General Relativity Research Articles

Fill-ins with scalar curvature lower bounds and applications to positive mass theorems

Given a constant C and a smooth closed (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional Riemannian manifold (Σ,g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Sigma , g)$$\\end{document} equipped with a positive function H, a natural question to ask is whether this manifold can be realised as the boundary of a smooth n-dimensional Riemannian manifold with scalar curvature bounded below by C and boundary mean curvature H. That is, does there exist a fill-in of (Σ,g,H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Sigma ,g,H)$$\\end{document} with scalar curvature bounded below by C? We use variations of an argument due to Miao and the author (Int Math Res Not 7:2019, 2019) to explicitly construct fill-ins with different scalar curvature lower bounds, where we permit the fill-in to contain another boundary component provided it is a minimal surface. Our main focus is to illustrate the applications of such fill-ins to geometric inequalities in the context of general relativity. By filling in a manifold beyond a boundary, one is able to obtain lower bounds on the mass in terms of the boundary geometry through positive mass theorems and Penrose inequalities. We consider fill-ins with both positive and negative scalar curvature lower bounds, which from the perspective of general relativity corresponds to the sign of the cosmological constant, as well as a fill-in suitable for the inclusion of electric charge.

Micro-cosmos model of a nucleon

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro-cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton’s radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro-cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics.

Imprints of cloud of strings and quintessence field on compact stellar configurations

This paper looks into how stellar configurations with quintessence and a cloud of string fields behave in general relativity in spherical symmetric spacetime. The goal is to find a stable, stellar model. We compute the unknown constants in the metric using the masses and radii of PSRJ1614 − 2230 stars. We employ the effective energy-momentum tensor in general relativity to analyze field equations. Additionally, we also demonstrate the anisotropic behavior, energy conditions, energy density, quintessence density, pressure profiles, gradients, anisotropic factor, energy conditions, sound speeds, compactification, mass function, EoS components, redshift, and stability of the compact stars. We demonstrate that according to the theory of general relativity, these compact stars exhibit physically plausible structures in the quintessence field with clouds of string.

Higher-order gravity, finite action, and a safe beginning for the universe

General relativity allows for inhomogeneous and anisotropic universes with finite action. By contrast, in quadratic gravity such solutions obtain infinite action and are thus eliminated. What remains are homogeneous and isotropic solutions undergoing accelerated expansion, thereby automatically inducing an early inflationary phase. In this manner, semi-classical consistency may explain some of the basic, coarse-grained features of the early universe. This includes suitable initial conditions for the second law of thermodynamics, in the spirit of the Weyl curvature hypothesis. We note that quadratic gravity is a renormalisable theory and may admit an asymptotically safe regime at high energies, rendering the theory trustworthy to high energies. We also comment on theories containing curvature terms up to infinite derivative order, and on the contrast with no-boundary initial conditions.

Maximal steered coherence in the background of Schwarzschild space-time

In the past two decades, the exploration of quantumness within Schwarzschild spacetime has garnered significant interest, particularly regarding the Hawking radiation’s impact on quantum correlations and quantum coherence. Building on this foundation, we investigate how Hawking radiation influences maximal steered coherence (MSC)-a crucial measure for gauging the ability to generate coherence through steering. We find that as the Hawking temperature increases, the physically accessible MSC degrade while the unaccessible MSC increase. This observation is attributed to a redistribution of the initial quantum correlations, previously acknowledged by inertial observers, across all bipartite modes. In particular, we find that in limit case that the Hawking temperature tends to infinity, the accessible MSC equals to 1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/\\sqrt{2}$$\\end{document} of its initial value, and the unaccessible MSC between mode A and B¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{B}$$\\end{document} also equals to the same value. Our findings illuminate the intricate dynamics of quantum information in the vicinity of black holes, suggesting that Hawking radiation plays a pivotal role in reshaping the landscape of quantum coherence and entanglement in curved spacetime. This study not only advances our theoretical understanding of black hole thermodynamics but also opens new avenues for investigating the interface between quantum mechanics and general relativity.

Nonexistence of a parent theory for general relativity and unimodular gravity

Nonexistence of a parent theory for general relativity and unimodular gravity

Observational feasibility of 4D Einstein-Gauss-Bonnet cosmology: bouncing and non-bouncing universes

This paper analyzes the possibility of bouncing and non-bouncing universes in the framework of four-dimensional Einstein-Gauss-Bonnet (4D-EGB) gravity,corresponding respectively to negative and positive coupling constants λ of the Gauss-Bonnet term. We also use the Horndeski-type scalar-tensor theory to assess the role of a scalar charge C as a geometrical contribution to the radiation in the Universe.We modify the expansion history of the universe to allow for modifications induced by the 4D-EGB gravity.Using Planck measurements of the cosmic microwave background anisotropies as well as various datasets of baryonic acoustic oscillations, we set the upper bounds λ ≤ 10-16(km/s/Mpc)-2 and λ ≤ 10-30(km/s/Mpc)-2 for the non-bouncing and bouncing scenarios.The upper limit in the latter case is mainly driven by the requirement to conservatively respect the thermal history at energy scales of the standard model of particle physics.We also find that the contribution of the geometrical radiation-like term of the model cannot exceed 10% of the current radiation in the Universe. The possibility of an early inflationary phase produced by a single scalar field is also studied and found to be feasible in both bouncing and non-bouncing scenarios.This study shows the feasibility of a bouncing universe, even with a normal matter sector, in the 4D-EGB gravity. More theoretical investigation is required to further explore possible observational predictions of the model that can distinguish between general relativity and 4D-EGB gravity.

No-go theorem for static spherically symmetric configurations composed of two charged pressureless fluid species

We present a no-go theorem for spherically symmetric configurations of two charged fluid species in equilibrium. The fluid species are assumed to be dusts, that is, perfect fluids without pressure, and the equilibrium can be attained for a single dust from the balance of electrostatic repulsion and gravitational attraction. We show that this is impossible for two dust species unless both of them are indistinguishable in terms of their electric charge density to matter density ratio. The result is obtained in the main three theories of mechanics, that is, in Newtonian Mechanics, in Special Relativity and in General Relativity. In particular, as charged dust solutions have been used to study the possibility of black hole mimickers, this result shows that such mimickers can not be constructed unless the underlying charged particle has the correct charge to mass ratio.

Effects of general relativistic post-Newtonian approximations on the configuration space properties of elliptical orbital trajectories

Post-Newtonian approximations have been successful in describing various astronomical phenomena that classical Newtonian gravity could not. One such phenomenon is the precession of the periapsis of elliptical orbits. Einstein originally solved the problem in 1916 and since then others have been applying the technique to numerous complex systems. However, not much attention has been given to studying the changes in the configuration space when switching from Newtonian to post-Newtonian mechanics. Here, we compare the sizes and topologies of the configuration spaces of both these approaches and further explore the likelihood of planetary collisions in other star systems when configuration space expansion due to general relativity is taken into account.

Probing black hole in Starobinsky-Bel-Robinson gravity with thermodynamical analysis, effective force and gravitational weak lensing

In this work, we investigate the effects of plasma and the coupling parameter β>0, on the thermodynamic properties and weak gravitational lensing by the Schwarzschild-like black hole in the Starobinsky-Bel-Robinson gravity (SBRG). We observe that the horizon radius and the corrected entropy of the Schwarzschild-like black hole in the SBRG are not much sensitive to the parameter β. On contrary the energy emission rate of the Schwarzschild-like black hole in the SBRG is sensitive to the parameter β and decreases with increase in the values of the parameter β. We see that the Schwarzschild-like black hoe in the SBRG is stable as the thermodynamicl temperature is positive for different values of the parameter β. Moreover we observe that the deflection angle of photon beam by the black hole in uniform plasma, nonuniform self-interacting scalar plasma and non-singular isothermal gas sphere reduces with the parameter β, against the impact parameter b. We see that the deflection angle enhances with increase in the concentration of the plasma fields for all the three types of plasma media. Further we find that the magnification of the image due to lensing increases in a higher concentration of plasma field. It is interesting to notice that the image magnification in uniform plasma is much higher as compared to the one in nonuniform plasma field. We compare our results with those for the Schwarzschild black hole of General Relativity. Further, effective force is also calculated for the Schwarzschild-like black hole in the SBRG.

Nonlinear gravitational waves in Horndeski gravity: scalar pulse and memories

We present and analyze a new non-perturbative radiative solution of Horndeski gravity. This exact solution is constructed by a disformal mapping of a seed solution of the shift-symmetric Einstein-Scalar system belonging to the Robinson-Trautman geometry describing the gravitational radiation emitted by a time-dependent scalar monopole. After analyzing in detail the properties of the seed, we show that while the general relativity solution allows for shear-free parallel transported null frames, the disformed solution can only admit parallel transported null frames with a non-vanishing shear. This result shows that, at the nonlinear level, the scalar-tensor mixing descending from the higher-order terms in Horndeski dynamics can generate shear out of a pure scalar monopole. We further confirm this analysis by identifying the spin-0 and spin-2 polarizations in the disformed solution using the Penrose limit of our radiative solution. Finally, we compute the geodesic motion and the memory effects experienced by two null test particles with vanishing initial relative velocity after the passage of the pulse. This exact radiative solution offers a simple framework to witness nonlinear consequences of the scalar-tensor mixing in higher-order scalar-tensor theories.

Why Einstein was Wrong Great Scientists and Great Mistakes

The article suggests that historical errors are fundamental to our current misunderstandings of both special and general relativity theories.

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.

Unification of Gravity and Light Using the Gertsenshtein Effect

This study examines the Gertsenshtein effect, which theorizes the conversion of electromagnetic waves into gravitational waves in the presence of a strong magnetic field. First proposed by Mark Gertsenshtein in 1962 and grounded in general relativity, this effect forms a bridge between electromagnetism and gravity, providing insights into the fundamental interactions within spacetime. Through the use of Maxwell's and Einstein's equations, we analyze the conditions necessary for this conversion and discuss its theoretical significance as well as the challenges in observation. Given the inherently weak nature of gravitational waves, their detection proves difficult; however, the Gertsenshtein effect holds the potential to shed light on cosmic events and the structure of the universe. This paper elucidates the physics of the effect, its astrophysical and cosmological implications, and the pathway toward experimental verification. It concludes that, in the context of the Gertsenshtein effect, gravity and light—similar to mass and energy in the special theory of relativity—are different manifestations of the same fundamental essence of the universe.

Constant velocity physical warp drive solution

Abstract Warp drives are exotic solutions of general relativity that offer novel means of transportation. In this study, we present a solution for a constant-velocity subluminal warp drive that satisfies all of the energy conditions. The solution involves combining a stable matter shell with a shift vector distribution that closely matches well-known warp drive solutions such as the Alcubierre metric. We generate the spacetime metric numerically, evaluate the energy conditions, and confirm that the shift vector distribution cannot be reduced to a coordinate transformation. This study demonstrates that classic warp drive spacetimes can be made to satisfy the energy conditions by adding a regular matter shell with a positive ADM mass.

Robust test of general relativity at the galactic scales by combining strong lensing systems and gravitational wave standard sirens

Robust test of general relativity at the galactic scales by combining strong lensing systems and gravitational wave standard sirens

Catalog variance of testing general relativity with gravitational-wave data

Catalog variance of testing general relativity with gravitational-wave data

Effective cuscuton theory

Cuscuton field theory is an extension of general relativity that does not introduce additional propagating degrees of freedom, or violate relativistic causality. We construct a general geometric description of the cuscuton field theory by introducing curvature corrections to both the volume (potential) and the surface (kinetic) terms in the original cuscuton action. Our assumptions involve a stack of spacelike branes, separated by 4-dimensional bulks. We conjecture that the cuscuton, initially a discrete field, becomes continuous in the limit, there are many such transitions. From this we derive an effective action for the cuscuton theory and show that at the quadratic level our theory propagates only the two tensorial degrees of freedom.

The Relativistic Spin Precession in the Compact Double Neutron Star System PSR J1946+2052

Abstract We observe systematic profile changes in the visible pulsar of the compact double neutron star system PSR J1946+2052 using observations with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The interpulse of PSR J1946+2052 changed from a single-peak to a double-peak shape from 2018–2021. We attribute this evolution as the result of the relativistic spin precession of the pulsar. With the high sensitivity of FAST, we also measure significant polarization for the first time, allowing us to model this with the precessional rotating vector model. Assuming, to the first order, a circular hollow-cone-like emission beam pattern and taking the validity of general relativity (GR), we derive the binary’s orbital inclination angle ( 63 ∘ − 3 ∘ + 5 ∘ ) and pulsar’s spin geometry. The pulsar’s spin vector and the orbital angular momentum vector are found to be only slightly misaligned ( 0. ∘ 21 − 0. ∘ 10 + 0. ∘ 28 ). The quoted uncertainties do not reflect the systematic uncertainties introduced by our model assumptions. By simulating future observations of profile and polarization evolution, we estimate that we could constrain the precession rate within a 43% uncertainty in 9 yr. Hence, we suggest that the system’s profile evolution could be combined with precise pulsar timing to test GR in the future.

Physically consistent gravitational waveform for capturing beyond general relativity effects in the compact object merger phase

Physically consistent gravitational waveform for capturing beyond general relativity effects in the compact object merger phase