General Relativity Field Research Articles

Modeling Anisotropic Charged Neutron Star in Isotropic Coordinates

We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for charged fluid with pressure anisotropy, compatible with a super dense star modeling. Further, we have constructed an anisotropic model of super dense star with all degree of suitability. We also observed that by increasing anisotropy, the maximum mass of super dense stars also decreases.

Completing the Standard Model with Gravity by General Relativizing Quantum Physics (RQP) (Coupling Spin-2 Gravitons with Spin-0 Particles to Generate Higgs Mass)

After a straightforward general relativistic calculation on a modified flat-spacetime metric (developed from the fluctuating vacuum energy interacting with a graviton field), a pair of n-valued covariant and contravariant energy momentum tensors emerged analogous to quantized raising and lower operators. Detaching these operators from the general relativistic field equations, and then transporting them to act on extreme spacetimes, these operators were able to generate fundamental particle boson masses. In particular, the operators precisely generated Higgs mass. Then by applying a consistency approach to the gravitational field equations—similar to how Maxwell applied to the electromagnetic ones—it allowed for the coupling of spin-to-mass, further restricting the particle mass to be in precise agreement with CODATA experimental values. Since this is a massless field approach integrated discretely with a massive one, it overcomes various renormalizing difficulties; moreover it solves the mass hierarchal problem of the Standard Model of particle physics, and generates its spin and therefore shows quantum physics to be a subset of General Relativity, just as Einstein had first imagined.

Relativized Quantum Physics Generating <i>N</i>-Valued Coulomb Force and Atomic Hydrogen Energy Spectrum

Though not well-known, Einstein endeavored much of his life to general-relativize quantum mechanics, (rather than quantizing gravity). Albeit he did not succeed, his legacy lives on. In this paper, we begin with the general relativistic field equations describing flat spacetime, but stimulated by vacuum energy fluctuations. In our precursor paper, after straightforward general relativistic calculations, the resulting covariant and contravariant energy-momentum tensors were identified as n-valued operators describing graviton excitation. From these two operators, we were able to generate all three boson masses (including the Higgs mass) in precise agreement as reported in the 2010 CODATA (NIST); moreover local, as-well-as large-scale, accelerated spacetimes were shown to naturally occur from this general relativized quantum physics approach (RQP). In this paper, applying the same approach, we produce an n-valued Coulombs Force Law leading to the energy spectrum for atomic hydrogen, without assuming quantized atomic radii, velocity and momentum, as Bohr did.

Anisotropic charged analogue of Heintzmann’s solution

We present an anisotropic charged analogue of Heintzmann’s (Z. Phys. 228:489, 1969) solution of the general relativistic field equations in curvature coordinates by using simple form of electric intensity E and pressure anisotropy factor Δ that involve charge parameter K and anisotropy parameter α respectively. Our solution is well behaved in all respects for all values of X lying in the range 0<X≤1.1, α lying in the range 0≤α≤6.2, K lying in the range 0<K≤9.7 and Schwarzschild compactness parameter “u” lying in the range 0<u≤0.391. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We present some models of super dense quark star and neutron stars corresponding to X=0.1, α=1 and K=3. By assuming surface density of quark star, ρ b =4.6888×1014 g cm−3 the mass and radius are 1.271M ⊙, 10.09 km respectively. For ρ b =2.7×1014 g cm−3 the mass and radius of neutron star are 1.675M ⊙, 13.297 km respectively. The well behaved class of relativistic stellar models obtained in this work might have astrophysical significance in the study of more realistic internal structure of compact stars.

Stephen Hawking’s 1966 Adams Prize Essay

The Adams Prize is awarded each year by the Faculty of Mathematics at the University of Cambridge and St John’s College to a young, UK based mathematician for first-class international research in the Mathematical Sciences. The Prize is named after the mathematician John Couch Adams. It was endowed by members of St John’s College and was approved by the senate of the university in 1848 to commemorate Adams’ discovery of the planet Neptune. Each year applications are invited from mathematicians who have worked in a specific area of mathematics. The prize has been awarded to many well known mathematicians and physicists, including James Clerk Maxwell (1857), J.J. Thomson (1882), John H. Poynting (1893), Joseph Larmor (1899), Geoffrey I. Taylor (1915), James H. Jeans (1917), Ralph H. Fowler (1924), Harold Jeffreys (1926), Abram S. Besicovitch (1930), William V.D. Hodge (1936), Subrahmanyan Chandrasekhar (1948), George Batchelor (1950), and Abdus Salam (1958). In 1966 the topic set was “Geometric Problems of Relativity, with special reference to the foundations of general relativity and cosmology”, with adjudicators Hermann Bondi, William V.D. Hodge, and A. Geoffrey Walker. Roger Penrose submitted an essay entitled “An analysis of the structure of spacetime” and Stephen Hawking one called “Singularities and the Geometry of Spacetime”. Penrose was awarded the Adams prize for his essay, and Hawking was awarded an auxiliary Adams Prize at the same time. Hawking’s essay, reprinted below [Hawking 2014], summarised his work on global properties of general relativity theory, and in particular developed a series of cosmological singularity theorems he had proved. Neither Adams Prize essay was published as a book at the time, although preprint versions of both were circulated in the relativity community. The context was the growing investigation of global properties of solutions of the general relativity field equations at that time. Two remarkable developments started this trend: first, Kurt Godel’s proof of the existence of exact solutions of the field equations for ordinary matter that allowed causality violation [Godel 1949].

Was Galileo Right?

An important scientific debate took place regarding falling bodies hundreds of years ago, and it still warrants close examination. Galileo argued that in a vacuum all bodies fall at the same rate relative to the earth, independent of their mass. As we shall see, the problem is more subtle than meets the eye ‐ even in vacuum. In principle the results of a free fall experiment depend on whether falling masses are sequential or concurrent, whether they fall side by side or diametrically opposed. In the current paper we will present both the classical mechanics treatment and the general relativity one. In the case of classical mechanics, we start from the basic equations of motion. On the other hand, the determination of particle equations of motion in gravitational fields in general relativity is done routinely via the use of covariant derivatives. Since the geodesic equations based on covariant derivatives are derived from the Euler-Lagrange equations and since the Euler-Lagrange formalism is very intuitive, easy to derive with no mistakes, there is every reason to use them even for the most complicated situations and this is exactly what we do in the second part of the current paper.

Static and rotating neutron stars fulfilling all fundamental interactions

We summarize the key ingredients of a new neutron star model fulfilling global, but not local, charge neutrality. The model is described by what we have called the Einstein-Maxwell-Thomas-Fermi equations, which account for the strong, weak, electromagnetic, and gravitational interactions, as well as thermodynamical equilibrium, within the framework of general relativity and relativistic nuclear mean field theory. We show the results for both static and uniformly-rotating neutron stars and discuss some astrophysical implications.

Holographic thermalization, stability of anti-de sitter space, and the Fermi-Pasta-Ulam paradox.

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti-de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.

A Class of Super Dense Stars Models Using Charged Analogues of Hajj-Boutros Type Relativistic Fluid Solutions

We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for perfect charged fluid, compatible with a super dense star modeling. The solution is well behaved for all the values of Schwarzschild parameter u lying in the range 0 < u < 0.1727 for the maximum value of charge parameter K = 0.08163. The maximum mass of the fluid distribution is calculated by using stellar surface density as ρ b = 4.6888×1014g cm−3. Corresponding to K = 0.08 and u max = 0.1732, the resulting well behaved solution has a maximum mass M = 0.9324M ⊙ and radius R = 8.00 and by assuming ρ b = 2×1014g cm−3 the solution results a stellar configuration with maximum mass M = 1.43M ⊙ and radius R b = 12.25 km. The maximum mass is found increasing with increasing K up to 0.08. The well behaved class of relativistic stellar models obtained in this work might has astrophysical significance in the study of internal structure of compact star such as neutron star or self-bound strange quark star like Her X-1.

The mass limit of white dwarfs with strong magnetic fields in general relativity

Recently, U. Das and B. Mukhopadhyay proposed that the Chandrasekhar limit of a white dwarf could reach a new high level (2.58M⊙) if a superstrong magnetic field were considered (Das U and Mukhopadhyay B 2013 Phys. Rev. Lett. 110 071102), where the structure of the strongly magnetized white dwarf (SMWD) is calculated in the framework of Newtonian theory (NT). As the SMWD has a far smaller size, in contrast with the usual expectation, we found that there is an obvious general relativistic effect (GRE) in the SMWD. For example, for the SMWD with a one Landau level system, the super-Chandrasekhar mass limit in general relativity (GR) is approximately 16.5% lower than that in NT. More interestingly, the maximal mass of the white dwarf will be first increased when the magnetic field strength keeps on increasing and reaches the maximal value M = 2.48M⊙ with BD = 391.5. Then if we further increase the magnetic fields, surprisingly, the maximal mass of the white dwarf will decrease when one takes the GRE into account.

Pulsar spin-down luminosity: Simulations in general relativity

Adopting our new method for matching general relativistic, ideal magnetohydrodynamics to its force-free limit, we perform the first systematic simulations of force-free pulsar magnetospheres in general relativity. We endow the neutron star with a general relativistic dipole magnetic field, model the interior with ideal magnetohydrodynamics, and adopt force-free electrodynamics in the exterior. Comparing the spin-down luminosity to its corresponding Minkowski value, we find that general relativistic effects give rise to a modest enhancement: the maximum enhancement for $n=1$ polytropes is $\ensuremath{\sim}23%$. Evolving a rapidly rotating $n=0.5$ polytrope we find an even greater enhancement of $\ensuremath{\sim}35%$. Using our simulation data, we derive fitting formulas for the pulsar spin-down luminosity as a function of the neutron star compaction, angular speed, and dipole magnetic moment. We expect stiffer equations of state and more rapidly spinning neutron stars to lead to even larger enhancements in the spin-down luminosity.

An Exact Solution of Perfect Fluid in Isotropic Coordinates, Compatible with Relativistic Modeling of Star

We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for perfect fluid, compatible with a super dense star modeling. The solution is well behaved for all the values of u lying in the range 0<u≤0.12. Further, we have constructed a super-dense star model with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to u=0.12, the resulting well behaved model has maximum mass M=0.912MΘ with radius Rb≈11.27 km and Moment of inertia 0.97×1045 gm cm2. The good matching of our results for Vela pulsars show the stoutness of our model.

Thermodynamical instabilities of perfect fluid spheres in General Relativity

For a static, perfect fluid sphere with a general equation of state, we obtain the relativistic equation of hydrostatic equilibrium, namely the Tolman–Oppenheimer–Volkov equation, as the thermodynamical equilibrium in the microcanonical, as well as the canonical, ensemble. We find that the stability condition determined by the second variation of entropy coincides with the dynamical stability condition derived by the variations to first order in the dynamical Einstein’s equations. Thus, we show the equivalence of microcanonical thermodynamical stability with linear dynamical stability for a static, spherically symmetric field in General Relativity. We calculate the Newtonian limit and find the interesting property that the microcanonical ensemble in General Relativity transforms to the canonical ensemble for non-relativistic dust particles. Finally, for specific kinds of systems, we study the effect of the cosmological constant on the microcanonical thermodynamical stability of fluid spheres.

THE LENSE-THIRRING EFFECT IN THE ANOMALISTIC PERIOD OF CELESTIAL BODIES

In the weak field and slow motion approximation, the general relativistic field equations are linearized, resembling those of the electromagnetic theory. In a way analogous to that of a moving charge generating a magnetic field, a mass-energy current can produce a gravitomagnetic field. In this contribution, the motion of a secondary celestial body is studied under the influence of the gravitomagnetic force generated by a spherical primary. More specifically, two equations are derived to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period). Kinematically, this influence results to an apsidal motion. The aforementioned quantities are numerically estimated for Mercury, the companion star of the pulsar PSR 1913+16, the companion planet of the star HD 80606 and the artificial Earth satellite GRACE-A. The case of the artificial Earth satellite GRACE-A is also considered, but the results present a low degree of reliability from a practical standpoint.

Artificial gravity field

Using computer algebra to run Einstein’s equations “backward”, from field to source rather than from source to field, we design an artificial gravity field for a space station or spaceship. Everywhere inside astronauts experience normal Earth gravity, while outside they float freely. The stress-energy that generates the field contains exotic matter of negative energy density but also relies importantly on pressures and shears, which we describe. The same techniques can be readily used to design other interesting spacetimes and thereby elucidate the connection between the source and field in general relativity.

Einstein’s Pseudo-Tensor in &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt; Spatial Dimensions for Static Systems with Spherical Symmetry

It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified; 2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.

Reconstruction of [formula omitted] models with scale-invariant power spectrum

Following our previous work in [T. Qiu, JCAP 1206 (2012) 041 [1]], in this Letter, we continue our study of reconstructing f(R) modified gravity models that can be connected to a single scalar field in general relativity via conformal transformation, which lead to scale-invariant power spectrum in the early universe. With f(R) modified gravity, one does not need to introduce extra scalar, the nature of which are to be explained. Different from general nonminimal coupling theory, the behavior of the f(R) theory has been fixed by its counterpart in Einstein frame, and thus have one-to-one correspondence. Numerical plots of the functional form of f(R) as well as the evolution of R in terms of cosmic time t are also presented.

Scale-dependent growth from a transition in dark energy dynamics

We investigate the observational consequences of the quintessence field rolling to and oscillating near a minimum in its potential, if it happens close to the present epoch ($z\ensuremath{\lesssim}0.2$). We show that in a class of models, the oscillations lead to a rapid growth of the field fluctuations and the gravitational potential on subhorizon scales. The growth in the gravitational potential occurs on time scales $\ensuremath{\ll}{H}^{\ensuremath{-}1}$. This effect is present even when the quintessence parameters are chosen to reproduce an expansion history consistent with observations. For linearized fluctuations, we find that although the gravitational potential power spectrum is enhanced in a scale-dependent manner, the shape of the dark matter/galaxy power spectrum is not significantly affected. We find that the best constraints on such a transition in the quintessence field is provided via the integrated Sachs-Wolfe effect in the CMB-temperature power spectrum. Going beyond the linearized regime, the quintessence field can fragment into large, localized, long-lived excitations (oscillons) with sizes comparable to galaxy clusters; this fragmentation could provide additional observational constraints. Two quoted signatures of modified gravity are a scale-dependent growth of the gravitational potential and a difference between the matter power spectrum inferred from measurements of lensing and galaxy clustering. Here, both effects are achieved by a minimally coupled scalar field in general relativity with a canonical kinetic term. In other words we show that, with some tuning of parameters, scale-dependent growth does not necessarily imply a violation of General Relativity.

A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. The maximum mass of the Neutron star comes out to be M=1.591 M Θ with radius R b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.

Wormhole geometries in modified teleparallel gravity and the energy conditions

In this work, we explore the possibility that static and spherically symmetric traversable wormhole geometries are supported by modified teleparallel gravity or $f(T)$ gravity, where $T$ is the torsion scalar. Considering the field equations with an off-diagonal tetrad, a plethora of asymptotically flat exact solutions are found, which satisfy the weak and the null energy conditions at the throat and its vicinity. More specifically, considering $T\ensuremath{\equiv}0$, we find the general conditions for a wormhole satisfying the energy conditions at the throat and present specific examples that satisfy the energy conditions throughout the spacetime. As a consistency check, we also verify that in the teleparallel equivalent of general relativity, i.e., $f(T)=T$, one regains the standard general relativistic field equations for wormhole physics. Furthermore, considering specific choices for the $f(T)$ form and for the redshift and shape functions, several solutions of wormhole geometries are found that satisfy the energy conditions at the throat and its neighborhood. As in their general relativistic counterparts, these $f(T)$ wormhole geometries present far-reaching physical and cosmological implications, such as being theoretically useful as shortcuts in spacetime and for inducing closed timelike curves, possibly violating causality.