Spacetime Metric Research Articles

Multiparticle Solutions to Einstein's Equations.

In this Letter, we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well. Our construction provides a simple layout for the computation of tree level field theory amplitudes in D spacetime dimensions involving any number of gravitons and matter fields, with or without supersymmetry.

A Lie algebra based approach to asymptotic symmetries in general relativity

Asymptotic symmetries of black hole spacetimes have received much attention as a possible origin of the Bekenstein–Hawking entropy in black hole thermodynamics. In general, it takes hard efforts to find appropriate asymptotic conditions on a metric and a Lie algebra generating the transformation of symmetries with which the corresponding charges are integrable. We here propose an alternative approach to construct building blocks of asymptotic symmetries of a given spacetime metric. Our algorithmic approach may make it easier to explore asymptotic symmetries in any spacetime than in conventional approaches. As an explicit application, we analyze the asymptotic symmetries on Rindler horizon. We find a new class of symmetries related with dilatation transformations in time and in the direction perpendicular to the horizon, which we term superdilatations.

Electric Penrose process: High-energy acceleration of ionized particles by nonrotating weakly charged black hole

In many astrophysical scenarios the charge of the black hole is often neglected due to unrealistically large values of the charge required for the Reissner-Nordstr\"om spacetime metric. However, black holes may possess small electric charge due to various selective accretion mechanisms. In this paper we investigate the effect of a small hypothetical electric charge of a Schwarzschild black hole on the ionization of a freely falling neutral particle and subsequent escape of the ionized particle from the black hole. We show that the energy of ionized particle can grow ultra-high and discuss distinguishing signatures of particle acceleration by weakly charged black holes. We also discuss a possible application of the proposed mechanism as an alternative cosmic ray acceleration scenario. In particular we show that the Galactic centre supermassive black hole is capable to act as a PeVatron of protons. The presented mechanism can serve as a simple toy model of a non-rotating compact object acting as a particle accelerator with a potential astrophysical implementations related to the cosmic ray physics and beyond.

Generalized holographic cosmology: low-redshift observational constraint

Four-dimensional cosmological models are studied on a boundary of a five-dimensional Anti-de Sitter (AdS5) black hole with AdS Reissner-Nordström and scalar charged Reissner-Nordström black hole solutions, where we call the former a “Hairless” black hole and the latter a “Hairy” black hole. To obtain the Friedmann-Robertson-Walker (FRW) spacetime metric on the boundary of the AdS5 black hole, we employ Eddington-Finkelstein (EF) coordinates to the bulk geometry. We then derive modified Friedmann equations on a boundary of the AdS5 black hole via AdS/CFT correspondence and discuss its cosmological implications. The late-time acceleration of the universe is investigated in our models. The contributions coming from the bulk side is treated as dark energy source, and we perform MCMC analyses using observational data. Compared to the ΛCDM model, our models contain additional free parameters; therefore, to make a fair comparison, we use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to analyze our results. Our numerical analyses show that our models can explain the observational data as reliable as the ΛCDM model does for the current data.

On Asymptotic Behavior of Galactic Rotation Curves in Superfluid Vacuum Theory

The logarithmic superfluid theory of physical vacuum predicts that gravity is an induced phenomenon, which has a multiple-scale structure. At astronomical scales, as the distance from a gravitating center increases, gravitational potential and corresponding spacetime metric are dominated by a Newtonian (Schwarzschild) term, followed by a logarithmic term, finally by linear and quadratic (de Sitter) terms. Correspondingly, rotation curves are predicted to be Keplerian in the inner regions of galaxies, mostly flat in the outer regions, and non-flat in the utmost outer regions. We compare theory's predictions with the furthest rotation curves data points available for a number of galaxies: using a two-parameter fit, we perform a preliminary estimate which disregards the combined effect of gas and stellar disc, but is relatively simple and uses minimal assumptions for galactic luminous matter. The data strongly points out at the existence of a crossover transition from flat to non-flat regimes at galactic outskirts.

On exact analytical solution of Einstein–Maxwell-scalar field equations

The exact analytical solution of Einstein–Maxwell-scalar (EMS) field equations has been explored which covers several well-known solutions such as the Reissner–Nordström, Schwarzschild-MOG (Modified Gravity), Janis–Newman–Winicour, and Schwarzschild solutions. It has been assumed that the interactions between the tensor, vector, and scalar fields are negligible. The newly obtained solution is characterized by three free parameters as the total mass M , electric (magnetic) charge Q e ( Q m ), and scalar charge C (or n parameter) of the gravitational compact object. It is also shown that dual solution for the vector potential A ϕ = Q m cos θ is satisfied by the EMS field equations and the electric charge can be safely replaced by magnetic charge Q m . Finally, we have studied curvature invariants and test particle motion around the gravitational source described the obtained new spacetime metric. We have also provided analysis of degeneracy values of spin parameter of the rotating Kerr black hole and charge parameter of compact object described by the new spacetime metric through comparison of radii of ISCO, photonsphere and energy efficiency. It is shown that new black hole solution in Einstein–Maxwell-scalar field theory can mimic spin parameter of the Kerr black hole up to a ∗ ≲ 0 . 6 while the astrophysical black hole’ observations that it reaches up to a ∗ ≲ 0 . 99 . Consequently, one may conclude that the obtained new black hole solution can be considered as realistic candidate for the astrophysical black holes with a ∗ ≲ 0 . 6 .

Bulk reconstruction of metrics inside black holes by complexity

We provide a formula to reconstruct bulk spacetime metrics inside black holes by the time dependence of complexity in the dual quantum field theory, based on the complexity=volume (CV) conjecture in the holographic duality.

Isolating nonlinearities of light propagation in inhomogeneous cosmologies

A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop the BiGONLight Mathematica package, uniquely designed to apply this framework to compute optical observables in Numerical Relativity. Our package can be used for light propagation on a wide range of scales and redshifts and accepts numerical as well as analytical input for the spacetime metric. In this paper we focus on two cosmological observables, the redshift and the angular diameter distance, specializing our analysis to a wall universe modeled within the post-Newtonian approximation. With this choice and the input metric in analytical form, we are able to estimate non-linearities of light propagation by comparing and isolating the contributions coming from Newtonian and post-Newtonian approximations as opposed to linear perturbation theory. We also clarify the role of the dominant post-Newtonian contribution represented by the linear initial seed which, strictly speaking, is absent in the Newtonian treatment. We found that post-Newtonian non-linear corrections are below $1\%$, in agreement with previous results in the literature.

Sensitivity functions of space-borne gravitational wave detectors for arbitrary time-delay interferometry combinations regarding nontensorial polarizations

Direct observation of gravitational waves offers us numerous novel possibilities to further explore the Universe. In practice, the efficiency of the experimental facility for a given gravitational wave source can be measured in terms of the sensitivity function of the instrument. The latter essentially indicates the least incident amplitude required in order to achieve the desired level of the signal-to-noise ratio. Among others, the resultant sensitivity function depends on the specific polarization state of the incident gravitational wave as well as the spatial layout of the detector and its orientation to the wave source. Theoretically, Einstein's general relativity predicts two tensor polarization modes, from a total of six possible modes arising from an arbitrary perturbation of the spacetime metric. Therefore, in this context, the feasibility of measuring nontensorial polarization states provides access to an alternative theory of gravity. In the present study, we analytically evaluate the response functions for arbitrary time-delay interferometry combinations while enumerating all possible polarization modes. The derivation is accomplished by separating the average on the all-sky solid angle from the remaining expression, which, in turn, gives rise to a few factors independent of the time-delay interferometry combination in question. Moreover, we applied the obtained results to the LISA and TianQin missions, and the asymptotic behavior of the resultant sensitivity functions is analyzed and discussed. Among others, it is observed that, for Sagnac combinations, the averaged response function of the breathing mode attains zero at specific discrete frequencies. Such a frequency value corresponds to a multiple of the reciprocal of the one-way light propagation time along the detector arm, irrelevant to the orientation of the wave source. For all six polarization modes, the present findings can be readily applied to an arbitrary time-delay interferometry combination with improved efficiency and accuracy.

A new approach to the evolving 4+1 spacetime metric

We recently proposed [1, 2] field equations that prescribe a metric gαβ (x, τ) that is local in the spacetime coordinates x and evolves with the external “worldtime” τ of the Stueckelberg Horwitz Piron (SHP) framework. As in SHP electrodynamics, these field equations exhibit a formal 5D symmetry (α,β = 0, 1, 2, 3, 5), that is strategically broken to 4+1 representations of the Lorentz group. The resulting canonical formalism for this metric embodies a natural foliation of a 5D pseudo-manifold (encompassing both geometry and dynamics) into the τ-parameterized 4D spacetime posed in SHP theory. In this paper, we consider the linearized equations for weak gravitation in this 4+1 formalism, leading to a more straightforward and intuitive derivation of the coupled first-order evolution equations for the metric.

The neutrino gravitational memory from a core collapse supernova: phenomenology and physics potential

General Relativity predicts that the passage of matter or radiation from an asymmetrically-emitting source should cause a permanent change in the local space-time metric. This phenomenon, called the gravitational memory effect, has never been observed, however supernova neutrinos have long been considered a promising avenue for its detection in the future. With the advent of deci-Hertz gravitational wave interferometers, observing the supernova neutrino memory will be possible, with important implications for multimessenger astronomy and for tests of gravity. In this work, we develop a phenomenological (analytical) toy model for the supernova neutrino memory effect, which is overall consistent with the results of numerical simulations. This description is then generalized to several case studies of interest. We find that, for a galactic supernova, the dimensionless strain, h(t), is of order ∼ 10-22 - 10-21, and develops over a typical time scale that varies between ∼ 0.1 - 10 s, depending on the time-evolution of the anisotropy of the neutrino emission. The characteristic strain, h c(f), has a maximum at a frequency f max ∼ \U0001d4aa(10-1) - \U0001d4aa(1) Hz. The detailed features of the time- and frequency-structure of the memory strain will inform us of the matter dynamics near the collapsed core, and allow to distinguish between different stellar collapse scenarios. Next generation gravitational wave detectors like DECIGO and BBO will be sensitive to the neutrino memory effect for supernovae at typical galactic distances and beyond; with Ultimate DECIGO exceeding a detectability distance of 10 Mpc.

Gravitational field of scalar lumps in higher-derivative gravity

We study the gravitational field sourced by localized scalar fields (lumps) in higher-derivative theories of gravity. By working in a static and spherically symmetric configuration, we find the linearized spacetime metrics generated by scalar lumps for several Lagrangians: the vanishing potential, i.e., free massive scalar field, a polynomial potential, and the tachyon potential in open string field theory. We perform the analysis for different theories of gravity: Einstein's general relativity, four-derivative gravity, and ghost-free nonlocal gravity. We discuss the limit of validity of our analysis and comment on possible future applications in the context of astrophysical compact objects.

Causality theory of spacetimes with continuous Lorentzian metrics revisited

We consider the usual causal structure (I +, J +) on a spacetime, and a number of alternatives based on Minguzzi’s D + and Sorkin and Woolgar’s K +, in the case where the spacetime metric is continuous, but not necessarily smooth. We compare the different causal structures based on three key properties, namely the validity of the push-up lemma, the openness of chronological futures, and the existence of limit causal curves. Recall that if the spacetime metric is smooth, (I +, J +) satisfies all three properties, but that in the continuous case, the push-up lemma fails. Among the proposed alternative causal structures, there is one that satisfies push-up and open futures, and one that has open futures and limit curves. Furthermore, we show that spacetimes with continuous metrics do not, in general, admit a causal structure satisfying all three properties at once.

Geodesic noise and gravitational wave observations by pulsar timing arrays

Signals from millisecond pulsars travel to us on geodesics along the line-of-sight that are affected by the space–time metric. The exact path-geometry and redshifting along the geodesics determine the observed Time-of-Arrival (ToA) of the pulses. The metric is determined by the distribution of dark matter, gas, and stars in the galaxy and, in the final stages of travel, by the distribution of solar system bodies. The inhomogeneous distribution of stellar masses can have a small but significant statistical effect on the ToAs through the perturbation of geodesics. This will result in additional noise in ToA observations that may affect Pulsar Timing Array (PTA) constraints on gravitational waves at very low frequencies. We employ a simple model for the stellar distribution in our galaxy to estimate the scale of both static and dynamic sources of what we term generically “geodesic noise”. We find that geodesic noise has a standard deviation of O(10) ns for typical lines-of-sight. This suggests geodesic noise is relevant for estimates of PTA sensitivity and may limit future efforts for detection of gravitational waves by PTAs.

Stationary spacetimes with time-dependent real scalar fields

In 1981 Wyman classified the solutions of the Einstein–Klein–Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.

Circumbinary Disk Accretion into Spinning Black Hole Binaries

Abstract Supermassive black hole binaries are likely to accrete interstellar gas through a circumbinary disk. Shortly before merger, the inner portions of this circumbinary disk are subject to general relativistic effects. To study this regime, we approximate the spacetime metric of close orbiting black holes by superimposing two boosted Kerr–Schild terms. After demonstrating the quality of this approximation, we carry out very long-term general relativistic magnetohydrodynamic simulations of the circumbinary disk. We consider black holes with spin dimensionless parameters of magnitude 0.9, in one simulation parallel to the orbital angular momentum of the binary, but in another anti-parallel. These are contrasted with spinless simulations. We find that, for a fixed surface mass density in the inner circumbinary disk, aligned spins of this magnitude approximately reduce the mass accretion rate by 14% and counter-aligned spins increase it by 45%, leaving many other disk properties unchanged.

Accretion-induced Black Hole Spin-up Revised by Numerical General Relativistic MHD

Abstract We investigate the accretion-induced spin-up of the black hole via numerical simulations. Our method is based on general relativistic magnetohydrodynamics of the slowly rotating flows in the Kerr metric, where possibly transonic shock fronts may form. We account for the changing black hole mass and spin during accretion that enforces dynamical evolution of the spacetime metric. We first study nonmagnetized flows with shocks, and we also include magnetic field endowed in the gas. The aim of this study is to verify whether the high-mass black holes may be produced with large spins, even though at birth the collapsars might have contained slowly or moderately spinning cores. In this way, we put constraints on the content of angular momentum in the collapsing massive stars. Our studies are also showing that shock fronts and magnetic fields may halt accretion and limit the black hole spin-up in the exploding supernovae.

Classical solutions and their double copy in split signature

The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

The physically realizable anisotropic strange star models

In the present work, we search a new exact solution of Einstein’s field equations using Karmarkar condition of embedded class one space time. The new solution is analyzed graphically as well as analytically to check its viability for compact star modeling. The different parameters of the solution are ascertained by matching the interior space time metric with the Schwarzschild’s exterior space time metric. We tune our solution for the modeling of strange stars EXO1785-248, SAXJ1808.4-3658 and HER X-1 and found their masses and radii as 8.849 km, 1.3 $$M_{\Theta }$$ : 7.951 km, 0.9 $$M_{\Theta }$$ : 8.1 km, 0.85 $$M_{\Theta }$$ , respectively. The physical reliability of the solution depends on the values of the independent parameters b and c. The solution is well behaved for the range of the values $$0.000009\le b\le 0.0039$$ and $$0.0000005\le c\le 0.0000182$$ . Our models satisfy the causality condition and adiabatic index is well behaved everywhere inside the fluid sphere. The compactness parameter is well defined as it does not cross the Buchdahl limit. All the energy conditions hold good inside the compact fluid spheres. The stability of models is assessed via Herrera’s cracking concept. The hydrostatic equilibrium condition is well maintained by our models as gravitational force is counterbalanced by the combined effects of anisotropic force and hydrostatic force. The proper graphical analysis is provided to authenticate the physically admissible character of proposed models.

ФИЗИЧЕСКИЕ СВОЙСТВА ТОНКОГО АККРЕЦИОННОГО ДИСКА ЧЕРНОЙ ДЫРЫ ТАУБ-НУТ

The Taub-NUT space-time metric is one of the vacuum solutions to Einstein's gravitational field equations. In this metric, the Newman-Unti-Tamburino parameter (NUT) and its effect on the physical properties of a thin accretion disk are of particular interest. In this paper, calculations are performed to determine the physical properties of a thin accretion disk around the Taub-NUT black hole based on the Page-Thorne model. The influence of the NUT parameter on the angular velocity, binding energy, angular momentum of particles, effective potential, energy flow, and temperature of the accretion disk is revealed. According to the data obtained, the temperature of the accretion disk of the Taub-NUT black hole decreases as the value of the NUT parameter increases.