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DOE OSTI2019

First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42 ± 3 μas, which is circular and encompasses a central depression in brightness with a flux ratio gsim10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5 ± 0.7) × 109 M⊙. Our radio-wave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Hydrostatic equilibrium and stellar structure in f(R) gravity

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lane-Emden equation coming out from f(R) gravity. Such an equation is obtained in a metric approach by considering the Newtonian limit of f(R) gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index n. The modified equation results an integro-differential equation, which, in the limit f(R){yields}R, becomes the standard Lane-Emden equation. We find the radial profiles of the gravitational potential by solving for some values of n. The comparison of solutions with those coming from general relativity shows that they are compatible and physically relevant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Cosmic black-hole hair growth and quasar OJ287

An old result (astro-ph/9905303) by Jacobson implies that a black hole with Schwarzschild radius r{sub s} acquires scalar hair, Q∝r{sub s}{sup 2}μ, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, ∂{sub t}φ ≅ μM{sub p} with μr{sub s} << 1 time-independent. Such a time dependence could arise in scalar-tensor theories either from cosmological evolution, or due to the slow motion of the black hole within an asymptotic spatial gradient in the scalar field. Most remarkably, the amount of scalar hair so induced is independent of the strength with which the scalar couples to matter. We argue that Jacobson's Miracle Hair-Growth Formula{sup ©} implies, in particular, that an orbiting pair of black holes can radiate dipole radiation, provided only that the two black holes have different masses. Quasar OJ287, situated at redshift z ≅ 0.306, has been argued to be a double black-hole binary system of this type, whose orbital decay recently has been indirectly measured and found to agree with the predictions of General Relativity to within 6%. We argue that the absence of observable scalar dipole radiation in this system yields the remarkable bound |μ| < (16 days){sup −1} on the instantaneous time derivative at this redshift (as opposed to constraining an average field difference, Δφ, over cosmological times), provided only that the scalar is light enough to be radiated — i.e. m∼<10{sup −23} eV — independent of how the scalar couples to matter. This can also be interpreted as constraining (in a more model-dependent way) the binary's motion relative to any spatial variation of the scalar field within its immediate vicinity within its host galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Virialisation-induced curvature as a physical explanation for dark energy

The geometry of the dark energy and cold dark matter dominated cosmological model (ΛCDM) is commonly assumed to be given by a Friedmann-Lemaître-Robertson-Walker (FLRW) metric, i.e. it assumes homogeneity in the comoving spatial section. The homogeneity assumption fails most strongly at (i) small distance scales and (ii) recent epochs, implying that the FLRW approximation is most likely to fail at these scales. We use the virialisation fraction to quantify (i) and (ii), which approximately coincide with each other on the observational past light cone. For increasing time, the virialisation fraction increases above 10% at about the same redshift ( ∼ 1–3) at which Ω{sub Λ} grows above 10% ( ≈ 1.8). Thus, instead of non-zero Ω{sub Λ}, we propose an approximate, general-relativistic correction to the matter-dominated (Ω{sub m}; = 1,Ω{sub Λ} = 0), homogeneous metric (Einstein-de Sitter, EdS). A low-redshift effective matter-density parameter of Ω{sub m}{sup eff}(0) = 0.26±0.05 is inferred. Over redshifts 0 < z < 3, the distance modulus of the virialisation-corrected EdS model approximately matches the ΛCDM distance modulus. This rough approximation assumes ''old physics'' (general relativity), not ''new physics''. Thus, pending more detailed calculations, we strengthen the claim that ''dark energy'' should be considered as an artefact of emerging average curvature in the void-dominated Universe, via a novel approach that quantifies the relation between virialisation and average curvature evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Infrared limit of Horava's gravity with the global Hamiltonian constraint

We show that Horava's theory of gravitation with the global Hamiltonian constraint does not reproduce general relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with the massless graviton, which does not decouple.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Post-Newtonian limit of f(R) gravity in the harmonic gauge

A general analytic procedure is developed for the post-Newtonian limit of f(R) gravity with the metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method, a general scheme of solutions up to (v/c){sup 4} order is shown. Considering the Taylor expansion of a generic function f, it is possible to parametrize the solutions by derivatives of f. At Newtonian order, (v/c){sup 2}, the most important topics about the Gauss and Birkhoff theorems are discussed. The corrections to the 'standard' gravitational potential (tt component of the metric tensor) generated by an extended uniform mass ball-like source are calculated up to (v/c){sup 4} order. The corrections, Yukawa and oscillating-like, are found inside and outside the mass distribution. At last, when the limit f{yields}R is considered, the f(R) gravity converges in general relativity at the level of the Lagrangian, field equations, and their solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Collinear solution to the general relativistic three-body problem

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence, it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L{sub 1}, L{sub 2}, and L{sub 3} are also evaluated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method

The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we first use the Hamilton-Jacobi method to derive the deformed equations of motion in the context of Newtonian mechanics and general relativity. We then employ them to study the precession of planetary orbits, deflection of light, and time delay in radar propagation. We also set limits on the deformation parameter by comparing our results with the observational measurements. Finally, comparison with results from previous papers is given at the end of this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

IMAGING AN EVENT HORIZON: MITIGATION OF SOURCE VARIABILITY OF SAGITTARIUS A*

The black hole in the center of the Galaxy, associated with the compact source Sagittarius A* (Sgr A*), is predicted to cast a shadow upon the emission of the surrounding plasma flow, which encodes the influence of general relativity (GR) in the strong-field regime. The Event Horizon Telescope (EHT) is a Very Long Baseline Interferometry (VLBI) network with a goal of imaging nearby supermassive black holes (in particular Sgr A* and M87) with angular resolution sufficient to observe strong gravity effects near the event horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that radio emission from Sgr A* exhibits variability on timescales of minutes, much shorter than the duration of a typical VLBI imaging experiment, which usually takes several hours. A changing source structure during the observations, however, violates one of the basic assumptions needed for aperture synthesis in radio interferometry imaging to work. By simulating realistic EHT observations of a model movie of Sgr A*, we demonstrate that an image of the average quiescent emission, featuring the characteristic black hole shadow and photon ring predicted by GR, can nonetheless be obtained by observing over multiple days and subsequent processing of the visibilities (scaling, averaging, and smoothing) before imaging. Moreover, it is shown that this procedure can be combined with an existing method to mitigate the effects of interstellar scattering. Taken together, these techniques allow the black hole shadow in the Galactic center to be recovered on the reconstructed image.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Central Magnetic Field of a Magnetic White Dwarf Star

Observations of over-luminous Type 1a supernovae have prompted researchers to come up with various hypotheses in order to explain them. One hypothesis is based on the explosion of a progenitor super-massive magnetic white dwarf star. These stars are assumed to have very strong magnetic fields inside of them. However, there is a lack of analytic proof of the existence of such magnetic fields in the magnetic white dwarf stars. In this work, we plan to address an analytic proof of the existence of very strong magnetic fields in the center of these magnetic white dwarfs. We will see that for a one Landau-level white dwarf star, with central density 10{sup 9}--10{sup 11} g cm{sup −3}, it is possible to have central magnetic fields of the order of 10{sup 13}--10{sup 15}G at least. In the presence of strong magnetic fields, the threshold densities chosen for this work that correspond to instabilities due to general relativity and pycnonuclear reactions have been found to increase so that the matter does not acquire instability at such central densities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Interactions in Theories with Mixed Symmetry Tensor Fields: Yes-Go Results

Some recent yes-go results concerning consistent couplings involving mixed symmetry tensor fields are reported. Only particular classes of mixed symmetry tensor fields, which are dual to linearized gravity in various dimensions, are considered. The method used to generate consistent couplings is based on the deformation of the solution to the master equation combined with specific techniques of local Becchi-Rouet-Stora-Tyutin cohomology. In each case the deformations are constructed under the general hypotheses of analyticity in the coupling constant, space-time locality, Lorentz covariance, Poincare invariance, preservation of the differential order of the interacting field equations with respect to their free limit. The emerging results indicate that dual formulations of linearized gravity are far from being rigid under the introduction of consistent couplings, so there is still hope for providing an alternative, finite setting for General Relativity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

On separate universes

The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity f{sup loc}{sub NL}, and hence does not contribute to a scale-dependent galaxy bias Δ b ∝ k{sup −2} on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent f{sup loc}{sub NL}-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of f{sup loc}{sub NL} beyond these projection effects signals a departure from standard single-clock inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cosmological singularities and bounce in Cartan-Einstein theory

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh ( in-in ) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins in a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce . We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

MAGNETARS AS HIGHLY MAGNETIZED QUARK STARS: AN ANALYTICAL TREATMENT

We present an analytical model of a magnetar as a high-density magnetized quark bag. The effect of strong magnetic fields (B > 5 x 10{sup 16} G) in the equation of state is considered. An analytic expression for the mass-radius relationship is found from the energy variational principle in general relativity. Our results are compared with observational evidence of possible quark and/or hybrid stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Observed galaxy number counts on the lightcone up to second order: II. Derivation

We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a general gauge, and applies to all dark energy models (including interacting dark energy) and to metric theories of modified gravity. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Astrophysical tests of modified gravity: the morphology and kinematics of dwarf galaxies

This paper is the third in a series on tests of gravity using observations of stars and nearby dwarf galaxies. We carry out four distinct tests using published data on the kinematics and morphology of dwarf galaxies, motivated by the theoretical work of Hui et al. (2009) and Jain and Vanderplas (2011). In a wide class of gravity theories a scalar field couples to matter and provides an attractive fifth force. Due to their different self-gravity, stars and gas may respond differently to the scalar force leading to several observable deviations from standard gravity. HI gas, red giant stars and main sequence stars can be displaced relative to each other, and the stellar disk can display warps or asymmetric rotation curves aligned with external potential gradients. To distinguish the effects of modified gravity from standard astrophysical phenomena, we use a control sample of galaxies that are expected to be screened from the fifth force. In all cases we find no significant deviation from the null hypothesis of general relativity. The limits obtained from dwarf galaxies are not yet competitive with the limits from cepheids obtained in our first paper, but can be improved to probe regions of parameter space that are inaccessible using other tests. We discuss how our methodology can be applied to new radio and optical observations of nearby galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The Poisson equation at second order in relativistic cosmology

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

A brief study of quasi-normal modes in relativistic stars using algebraic computation

The damped oscillations in relativistic stars generate gravitational waves that in the literature appear under the general denomination of quasi-normal modes. In this brief note we want offer some information about the use of algebraic computation to obtain the field equations and the perturbed version of them, in the context of general relativity theory, that is the framework to study gravitational waves in this work.

79 ASTRONOMY AND ASTROPHYSICS↗