We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver developed for this purpose. We then apply the standard tools of numerical relativity to calculate the time development of this initial dataset and derive quantities of cosmological relevance, such as the scaling of proper lengths. Similarly to the case of S3 lattices, we find that the length scaling remains close to the analytical solution for Friedmann-Lemaitre-Robertson-Walker cosmologies throughout our simulations, which span a window of about one order of magnitude in the growth of the scale factor. We highlight, however, a number of important departures from the Friedmann-Lemaitre-Robertson-Walker class.
A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorenzian isometries of our new de Sitter relativity [I. I. Cot\u aescu, {Eur. Phys. J. C} {\bf 77} (2017) 485]. This formula combines in a non-trivial manner the well-known cosmological contribution given by Lama\' itre's law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagati…
It has been demonstrated that a modern stage of the Universe expansion may be described in accordance with the observations within the scope of the space-time conformal geometry. The clock synchronization procedure in SR has been generalized to the case of the expanding space. It has been found that a universal local manifestation of the cosmological expansion is a background acceleration, the value of which is determined by Hubble constant. The formulae defining an explicit red-shift dependence of the cosmological distance and expressions for Hubble law have been obtained in a pure kinematic …
The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabes-Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition R_{AB}g^{AB} = 0, (A, B = z, phi), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the col…
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster. Mach principle is that the matter of the whole universe can affect local dynamic systems. That is, the matter of the whole universe sets up the local absolute reference frames. However, Einstein's general theory of relativity is against the absolute reference frames of Mach Principle.
We conduct a preliminary investigation into the phenomenological implications of Einsteinian cubic gravity (ECG), a 4-dimensional theory of gravity cubic in curvature of interest for its unique formulation and properties. We find an analytic approximation for a spherically symmetric black hole solution to this theory using a continued fraction ansatz. This approximate solution is valid everywhere outside of the horizon and we use it to study the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. We compute constraints on the ECG coupling…
Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Plebański--Demiański (PD)---to demonstrate these analogies for a physically meaningful spacetime: The two quadratic curvature invariants $\bf{B}^2-\bf{E}^2$ and $\bf{E}\cdot\bf{B}$ are evaluated analytically. In the asymptotically flat case, the leading terms of $\bf{E}$ and $\bf{B}$ can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic mono…
The multiple detections of gravitational waves by LIGO (the Laser Interferometer Gravitational-Wave Observatory), operated by Caltech and MIT, have been acclaimed as confirming Einstein's prediction, a century ago, that gravitational waves propagating as ripples in spacetime would be detected. Yunes and Pretorius (2009) investigate whether LIGO's template-based searches encode fundamental assumptions, especially the assumption that the background theory of general relativity is an accurate description of the phenomena detected in the search. They construct the parametrized post-Einsteinian (pp…
In \cite{Bahamonde:2019zea}, a spherically symmetric black hole (BH) was derived from the quadratic form of $f(T)$. Here we derive the associated energy, invariants of curvature, and torsion of this BH and demonstrate that the higher-order contribution of torsion renders the singularity weaker compared with the Schwarzschild BH of general relativity (GR). Moreover, we calculate the thermodynamic quantities and reveal the effect of the higher--order contribution on these quantities. Therefore, we derive a new spherically symmetric BH from the cubic form of $f(T)=T+ε\Big[\frac{1}{2}αT^2+\frac{1}…
We test the validity of Isaacson's formula which states that high frequency and low amplitude gravitational waves behave as a radiation fluid on average. For this purpose, we numerically construct a solution of the vacuum Einstein equations which contains nonlinear standing gravitational waves. The solution is constructed in a cubic box with periodic boundary conditions. The time evolution is solved in a gauge in which the trace of the extrinsic curvature $K$ of the time slice becomes spatially uniform. Then, the Hubble expansion rate $H$ is defined by $H=-K/3$ and compared with the effective …
Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $ω=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small parameter. The exterior space-time of one family of solutions is arbitrarily close to the exterior Schwarzschild space-time. These nontopological solitons have some similarity with soliton stars, and are proposed as candidates for {\em approximate black holes} for the use in numerical relativity, in particular for treatment of horizon boundary conditions.
Null and timelike equatorial orbits are investigated in a family of hairy black holes in the cubic Galileon theory. These include rotating generalizations of static black hole metrics supporting a time-dependent scalar field. Depending on the coupling and rotation, the properties of the geodesics expectedly deviate from general relativity. In particular, it is found that stable circular geodesics only exist below a critical coupling, which is related to the existence of an outermost stable circular orbit. Focusing on the strong-field region, images of an accretion disk are also produced to hig…
The Sultana-Dyer solution of general relativity representing a black hole embedded in a special cosmological background is analysed. We find an expanding (weak) spacetime singularity instead of the reported conformal Killing horizon, which is covered by an expanding black hole apparent horizon (internal to a cosmological apparent horizon) for most of the history of the universe. This singularity was naked early on. The global structure of the solution is studied as well.
We investigate the predictions of Einsteinian Cubic Gravity (ECG) for the lensing effects due to supermassive black holes at the center of Milky Way and other galaxies. Working in the context of spherical symmetry, we obtain the metric function from a continued fraction method and find that both time delays and the angular positions of images considerably deviate from general relativity, as large as milliarcseconds. This suggests that observational tests of ECG are indeed feasible.
We present an up to cubic curvature correction to General Relativity with the following features: (i) its vacuum spectrum solely consists of a graviton and is ghost-free, (ii) it possesses well-behaved black hole solutions which coincide with those of Einsteinian cubic gravity, (iii) its cosmology is well-posed as an initial value problem and, most importantly, (iv) it entails a geometric mechanism triggering an inflationary period in the early universe (driven by radiation) with a graceful exit to a late-time cosmology arbitrarily close to $Λ$CDM.
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive asymptotic direction and that quadratic diagonal Bianchi IX models do not recollapse and may be regular initially. Although the global existence and isotropization results we prove hold quite generally, they are applied to specific Bianchi models in an attempt to describe how certain dynamical properties uncommon to the general relativity case, become generic fea…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble …
We consider the dynamics of tensor and scalar gravitational fields in the Relativistic Theory of Gravitation with the Minkowskian vacuum metric and generalize the formulation to the massless graviton. The potential of scalar field is determined in the presence of cosmological term under clear physical motivations. We find cosmological inflationary solutions and analyze conditions providing the transition to the regime of hot expanding universe.
We study black hole binary mergers in certain cubic Horndeski theories of gravity, treating them fully non-linearly. In the regime of validity of effective field theory, the mismatch of the gravitational wave strain between Horndeski and general relativity (coupled to a scalar field) can be as large as $10-13\%$ in the Advanced LIGO mass range. The initial data and coupling constants are chosen such the theory remains in the weakly coupled regime throughout the evolution. In all cases that we have explored, we observe that the waveform in the Horndeski theory is shifted by an amount much large…
We present an alternate formula for calculating gravitational time delay. We use this formula to reduce geodetic Very Long Baseline Interferometry (VLBI) data, taking into account gravitational effects within the solar system, and to test general relativity. The alternate formula was obtained by expanding the conventional formula in a Taylor series. We show that the gravitational delay can be split into several terms including a term due to the coordinate transformation and terms that are explicitly linked to the light deflection angle. Our formula is compared numerically with the conventional…
Observations of neutron star mergers in the late Universe have given significant restrictions to the class of viable scalar-tensor theories. In this paper we construct black holes within the "self-tuning" class of this restricted set, whereby the bare cosmological constant is absorbed by the dynamics of the scalar, giving a lower effective cosmological constant. We use analytic expansions at the singularity, black hole and cosmological horizon, and asymptotic region, coupled with numerical solutions, to find well-behaved black holes that asymptote to the self-tuned de Sitter geometry. The geom…
Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a fully covariant formulation in the language of Newton-Cartan geometry but we revisit it here in a 3+1 formulation. The appropriate 3+1 formulation of General Relativity is one first described by Kol and Smolkin (KS), rather than the better known Arnowitt-Deser-Misner (ADM) formalism. As we review, the KS formulation is dual to the ADM formulation in that the ro…
We study the black-box parameter estimation of expanding parameters and the dynamics of Gaussian interferometric power for the de Sitter space. We find that the state between separated open charts can be employed as probe state for the black-box quantum metrology. This is nontrivial because the open charts are causally disconnected and classical information can not be exchanged between them according to the general relativity. It is shown that the mass of the scalar field remarkably affects the accuracy of the black-box parameter estimation in the de Sitter space, which is quite different from…
We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to General Relativity, and discuss multiple ways in which it can be useful for studying gravity, both classical and quantum. In particular, we show that the dynamics of the model when all matrices are close to the identity corresponds exactly to a finite-difference discretization of weak-field gravity in harmonic gauge. We also show that the action which defines the …
We find an exact solution of Scalar-Tensor-Vector Gravity field equations that represents a black hole embedded in an expanding universe. This is the first solution of the kind found in the theory. We analyze the properties of the apparent horizons as well as the essential singularities of the metric, and compare it with the McVittie spacetime of General Relativity. Depending on the cosmological model adopted and the value of the free parameter $α$ of the theory, the solution describes a cosmological black hole, an inhomogeneity in an expanding universe, or a naked singularity. We use the latt…
Neutron stars with strong magnetic fields are considered in the framework of f(R) gravity. In order to describe dense matter in magnetic field, the model with baryon octet interacting through $σ$$ρ$$ω$-fields is used. The hyperonization process results in softening the equation of state (EoS) and in decreasing the maximal mass. We investigate the effect of strong magnetic field in models involving quadratic and cubic corrections in the Ricci scalar $R$ to the Hilbert-Einstein action. For large fields, the Mass-Radius relation differs considerably from that of General Relativity only for stars …
In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in General Relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein's theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly …
Detecting gravitational waves from coalescing compact binaries allows us to explore the dynamical, nonlinear regime of general relativity and constrain modifications to it. Some of the gravitational-wave events observed by the LIGO-Virgo Collaboration have sufficiently high signal-to-noise ratio in the merger, allowing us to probe the relaxation of the remnant black hole to its final, stationary state - the so-called black-hole ringdown, which is characterized by a set of quasinormal modes. Can we use the ringdown to constrain deviations from general relativity, as predicted by several of its …
Quasinormal modes and their excitation beyond general relativity. II: isospectrality loss in gravitational waveforms
The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；ETH Zürich（苏黎世联邦理工学院）；Universidad de Murcia（穆尔西亚大学）；University of Tübingen（蒂宾根大学）；University of Virginia（弗吉尼亚大学）
A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. Such models have been previously found as solutions of general relativity with a phantom scalar field as a source of gravity and, without phantoms, in a brane world of RS2 type. Here we construct examples of static, spherically symmetric black-universe solutions in general relativity with a minimally coupled scalar field ϕwhose kinetic energy is negative in a restricted strong-field region of space-time and positive outside it. Thus in such configurations a "ghost" …
Black holes are the simplest objects in the universe. They correspond to extreme deformations of spacetime geometry, and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theo…
