Frame Of General Relativity Research Articles

Relativistic Exploration of Dark Matter Effectsin Rotating Galaxy, Studied Fluid-Dynamically

Galactic space is filled with interstellar clouds of neutral gases. Motion of the space-clouds is viewed as a flow of continuous fluid in curved space with gravity. Dynamical motions of the space-fluid of rotating galaxies are investigated by extending Fluid Dynamics to that in the frame of general relativity. Fluid flow field to be extended to that of a relativistic theory is reinforced by the fluid gauge theory equipped with a background (dark) gauge field conditioning the fluid continuity. The Gravity-space Fluid Dynamics thus developed captures main feature of the dark-matter effect as the action of the gauge field on the motion of space fluids. In the present formulation, the stress-energy tensor in the general relativity is revised in order to take account of general nature of stress field by extending the isotropic pressure to an-isotropic stress field.

Reference frames in general relativity and the galactic rotation curves

Reference frames in general relativity and the galactic rotation curves

Compact objects in quadratic Palatini gravity generated by a free scalar field

We study the correspondence that connects the space of solutions of General Relativity (GR) with that of Ricci-based Gravity theories (RBGs) of the $f(R,Q)$ type in the metric-affine formulation, where $Q=R_{(\mu\nu)}R^{(\mu\nu)}$. We focus on the case of scalar matter and show that when one considers a free massless scalar in the GR frame, important simplifications arise that allow to establish the correspondence for arbitrary $f(R,Q)$ Lagrangian. We particularize the analysis to a quadratic $f(R,Q)$ theory and use the spherically symmetric, static solution of Jannis-Newman-Winicour as seed to generate new compact objects in our target theory. We find that two different types of solutions emerge, one representing naked singularities and another corresponding to asymmetric wormholes with bounded curvature scalars everywhere. The latter solutions, nonetheless, are geodesically incomplete.

Spherical gravitational waves and quasi-spherical waves scattered from black string in massive gravity

Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution with a special singular reference metric. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear perturbations. We find that the graviton ray can be null in massive gravity by considering full back reaction of the massive gravitational waves to the metric. We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton.

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

Tail wavelets in merger of binary compact objects * * Supported in part by the National Natural Science Foundation of China (NSFC) (11805166, 11575083); as well as Shandong Province Natural Science Foundation (ZR201709220395). We also gratefully acknowledge the financial support from Brazilian funding agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Conselho Nacional de Desenvolvimento Científico

We present a model for tail wavelets, a phenomenon known as “echo” in the literature. The tail wavelet may appear in signal reconnaissances in the merger of binary compact objects, including black holes and neutron stars. We show that the dark matter surrounding the compact objects lead to a speculated tail wavelet following the main gravitational wave (GW). We demonstrate that the radiation pressure of the main wave is fully capable of pushing away the surrounding matter to some altitude, and splashing down of the matter excites the tail wavelet after ringing down of the main wave. We illustrate this concept in a simplified model, where numerical estimations are conducted on the specific distribution of dark matter outside the black hole horizon and the threshold values in accordance with observations. We study the full back reaction of the surrounding dark matter to the metric and find that the effect on to the tail wavelets is insignificant. We reveal the fine difference between the tail wavelets of a dressed and a bare black hole. We demonstrate that the tail wavelet can appear as a natural phenomenon in the frame of general relativity, without invoking modified gravities or quantum effects.

The Polarization of X-Rays from Warped Black Hole Accretion Disks

Abstract It is commonly assumed that in black hole (BH) accretion disks the angular momenta of the disk and the BH are aligned. However, for a significant fraction of stellar-mass BHs and supermassive BHs, the momenta may not be aligned. In such systems, the interplay of disk viscosity and general relativistic frame dragging can cause the disk to warp or break into two (or more) distinct planes; this is called the Bardeen–Petterson effect. We have developed a general relativistic ray-tracing code to find the energy spectra and polarization of warped accretion disks, accounting for the emission from the disk and for photons reflecting one or multiple times off the warped accretion disk segments. We find that polarization angle can be used to give a lower limit on the misalignment angle when a previous measurement of the jet, which is thought be aligned with the BH angular momentum, can be spatially resolved.

Shock Wave Interactions and the Riemann-Flat Condition: The Geometry Behind Metric Smoothing and the Existence of Locally Inertial Frames in General Relativity

We prove that the essential smoothness of the gravitational metric at shock waves in GR, a PDE regularity issue for weak solutions of the Einstein equations, is determined by a geometrical condition which we introduce and name the {\it Riemann-flat condition}. The Riemann-flat condition determines whether or not the essential smoothness of the gravitational metric is two full derivatives more regular than the Riemann curvature tensor. This provides a geometric framework for the open problem as to whether {\it regularity singularities} (points where the curvature is in $L^\infty$ but the essential smoothness of the gravitational metric is only Lipschitz continuous) can be created by shock wave interaction in GR, or whether metrics Lipschitz at shocks can always be smoothed one level to $C^{1,1}$ by coordinate transformation. As a corollary of the ideas we give a proof that locally inertial frames always exist in a natural sense for shock wave metrics in spherically symmetric spacetimes, independent of whether the metric itself can be smoothed to $C^{1,1}$ locally. This latter result yields an explicit procedure (analogous to Riemann Normal Coordinates in smooth spacetimes) for constructing locally inertial coordinates for Lipschitz metrics, and is a new regularity result for GR solutions constructed by the Glimm scheme.

Gravity as the Sole Fundamental Force

We had explained electromagnetism by gravity before a recent publication in this Journal, in which we further incorporated the nuclear strong force in the framework of gravity. This paper, summarizing our cumulative results, continues to integrate the nuclear weak force with gravity, where we go by the following line of logic: Planck’s formula shows energy E = frequency = probability = wave; hence quantum waves have energies and the Universe is a diagonal spacetime manifold containing {(particle pi, electromagnetic wave λ (pi))}. By Feynman’s analysis on electromagnetic mass, we assume that the distribution of E over (p, λ (p)) is (3/4 , 1/4)E. Then Newton’s gravitational acceleration formula yields E = 1.6 × the observed energy o f p, so that p exists only for a duration of 5/8 λ/c over the cycle [0, λ/c], such as evidenced in quantum tunneling, opening the possibility for λ (p) to be combined with other waves forming new particle(s) for t > 58/ λ/c. By the time ratios of two frames in General Relativity we deduce neutron’s lifetime, and by the Higgs mechanism we show neutron’s decay products.

Analytical Models for Quark Stars with Van Der Waals Modified Equation of State

Stellar models consisting of spherically symmetric distribution of charged matter locally anisotropic in strong gravitational fields have been widely considered in the frame of general relativity. These investigations require the generation of exact models through the resolution of the Einstein-Maxwell system of equations. The presence of charge produces values for redshifts, luminosity and mass for the stars different in relation to neutral matter. Some applications for dense charged matter we have them in the description of quark stars, spheres with linear or non-linear equation of state, hybrid stars and accreting process in compact objects where the matter acquires large amounts of electric charge. In this paper, we studied the behavior of relativistic compact objects with anisotropic matter distribution considering Van der Waals modified equation of state proposed in 2013 for Malaver and a gravitational potential Z(x) that depends on an adjustable parameter α in order to integrate analytically the field equations. They generalize the ideal gas law based on plausible reasons that real gases do not act ideally. New exact solutions of the Einstein-Maxwell system are generated and the physical variables as the energy density, radial pressure, mass function, anisotropy factor and the metric functions are written in terms of elementary and polynomial functions. We obtained expressions for radial pressure, density and mass of the stellar object physically acceptable with two different values of the adjustable parameter. The proposed models satisfy all physical features of a realistic star.

Affine inflation

Affine gravity, a gravity theory based on affine connection with no notion of metric, supports scalar field dynamics only if scalar fields have nonvanishing potential. The nonvanishing vacuum energy ensures that the cosmological constant is nonvanishing. It also ensures that the energy-momentum tensor of vacuum gives the dynamically generated metric tensor. We construct this affine setup and study primordial inflation in it. We study inflationary dynamics in affine gravity and general relativity, comparatively. We show that nonminimally coupled inflaton dynamics can be transformed into minimally coupled ones with a modified potential. We also show that there is one unique frame in affine gravity, as opposed to the Einstein and Jordan frames in general relativity. Future observations with higher accuracy may be able to test affine gravity.

Looking for extra dimensions in compact stars

The properties of spherically symmetric static compact stars are studied in the Randall-Sundrum II type braneworld model assuming that the spacetime outside the star is described by a Schwarzschild metric. The integration of the stellar structure equations employing the so called causal limit equation of state (EoS) shows that the equilibrium solutions can violate the general relativistic causal limit. An analysis of the properties of hadronic and strange quark stars using standard EoSs confirm the same result: there is a branch in the mass-radius diagram that shows the typical behaviour found within the frame of General Relativity and another branch of stars that are supported against collapse by the nonlocal effects of the bulk on the brane. Stars belonging to the new branch can violate the general relativistic causal limit, may have an arbitrarily large mass, and are stable under small radial perturbations. If they exist in Nature, these objects could be hidden among the population of black hole candidates. The future observation of compact stars with masses and radii falling above the causal limit of General Relativity but below the Schwarzschild limit maybe a promising astrophysical evidence for the existence of extra dimensions.

Compact stars in the braneworld: A new branch of stellar configurations with arbitrarily large mass

We study the properties of compact stars in the Randall-Sundrum II type braneworld model. To this end, we solve the braneworld generalization of the stellar structure equations for a static fluid distribution with spherical symmetry considering that the spacetime outside the star is described by a Schwarzschild metric. First, the stellar structure equations are integrated employing the so called causal limit equation of state (EOS), which is constructed using a well established EOS at densities below a fiducial density, and the causal EOS $P= \rho$ above it. It is a standard procedure in general relativistic stellar structure calculations to use such EOS for obtaining a limit in the mass radius diagram, known as causal limit, above which no stellar configurations are possible if the EOS fulfills that the sound velocity is smaller than the speed of light. We find that the equilibrium solutions in the braneworld model can violate the general relativistic causal limit and, for sufficiently large mass they approach asymptotically to the Schwarzschild limit $M = 2 R$. Then, we investigate the properties of hadronic and strange quark stars using two typical EOSs. For masses below $\sim 1.5 - 2 M_{\odot}$, the mass versus radius curves show the typical behavior found within the frame of General Relativity. However, we also find a new branch of stellar configurations that can violate the general relativistic causal limit and that in principle may have an arbitrarily large mass. The stars belonging to this new branch are supported against collapse by the nonlocal effects of the bulk on the brane. We also show that these stars are always stable under small radial perturbations. These results support the idea that traces of extra-dimensions might be found in astrophysics, specifically through the analysis of masses and radii of compact objects.

Dark Matter without New Matter Is Compliant with General Relativity

A recent publication revealed unexpected observations about dark matter. In particular, the observed baryonic mass should probably be sufficient to explain the observed rotation curves (i.e. without dark matter) and their observations gave an empirical relation for weak accelerations. This present work demonstrated that the equations of general relativity allow explaining the term of dark matter (without new matter) in agreement with the results of this publication and allow retrieving this empirical relation (observed values and characteristics of this correlation’s curve). These observations constrain drastically the possible gravitational potential in the frame of general relativity to explain the term of dark matter. This theoretical solution has already been studied with several unexpected predictions that have recently been observed. For example, an article revealed that early galaxies (ten billion years ago) didn’t have dark matter and a more recent paper showed unlikely alignments of galaxies. To finish the main prediction of this solution, it is recalled: the term of dark matter should be a Lense-Thirring effect, around the earth, of around 0.3 and 0.6 milliarcsecond/year.

Towards the Unification, Part 2: Simplified Equations, Covariant Derivative, Photons

We continue the study of the Standard Model of Quantum Physics in the Clifford algebra of space. We get simplified mass terms for the fermion part of the wave. We insert the simplified equations in the frame of General Relativity. We construct the electromagnetic field of the photon, alone boson without proper mass. We explain how the Pauli principle comes from the equivalence principle of General Relativity. We transpose in the frame of the algebra of space the second quantification of the electromagnetic field. We discuss the changes introduced here.

Generating Theorems for Charged Anisotropy in General Relativity

For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.

Frame dragging and Eulerian frames in general relativity

The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger's Poisson gauge with a Eulerian/observer's frame of reference. We obtain such an association by using a Lagrangian approach to relativistic cosmological structure formation. Explicitly, we begin with the second-order solution of the Einstein equations in a synchronous/comoving coordinate system---which defines the Lagrangian frame, and transform it to a Poissonian coordinate system. The generating vector of this coordinate/gauge transformation is found to be the relativistic displacement field. The metric perturbations in the Poissonian coordinate system contain known results from standard/Eulerian Newtonian perturbation theory, but contain also purely relativistic corrections. On sub-horizon scales these relativistic corrections are dominated by the Newtonian bulk part. These corrections however set up non-linear constraints for the density and for the velocity which become important on scales close to the horizon. Furthermore, we report the occurence of a transverse component in the displacement field, and find that it induces a non-linear frame dragging as seen in the observer's frame, which is sub-dominant at late-times and sub-horizon scales. Finally, we find two other gauges which can be associated with a Eulerian frame. We argue that the Poisson gauge is to be preferred because it comes with the simplest physical interpretation.

Thermodynamic quantities of a black hole with anf(R)global monopole

The thermodynamic quantities such as the local temperature, heat capacity, off-shell free energy and the stability of a black hole involving a global monopole within or outside the $f(R)$ gravity are examined. We compare the two classes of results to show the influence from the generalization of the general relativity. It is found that the $f(R)$ theory will modify the thermodynamic properties of black holes, but the shapes of curves for thermodynamic quantities with respect to the horizon are similar to the results within the frame of general relativity. In both cases there will exist a small black hole which will decay and a large stable black hole in the case that the temperatures are higher than their own critical temperature.

A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES

We calculate the structure of a standard accretion disk with corona surrounding a massive Kerr black hole in general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of the accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of the disk-corona systems with a modified $\alpha$-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor $L_{\rm bol}/L_{\rm X,2-10keV}$ increase with the dimensionless mass accretion rate, which are qualitatively consistent with the observations of active galactic nuclei (AGNs). The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter $a$, which leads to lower electron temperatures of the coronas for rapidly spinning black holes. The X-ray emission from the coronas surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive with the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin $a$, which deviates from $f_\nu\propto\nu^{1/3}$ expected by the standard thin disk model.

Classical bouncing Universes from vector fields

For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of R,RμνRμν,RμναβRμναβ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant or dust. We also discuss bouncing solution for massless vector field domination in n+2-dimensional space–time.