An approximate realistic metric representing the spacetime of neutron stars is obtained by perturbing the Kerr metric. This metric has five parameters, namely the mass, spin or angular momentum, mass quadrupole, spin octupole and mass hexadecapole. Moreover, a version of the Hartle-Thorne metric containing these parameters is constructed by means of a series transformation between these spacetimes and solving the Einstein field equations. The form of the Pappas metric in Schwarzschild spherical coordinates is found. The three relativistic multipole structures are compared.
We systematically study late-time tails of scalar waves propagating in neutron star spacetimes. We consider uniform density neutron stars, for which the background spacetime is analytic and the compaction of the star can be varied continously between the Newtonian limit 2M/R << 1 and the relativistic Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off neutron stars of different compactions 2M/R and find that a Newtonian, an intermediate, and a highly relativistic regime can be clearly distinguished. In the highly relativistic regime, the reflected signal is dominated…
The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that …
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial first-order approximate symmetry.
We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the…
Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfluidity, strong magnetic fields, hyperons, pion-condesation. Therefore an anisotropic neutron star core seems more realistic than an ideally isotropic one. We model anisotropic neutron stars working in the Krori-Barua (KB) ansatz without preassuming an equation of state. We show that the physics of general KB solutions is encapsulated in the compactness. Imposing physical and stability requirements yields a maximum allowed compactness $2GM/Rc^2 < 0.71$ for a KB-spacetime. We further input observatio…
We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, this slow decay is highly suggestive of nonlinear instability. We also prove that, in a large class of asymptotically flat, spherically symmetric spacetimes, logarithmic decay actually holds as a uniform upper bound. In the presence of stable trapping, this result is therefore the best one can obtain. In addition, we provide an application of thes…
The exterior geometry of a neutron star can be approximated by relativistic multipole moments of a parametrized metric using Ernst potential formalism. This spacetime can be tested with electromagnetic wave observation of astrophysical black holes. In the present paper, I simulate X-ray reflection spectra of a thin accretion disk with future X-ray missions. The purpose of this work is to understand whether X-ray reflection spectroscopy can distinguish the neutron star from the Kerr solution of General Relativity. I found that for the higher value of spin and multipole moment parameters, there …
We examine the effects of higher-order multipole contributions of rotating neutron star (NS) spacetimes on the propagation of corrugation (c-)modes within a thin accretion disk. We find that the Lense-Thirring precession frequency, which determines the propagation region of the low-frequency fundamental corrugation modes, can experience a turnover allowing for c-modes to become self-trapped for sufficiently high dimensionless spin $j$ and quadrupole rotational deformability $α$. If such self-trapping c-modes can be detected, e.g. through phase-resolved spectroscopy of the iron line for a high-…
Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed by I. Hussain and A. Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed by I. Hussain and A. Qadir [3,4], where they obtained approximate Noether symmetries from Lagrangian for a particular…
A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the lightcurve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its…
The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in a good agreement with the numerical calculations. The back reaction of the quantized field upon the spacetime metric is briefly discussed.
Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minkowski spacetime. First introducing spin angular momentum per unit mass as a small parameter we consider first-order approximate symmetries of the Kerr metric as a first perturbation of the Schwarzschild m…
The problem of having an accurate description of the spacetime around neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a neutron star. Furthermore, an accurate appropriately parameterised metric, i.e., a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work we p…
We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis to the spacetime of Bardeen model up to third-order approximate Noether gauge symmetries is presented.
In order to solve the Tolman-Oppenheimer-Volkoff equations for neutron stars, one routinely uses the equation of states which are computed in the Minkowski spacetime. Using a first-principle approach, it is shown that the equation of states which are computed within the curved spacetime of the neutron stars include the effect of gravitational time dilation. It arises due to the radially varying interior metric over the length scale of the star and consequently it leads to a much higher mass limit. As an example, for a given set of parameters in a $σ-ω$ model of nuclear matter, the maximum mass…
The phase shift a neutron interferometer caused by the gravitational field and the rotation of the earth is derived in a unified way from the standpoint of general relativity. General relativistic quantum interference effects in the slowly rotating braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-tim…
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is…
The relativistic equations of hydrostatic equilibrium for a spherically symmetric star, or the Tolman-Oppenheimer-Volkoff equations are known in higher dimensions. In this paper, these equations have been expressed in terms of parameters of 4 dimensional spacetime and solved numerically for 4, 5, 6, and 7 dimensions using a standard equation of state for the neutron star matter derived for the 4 dimensional spacetime. It has been shown that with the increase of the dimensionality, the maximum value of the mass of the neutron star decreases and the stars become less compact. Thus, although the …
We describe a set of time evolution equations and its numerical implementation for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full General Relativity, taking into account the contribution of a dynamic spacetime. We derive the perturbation equations for the spacetime in the Hilbert gauge, while the hydrodynamical evolution is based on perturbations of the energy-momentum tensor. In our numerical implementation, we use Kreiss-Oliger dissipation in order to achieve a stable time evolution. Our code features high accuracy at comparably low computation…
We construct a fully analytic, general relativistic, nonspinning black hole binary spacetime that approximately solves the vacuum Einstein equations everywhere in space and time for black holes sufficiently well separated. The metric is constructed by asymptotically matching perturbed Schwarzschild metrics near each black hole to a two-body post-Newtonian metric far from them, and a two-body post-Minkowskian metric farther still. Asymptotic matching is done without linearizing about a particular time slice, and thus it is valid dynamically and for all times, provided the binary is sufficiently…
In recent years, a lot of work was done that has revealed some very interesting properties of neutron stars. One can relate the first few multipole moments of a neutron star, or quantities that can be derived from them, with relations that are independent of the equation of state (EoS). This is a very significant result that has great implications for the description of neutron stars and in particular for the description of the spacetime around them. Additionally, it was recently shown that there is a four parameter analytic spacetime, known as the two-soliton spacetime, which can accurately c…
The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods.
Regarding the strong magnetic field of neutron stars and high energy regime scenario which is based on high curvature region near the compact objects, one is motivated to study magnetic neutron stars in an energy dependent spacetime. In this paper, we show that such strong magnetic field and energy dependency of spacetime have considerable effects on the properties of neutron stars. We examine the variations of maximum mass and related radius, Schwarzschild radius, average density, gravitational redshift, Kretschmann scalar and Buchdahl theorem due to magnetic field and also energy dependency …
We compare three different models of rotating neutron star spacetimes: the Hartle-Thorne (HT) slow-rotation approximation at second order in rotation, the exact analytic vacuum solution of Manko et al. and a numerical solution of the full Einstein equations. We integrate the HT structure equations for five representative equations of state. Then we match the HT models to numerical solutions of the Einstein equations, imposing that the mass and angular momentum of the models be the same. We estimate the limits of validity of the HT expansion computing relative errors in the spacetime's quadrupo…
Neutron stars are regarded as natural laboratories for the study of dense strong interaction matter. The equation of state (EoS) of dense matter computed in flat spacetime is used to predict the structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. Recently, it has been reported that the curved spacetime effect or specifically gravitational time dilation effect on the EoS of dense matter leads to a significant increase of the maximum mass limit of neutron stars [Phys. Rev. D \textbf{104}, 123005 (2021) and J. Cosmol. Astropart. Phys. 02 (2021) 026]. However, in t…
The Neutron Star Interior Composition Explorer (NICER) mission has provided a unique opportunity to constrain the equation of state of neutron stars by using the technique of pulse-profile modelling. This technique requires accurate and efficient ray tracing, that in turn requires a robust representation of the spacetime around a neutron star. Several exact and approximate metrics have been proposed, and used, to perform ray tracing around neutron stars, with both moderate and fast rotation. In this paper, we perform a comparison between several of these metrics, when used for ray tracing. We …
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes that can approximate well the previously mentioned numerical spacetimes. We also present expressions that give the quadrupole and the spin octupole as functions of the spin parameter of a neutron star for various equations of state and in a range of masses for every equation of state used. These results are relevant for describing the exterior spacetime of …
The spacetime around compact objects is an excellent place to study gravity in the strong, nonlinear, dynamical regime where solar system tests cannot account for the effects of large curvature. Understanding the dynamics of this spacetime is important for testing theories of gravity and probing a regime which has not yet been studied with observations. In this paper, we construct an analytical solution for the exterior spacetime of a neutron star in scalar-Gauss-Bonnet gravity that is independent of the equation of state chosen. The aim is to provide a metric that can be used to probe the str…
Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. The gravitational waves generated during such inspirals encode information about the background in which the small object is moving, providing a tracer of the spacetime geometry and a probe of strong-field physics. In this paper, we construct approximate, "analytic-kludge" waveforms for such inspirals with parameterized post-Einsteinian correcti…
Gravitational wave and electromagnetic observations can provide new insights into the nature of matter at supra-nuclear densities inside neutron stars. Improvements in electromagnetic and gravitational wave sensing instruments continue to enhance the accuracy with which they can measure the masses, radii, and tidal deformability of neutron stars. These better measurements place tighter constraints on the equation of state of cold matter above nuclear density. In this article, we discuss a complementary approach to get insights into the structure of neutron stars by providing a model prediction…
As a black hole and neutron star approach during inspiral, the field lines of a magnetized neutron star eventually thread the black hole event horizon and a short-lived electromagnetic circuit is established. The black hole acts as a battery that provides power to the circuit, thereby lighting up the pair just before merger. Although originally suggested as a promising electromagnetic counterpart to gravitational-wave detection, the luminous signals are promising more generally as potentially detectable phenomena, such as short gamma-ray bursts. To aid in the theoretical understanding, we pres…
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.
We compare different gravitational-wave extraction methods used in three-dimensional nonlinear simulations against linear simulations of perturbations of spherical spacetimes with matter. We present results from fully general-relativistic simulations of a system composed by an oscillating and non-rotating star emitting gravitational radiation. Results about the onset of non-linear effects are also shown.
An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and non-dynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that : the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a non-minimal interaction between spinor and el…
In numerically constructing a spacetime that has an approximate timelike Killing vector, it is useful to choose spacetime coordinates adapted to the symmetry, so that the metric and matter variables vary only slowly with time in these coordinates. In particular, this is a crucial issue in numerically calculating a binary black hole inspiral. An approximate homothetic vector plays a role in critical gravitational collapse. We summarize old and new suggestions for finding such coordinates from a general point of view. We then test some of these in various toy models with spherical symmetry, incl…
Using stellar structure calculations in the Hartle-Thorne approximation, we derive analytic expressions connecting the ellipticity of the stellar surface to the compactness, the spin angular momentum, and the quadrupole moment of the spacetime. We also obtain empirical relations between the compactness, the spin angular momentum, and the spacetime quadrupole. Our formulae reproduce the results of numerical calculations to within a few percent and help reduce the number of parameters necessary to model the observational appearance of moderately spinning neutron stars. This is sufficient for com…
We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of weak gravitational fields in a static or expanding background, and the nonrelativistic (Newtonian) limit. The Klein-Gordon-Maxwell-Einstein equations govern the evolution of a complex scalar field, possibly describing self-gravitating Bose-Einstein condensates, coupled to an electromagnetic field. They may find applications in the context of dark matter, bo…
A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space…
A method is presented for computing approximate expressions for the stochastic force term $ξ_{ab}$ which appears in the Einstein-Langevin equation of stochastic gravity. Within this framework, $ξ_{ab}$ is a stochastic tensor field whose probability distribution mimics the probability distribution of the fluctuations of the quantum stress tensor operator; it is defined to be a random tensor field of zero mean whose correlation function is given by the expectation value of the symmetrized two point function of the stress energy fluctuation operator, called the noise kernel. Approximate expressio…
We present tests and results of a new axisymmetric, fully general relativistic code capable of solving the coupled Einstein-matter system for a perfect fluid matter field. Our implementation is based on the Bondi metric, by which the spacetime is foliated with a family of outgoing light cones. We use high-resolution shock-capturing schemes to solve the fluid equations. The code can accurately maintain long-term stability of a spherically symmetric, relativistic, polytropic equilibrium model of a neutron star. In axisymmetry, we demonstrate global energy conservation of a perturbed neutron star…
We compute the red and blue shifts for astrophysical and cosmological sources. In particular, we consider low, intermediate and high gravitational energy domains. Thereby, we handle the binary system Earth - Mars as low energy landscape whereas white dwarfs and neutron stars as higher energy sources. To this end, we take into account a spherical Schwarzschild - de Sitter spacetime and an axially symmetric Zipoy - Voorhees metric to model all the aforementioned systems. Feasible outcomes come from modelling neutron stars and white dwarfs with the Zipoy - Voorhees metric, where quadrupole effect…
We investigate the properties of a closed-form analytic solution recently found by Manko et al. (2000) for the exterior spacetime of rapidly rotating neutron stars. For selected equations of state we numerically solve the full Einstein equations to determine the neutron star spacetime along constant rest mass sequences. The analytic solution is then matched to the numerical solutions by imposing the condition that the quadrupole moment of the numerical and analytic spacetimes be the same. For the analytic solution we consider, such a matching condition can be satisfied only for very rapidly ro…
The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of $10^{15-16}$G. How such a strong magnetic field can originate during the formation of a neutron star is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical c…
Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of charged black hole being a solution of coupled equations of nonlinear electrodynamics and general relativity is constructed and analysed. It is shown that in a few limiting cases, the analytical expressions relating obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordström black hole could be derived. A detailed numerica…
We present analytic solutions of Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat spacetime solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections due to the dragging of reference frames are present, but only i…
Thermal dominated X-ray spectra of neutron stars in quiescent transient X-ray binaries and neutron stars that undergo thermonuclear bursts are sensitive to mass and radius. The mass-radius relation of neutron stars depends on the equation of state that governs their interior. Constraining this relation accurately is thus of fundamental importance to understand the nature of dense matter. In this context we introduce a pipeline to calculate realistic model spectra of rotating neutron stars with hydrogen and helium atmospheres. An arbitrarily fast rotating neutron star with a given equation of s…
The x-ray emission of hot spots on the surface of neutron stars is the prime target of the Neutron star Interior Composition Explorer (NICER). These x-ray pulse profiles not only encode information of the bulk properties of these stars, which teaches us about matter at supranuclear densities, but also about the spacetime curvature around them which teaches us about relativistic gravity. We explore the possibility of performing strong-gravity tests with NICER observations using a recently developed pulse profile model beyond general relativity. Our results suggest that NICER can place constrain…
Recently, spacetimes described by metrics with three parameters (mass, rotation and small quadrupole moment) was found, and in this paper, null geodesics for these metrics are calculated and visualized. Light scattering, as well as the role that the quadrupole moment plays in deforming these kinds of spacetimes are studied. This is a new application of a symbolic--numeric program that we previously used to study the Bonnor metric.
Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features --- a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not --- with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spac…
