresh perspectives and potential breakthroughs in our understanding of the cosmos.

Fermionic Quartet and Vestigial Gravity

We discuss the two-step transitions in superconductors, where the intermediate state between the Cooper pair state and the normal metal is the 4-fermion condensate, which is called the intertwined vestigial order. We discuss different types of the vestigial order, which are possible in the spin-triplet superfluid 3He, and the topological objects in the vestigial phases. Since in 3He the order parameter \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{A}_{{\\alpha i}}}$$\\end{document} represents the analog of gravitational tetrads, we suggest that the vestigial states are possible in quantum gravity. As in superconductors, the fermionic vacuum can experience two consequent phase transitions. At first transition the metric appears as the bilinear combination of tetrads \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{g}_{{\\mu \ u }}} = {{\\eta }_{{ab}}}\\langle \\hat {E}_{\\mu }^{a}\\hat {E}_{\ u }^{b}\\rangle $$\\end{document}, while the tetrad order parameter is still absent, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_{\\mu }^{a} = \\langle \\hat {E}_{\\mu }^{a}\\rangle = 0$$\\end{document}. This corresponds to the bosonic Einstein general relativity, which emerges in the fermionic vacuum. The nonzero tetrads \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_{\\mu }^{a} = \\langle \\hat {E}_{\\mu }^{a}\\rangle \ e 0$$\\end{document} appear at the second transition, where a kind of the Einstein–Cartan–Sciama–Kibble tetrad gravity is formed. This suggests that on the levels of particles, gravity acts with different strength on fermions and bosons.

Prophetic detection and discovery of gravitational waves

Einstein's general relativity theory includes the gravitational wave as a key prediction. One of the most crucial areas of contemporary physics is gravitational wave detection. A fantastic addition to conventional electromagnetic radiation astronomy, gravitational wave astronomy is a brand-new field of study based on the discovery of gravitational waves. In this paper, the prediction and characteristics of gravitational waves are discussed, and the detection methods of gravitational waves are given, such as the limitations of the resonant rod of gravitational waves, the working principle and basic structure of the gravitational wave probe, the laser interferometer. The gravitational wave signal of the binary black hole merger detected by the LIGO laser interferometer gravitational wave detector in the United States for the first time on September 14, 2015, which opens a new "gravitational wave window" for human astronomy research. It is foreseeable that in the near future gravitational wave research will explore the unknown information of the universe from various gravitational wave frequency bands.

Application of gravitational wave detection technology in astronomical observations

Gravitational waves are waves that propagate through space and time due to the interaction of gravity, representing a completely new physical phenomenon. This article reviews the background and issues of gravitational wave detection, with a focus on the progress of interdisciplinary research. It was not until 2015 that researchers successfully detected gravitational waves for the first time, capturing gravitational wave signals from the merger of two black holes using laser interferometry technology. This breakthrough confirms the predictions of Einstein's general relativity and opens a new chapter in the study of gravitational waves. Gravitational wave detection technology not only provides a new way to observe the universe, but also provides clues for studying the mysteries of the universe such as black holes, dark matter, and dark energy. Gravity wave detection technology also has potential communication application prospects, such as quantum gravity communication and long-distance communication, which brings new possibilities for future communication technology. In the future, there expects to be more success of gravitational wave detection and the continuous contribution of gravitational wave research in unlocking the mysteries of the universe and advancing the forefront of science.

Examining the physical viability of the f(R) gravity via observational constraints

f(R) gravity is an extension of Einstein's General Relativity derived from relaxing the hypothesis that the Hilbert-Einstein action for the gravitational field is strictly linear in the Ricci curvature scalar R and explains the late-time cosmic acceleration of the Universe. We investigate the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) line element filled with two fluids, with the first being pressureless matter and the second being the Renyi holographic dark energy (RHDE) in this study. In this scenario, the Hubble horizon H acts as an Infrared (IR) cutoff. In this regard, the effects of IR cutoff with the Hubble horizon on the traits of RHDE models have been researched. The volumetric power law expansion and the two models of f(R) i.e. f(R)=R+bRm and f(R)=R−μ4R are taken into consideration for the solution of the field equations. The estimated model parameter values that would best fit and work with current observational datasets. This estimation uses 1048 points from the Pantheon supernovae datasets and 30 points from the Hubble datasets. The likelihood function and Bayesian analysis are integrated with the Markov Chain Monte Carlo (MCMC) method at the 1 σ and 2 σ confidence levels. It is crucial to remember that f(R) is a rising function ofR, demonstrating the model's plausibility. For both models, the equation of state (EoS) value is close to a Quintessence zone. The model behaves in a ΛCDM (ΛCold Dark Matter) like manner, as shown by the fact that the statefinder diagnostic pair falls to(r=1,s=0). The Om(z) parameter shows a discrète behaviour.

Shadows and photon rings of regular black holes and geonic horizonless compact objects

Abstract The optical appearance of a body compact enough to feature an unstable bound orbit, when surrounded by an accretion disk, is expected to be dominated by a luminous ring of radiation enclosing a central brightness depression typically known as the shadow. Despite observational limitations, the rough details of this picture have been now confirmed by the results of the Event Horizon Telescope (EHT) Collaboration on the imaging of the M87 and Milky Way supermassive central objects. However, the precise characterization of both features—ring and shadow—depends on the interaction between the background geometry and the accretion disk, thus being a fertile playground to test our theories on the nature of compact objects and the gravitational field itself in the strong-field regime. In this work we use both features in order to test a continuous family of solutions interpolating between regular black holes and horizonless compact objects, which arise within the Eddington-inspired Born–Infeld theory of gravity, a viable extension of Einstein’s general relativity (GR). To this end we consider seven distinctive classes of such configurations (five black holes and two traversable wormholes) and study their optical appearances under illumination by a geometrically and optically thin accretion disk, emitting monochromatically with three analytic intensity profiles previously suggested in the literature. We build such images and consider the sub-ring structure created by light rays crossing the disk more than once and existing on top of the main ring of radiation. We discuss in detail the modifications as compared to their GR counterparts, the Lyapunov exponents of unstable nearly-bound orbits, as well as the differences between black hole and traversable wormholes for the three intensity profiles. In addition we use the claim by the EHT Collaboration on the radius of the bright ring acting (under proper calibrations) as a proxy for the radius of the shadow itself to explore the parameter space of our solutions compatible with such a result.

Isotropic compact stellar model in Rastall's gravitational theory

Is Rastall's theory of gravity equivalent to Einstein's general relativity theory? This question has sparked a significant debate, prompting researchers to delve into the topic. To investigate further, we apply Rastall's theory's field equation to a spacetime characterized by spherical symmetry. This leads us to encounter a system of non-linear differential equations that is overdetermined. To address this, we make assumptions about the specific form of the metric potential's temporal component, denoted as gtt. Additionally, we impose constraints to eliminate the anisotropic condition, resulting in a vanishing effect. These steps allow us to determine the form of grr and ultimately achieve an isotropic spacetime. Furthermore, our investigation focuses on the potential of obtaining a set of parameters that align with the observed behavior of pulsars. To achieve this, we employ junction conditions to match the interior spacetime with the exterior Schwarzschild configuration, thereby constraining the model's relevant constants. Subsequently, we employ the pulsar SAXJ1748.9−2021, characterized by a measured mass of M=1.81±0.31,M⊙ and a radius of R=11.7±1.7 km, to numerically explore the physical properties of the model. Stability is assessed using the Tolman-Oppenheimer-Volkoff equation and the adiabatic index. Our findings suggest that Rastall's parameter, a key distinction of Rastall's theory from Einstein's general relativity, can play a crucial role in forming a realistic, compact object consistent with observational data. Furthermore, we verify the model's validity by comparing it with various observed masses and radii of different pulsars, ensuring a satisfactory fit between the model proposed in this study and the observed data.

Dynamical dark energy can amplify the expansion rate of the Universe

By adding a matter-coupled dark energy field to Einstein's general relativity, this paper proves that the dynamical dark energy field can change the frequency of photons from distant galaxies as well as from background radiation of remote Universe. Therefore, when the observed frequency shift of the photons is entirely attributed to the temporal variation of the cosmic scale factor, the calculated expansion rate of the Universe will be slightly greater than its actual value. The predicted values of the temperature of the cosmic blackbody radiation in the past (future) of the Universe are slightly larger (gradually smaller and smaller) than those in the standard cosmology. Since the blackbody radiation becomes the present cosmic microwave background and its present-day temperature is directly estimated according to the Planck's law of blackbody radiation, the measured value of the cosmic microwave background temperature is independent of whether to consider the scalar field or not.

Slow-rotating charged black hole solution in dynamical Chern-Simons modified gravity

Chern-Simons (CS) gravity is a modified theory of Einstein's general relativity. The CS theory arises from the low energy limit of string theory which involves anomaly correction to the Einstein-Hilbert action. The CS term is given by the product of the Pontryagin density with a scalar field. In this study, we derive a charged slowly rotating black hole (BH) solution. The main incentives of this BH solution are axisymmetric and stationary and form distortion of the Kerr-Newman BH solution with a dipole scalar field. Additionally, we investigate the asymptotic correction of the metric with the inverse seventh power of the radial distance to the BH solution, This indicates that it will escape any meaningful constraints from weak field experiments. To find this kind of BH by observations, we investigate the propagation of the photon near the BH and we show that the difference between the left-rotated polarization and the right-handed one could be observed as stronger than the case of the Kerr-Newman BH. Finally, we derived the stability condition using the geodesic deviations.

Slow-rotating black holes with potential in dynamical Chern-Simons modified gravitational theory

The Chern-Simons amended gravity theory appears as a low-energy effective theory of string theory.The effective theory includes an anomaly-cancelation correction to the Einstein-Hilbert action.The Chern-Simons expression consists of the product φRR̃ of the Pontryagin density RR̃ with a scalar field φ, where the latter is considered a background field(dynamical construction or non-dynamical construction).Many different solutions to Einstein's general relativity continue to be valid in the amended theories.The Kerr metric is, however, considered an exceptional case that raised a search for rotating black hole solutions.We generalize the solution presented in Phys. Rev. D 77 (2008) 064007 by allowing the potential V to have a non-vanishing value,and we discuss three different cases of the potential, that is, V = const., V ∝ φ, and V ∝ φ 2 cases.This study presents, for the first time, novel solutions prescribing rotating black holes in the frame of the dynamical formulation of the Chern-Simons gravity,where we include a potential and generalize the previously derived solutions.We derive solutions in the slow-rotation limit, where we write the parameter of the slow-rotation expansion by ε.These solutions are axisymmetric and stationary, and they make a distortion of the Kerr solution by a dipole scalar field.Furthermore, we investigate that the correction to the metric behaves in the inverse of the fourth order of radial distance from the centerof the black hole as V ∝ φ. This suggests that any meaningful limits from the weak-field experiments could be passed.We show that the energy conditions associated with the scalar field of the case V ∝ φ are non-trivial and have non-trivial values to the leading order.These non-trivial values come mainly from the contribution of the potential. Finally, we derived the stability condition using the geodesic deviations.We conclude this study by showing that other choices of the potential, i.e., V ∝ φn , where n > 2 are not allowedbecause all the solutions to these cases will be of order \U0001d4aa(ε 2), which is not covered in this study.

Black Holes with Electric and Magnetic Charges in F(R)$F(R)$ Gravity

AbstractWe construct spherically symmetric and static solutions in gravity coupled with electromagnetic fields. The solutions include new types of black holes with electric and magnetic charges. We show that the higher‐derivative terms make the curvature singularity much softer than that in the charged black holes in Einstein's general relativity. We calculate some thermodynamical quantities of the obtained black holes like entropy, Hawking radiation, and quasi‐local energy and we confirm that the black hole solutions satisfy the first law of thermodynamics. Finally, we study the stability analysis using the odd‐type mode and show that there are stable black hole solutions and the radial speed of the parity‐odd mode is unit, that is, the speed of light.

Stationary black holes and stars in the Brans-Dicke theory with Λ>0 revisited

It was shown a few years back that for a stationary regular black hole or star solution in the Brans-Dicke theory with a positive cosmological constant $\mathrm{\ensuremath{\Lambda}}$, endowed with a de Sitter or cosmological event horizon in the asymptotic region, not only there exists no nontrivial field configurations, but also the inverse Brans-Dicke parameter ${\ensuremath{\omega}}^{\ensuremath{-}1}$ must be vanishing. This essentially reduces the theory to Einstein's general relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $\ensuremath{\phi}$, couples directly to the $\mathrm{\ensuremath{\Lambda}}$-term in the energy-momentum tensor as well as $\mathrm{\ensuremath{\Lambda}}$ acts as a source in $\ensuremath{\phi}$'s equation of motion, it seems reasonable to ask: can $\ensuremath{\phi}$ become strong instead and screen the effect of $\mathrm{\ensuremath{\Lambda}}$, at very large scales, so that the asymptotic de Sitter structure is replaced by some alternative, yet still acceptable boundary condition? In this work we analytically argue that no such alternative exists, as long as the spacetime is assumed to be free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $\mathrm{\ensuremath{\Lambda}}$, irrespective of whether the asymptotic de Sitter boundary condition is imposed or not, a regular stationary black hole or even a star solution in the Brans-Dicke theory always necessitates ${\ensuremath{\omega}}^{\ensuremath{-}1}=0$, and thereby reducing the theory to general relativity. The qualitative differences of this result with that of the standard no hair theorems are also pointed out.

Constraint on Brans-Dicke theory from intermediate/extreme mass ratio inspirals

Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good toolto test the nature of gravity in strong field.Based on the method of osculating orbits,we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits inboth Einstein's general relativity and Brans-Dicke theory.The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay,so it is important to consider the effects of monopolar and dipolar emissions on the waveform.With the help of accurate orbital motion,we generate waveform templates which include both monopolar and dipolar contributions for I/EMRIs on eccentric orbits in Brans-Dicke theory.With a two-year observation of gravitational waves emitted from I/EMRIs by LISA,we get the most stringent constraint on the Brans-Dicke coupling parameter ω 0 > 106.

Black holes in a swirling universe

We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst equations for stationary and axisymmetric spacetimes. This kind of the Ehlers transformation is able to embed any given solution into a rotating background, which is not of NUT type. We analyse the physical properties, ergoregions and geodesics of the new metric, which is regular outside the event horizon and has a well defined thermodynamics. We finally consider the Kerr generalisation.

Internal structure and its connection with thermodynamics and dynamics in black holes

In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann scalars together with complete radial geodesics, while the latter is related to divergent Ricci and Kretschmann scalars together with incomplete radial geodesics. For the charged black hole in the four-dimensional Einstein-Gauss-Bonnet theory, we find that its metric function is finite at its center in one region of parameters but complex in the other region of parameters. The finite case describes a strange spacetime which presents the Ricci and Kretschmann scalars of a singular spacetime and the radial geodesics of a non-singular spacetime, while the complex case gives rise to the similar situation. We verify that the cosmic censorship conjecture is maintained for the black hole model. Further, we investigate the second-order phase transition, quasinormal modes of perturbation of a test scalar field in the eikonal limit, and shadow radius for the black hole and find that the thermodynamic and dynamic properties depend on the metrics. In this way, we connect the internal structure with the thermodynamics and dynamics for this black hole. Moreover, we compare such a black hole of modified gravity with the Reissner-Nordström black hole of Einstein's general relativity in these thermodynamic and dynamic properties.

Intrinsic General Relativity and Clifford Algebra

This paper proposes to go beyond the Einstein General Relativity theory in a noncommutative geometric framework. As a first step, we rewrite the General Relativity theory intrinsically (coordinate-free formulation). As a second step, we rewrite the first and the second Bianchi identities, including torsion, within minimal algebraic hypotheses. Then, in order to extend the General Relativity theory for dealing with noncommutative scalar fields on a manifold \(\mathcal {M}\), we are forced to adapt the definition of vector fields and connections. It leads to the consideration of one associative product p of vector fields and four derivations (\(\nabla \): (vector, vector) to vector, \(\partial \): (vector, scalar) to scalar, \(\delta \): (scalar, vector) to scalar, \(\mathcal {C}\): (scalar, scalar) to scalar). At last, the particular case where scalars are a Clifford numbers motivates future investigations towards a common writing of the Einstein field equations and the Dirac equation.

Conformal gravity: Newton's constant is not universal

Newton's gravitational constant G has been measured to high accuracy in a number of independent experiments. For currently unresolved reasons, indicated values from different well-designed and thoroughly analyzed experiments differ by more than the sum of estimated errors. It has recently been shown that requiring both Einstein general relativity and the Higgs scalar field model to satisfy conformal symmetry (local Weyl scaling covariance) introduces gravitational effects that explain anomalous galactic rotation, currently accelerating Hubble expansion, and dark galactic halos, without invoking dark matter. This implies different values G n and G p for neutron and proton, respectively, but retains the Einstein equivalence principle for test objects accelerated by a given gravitational field. Isotopic mass defect μ per nucleon determines independent G m . Thus G differs for each nuclear isotope. Several recent measurements are used here to estimate , , and in units .

Gravothermal phase transition, black holes and space dimensionality

In the framework of gravothermal evolution of an ideal monatomic fluid, I examine the dynamical instability of the fluid sphere in ($N$+1) dimensions by exploiting Chandrasekhar's criterion to each quasistatic equilibrium along the sequence of the evolution. Once the instability is triggered, it would probably collapse into a black hole if no other interaction halts the process. From this viewpoint, the privilege of (3+1)-dimensional spacetime is manifest, as it is the marginal dimensionality in which the ideal monatomic fluid is stable but not too stable. Moreover, it is the unique dimensionality that allows stable hydrostatic equilibrium with positive cosmological constant. While all higher dimensional ($N>3$) spheres are genuinely unstable. In contrast, in (2+1)-dimensional spacetime it is too stable either in the context of Newton's theory of gravity or Einstein's general relativity. It is well known that the role of negative cosmological constant is crucial to have the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole solution and the equilibrium configurations of a fluid disk. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk to collapse into a naked singularity, which supports the cosmic censorship conjecture. However, BTZ holes of mass $\mathcal{M}_{\rm BTZ}>0$ could emerge from collapsing fluid disks. The implications of spacetime dimensionality are briefly discussed.

Compact stellar model in higher torsion gravitational theory

In this study, we address the issue of a spherically symmetrical interior solution to the quadratic form of f(T)=T+ϵT2 gravitational theory using a physical tetrad that provides vanishing components of the off-components of the field equation, in contrast to what exists in the current literature. To be able to formulate the resulting differential equation in a closed form, we employ the Krori-Barua (KB) ansatz. Using the KB spacetime form, we derive the analytic form of the energy-density, radial, and tangential pressures and the anisotropic form. All of these quantities are affected by the dimensional parameter ϵ, which causes them to have a noted difference from those given in the frame of Einstein general relativity. The derived model of this study exhibits a non-trivial form of torsion scalar, and it also contains three constants that we drew from the matching of the boundary condition with a line element that also features a non-trivial form of torsion scalar. Having established the physical conditions that are needed for any real stellar, we check our model and show in detail that it bypasses all of these. Finally, we analyze the model's stability utilizing the Tolman-Oppenheimer-Volkoff equation and adiabatic index and show that our model satisfies these.

Black holes with Lagrange multiplier and potentialin mimetic-like gravitational theory: multi-horizon black holes

In this paper, we consider the mimetic-like field equations coupled with the Lagrange multiplier and the potential to derive non-trivial spherically symmetric black hole (BH) solutions. We divided this study into three cases: in the first one, we choose the Lagrange multiplier and the potential to vanish and derive a BH solution that coincides with the BH of the Einstein general relativity despite the non-vanishing value of the mimetic-like scalar field. The first case is consistent with the previous studies in the literature where the mimetic theory coincides with GR [1]. In the second case, we derive a solution with a constant value of the potential and a dynamical value of the Lagrange multiplier. This solution has no horizon, and therefore, the obtained space-time does not correspond to the BH. In this solution, there appears a region of the Euclidian signature where the signature of the diagonal components of the metric is (+,+,+,+) or the region with two times where the signature is (+,+,-,-). Finally, we derive a BH solution with non-vanishing values of the Lagrange multiplier, potential, and mimetic-like scalar field. This BH shows a soft singularity compared with the Einstein BH solution. The relevant physics of the third case is discussed by showing their behavior of the metric potential at infinity, calculating their energy conditions, and studying their thermodynamical quantities. We give a brief discussion on how our third case can generate a BH with three horizons as in the de Sitter-Reissner-Nordström black hole space-time, where the largest horizon is the cosmological one and two correspond to the outer and inner horizons of the BH. Even in the third case, the region of the Euclidian signature or the region with two times appears. We give a condition that such unphysical region(s) is hidden inside the black hole horizon and the existence of the region(s) becomes less unphysical. We also study the thermodynamics of the multi-horizon BH and consider the extremal case, where the radii of two horizons coincide with each other. We observe that the Hawking temperature and the heat capacity vanish in the extremal limit. Finally, we would like to stress the fact that in spite that the field equations we use have no cosmological constant, our BH solutions of the second and third case behave asymptotically as AdS/dS.