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NASA NTRS2021

A Superposed Metric for Spinning Black Hole Binaries Approaching Merger

We construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.

Luciano Combi↗
NASA NTRS1971

Linearization of Schwarzschild's line element - Application to the clock paradox.

This article studies the relativistic theory of the motion of a particle in the presence of a uniform acceleration field. The problem is introduced as a linearization of the fundamental line element of general relativity. The linearized line element is a solution of Einstein's field equations. The equations of geodesics corresponding to this line element are solved and applied to the clock paradox problem.-

Broucke, R.↗
NASA NTRS1971

An electromagnetic Thirring problem.

A neutral rotating mass shell surrounds a concentric stationary electrically charged insulating shell. The dipole-like magnetic field induced by (and proportional to) the rotation of the neutral shell is calculated on the basis of the coupled linearized Einstein-Maxwell field equations of general relativity. This field is apparently at variance with a conjecture made on Machian grounds, for which a possible explanation is suggested. The corresponding induced quadrupolar electric field is calculated for the region within the charged shell, and the potential is given for this field everywhere. Though understandable on mutually inconsistent elementary grounds, we regard this field as a useful example of a solution of linearized general relativity.-

Ehlers, J.↗
NASA NTRS1980

The approximation of radiative effects in relativistic gravity - Gravitational radiation reaction and energy loss in nearly Newtonian systems

An argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems. Several previous calculations are compared in the light of this argument, and some apparent discrepancies among them are resolved. The majority of these calculations support the 'quadrupole formulae' for gravitational radiation energy loss and radiation reaction.

Walker, M.↗
NASA NTRS1985

Gravitational lensing effects of vacuum strings - Exact solutions

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gott, J. R., III↗
NASA NTRS1991

Closed timelike curves produced by pairs of moving cosmic strings - Exact solutions

Exact solutions of Einstein's field equations are presented for the general case of two moving straight cosmic strings that do not intersect. The solutions for parallel cosmic strings moving in opposite directions show closed timelike curves (CTCs) that circle the two strings as they pass, allowing observers to visit their own past. Similar results occur for nonparallel strings, and for masses in (2+1)-dimensional spacetime. For finite string loops the possibility that black-hole formation may prevent the formation of CTCs is discussed.

Gott, J. Richard, III↗
NASA NTRS1982

Spin and gravitation

The fundamental variational principle for a perfect fluid in general relativity is extended so that it applies to the metric-torsion Einstein-Cartan theory. Field equations for a perfect fluid in the Einstein-Cartan theory are deduced. In addition, the equations of motion for a fluid with intrinsic spin in general relativity are deduced from a special relativistic variational principle. The theory is a direct extension of the theory of nonspinning fluids in special relativity.

Ray, J. R.↗
NASA NTRS1989

Conformal scalar field wormholes

The Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field are solved, taking the metric to be of the Robertson-Walker type. In the case Lambda = 0, solutions are found which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda greater than 0, the solutions represent tunneling from a small Tolman-like universe to a large Robertson-Walker universe.

Halliwell, Jonathan J.↗
NASA NTRS1980

Semi-classical Reissner-Nordstrom model for the structure of charged leptons

The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.

Rosen, G.↗
NASA NTRS1982

Axially symmetric gravitational two-body problem of Cooperstock, Lim, and Hobill

Cooperstock, Lim, and Hobill have constructed and analyzed a model spacetime describing the head-on free-fall from rest of two fluid balls under their mutual gravitational attraction. These authors find a gravitational radiation energy flux having a different dependence on the parameters of the problem than would be expected on the basis of the quadrupole formula. It is shown that this dependence is due to their having incorrectly solved Einstein's gravitational field equations. The correct solution is consistent with the quadrupole formula.

Walker, M.↗
NASA NTRS2006

Modeling Gravitational Radiation Waveforms from Black Hole Mergers

Gravitational radiation from merging binary black hole systems is anticipated as a key source for gravitational wave observations. Ground-based instruments, such as the Laser Interferometer Gravitational-wave Observatory (LIGO) may observe mergers of stellar-scale black holes, while the space-based Laser Interferometer Space Antenna (LISA) observatory will be sensitive to mergers of massive galactic-center black holes over a broad range of mass scales. These cataclysmic events may emit an enormous amount of energy in a brief time. Gravitational waves from comparable mass mergers carry away a few percent of the system's mass-energy in just a few wave cycles, with peak gravitational wave luminosities on the order of 10^23 L_Sun. Optimal analysis and interpretation of merger observation data will depend on developing a detailed understanding, based on general relativistic modeling, of the radiation waveforms. We discuss recent progress in modeling radiation from equal mass mergers using numerical simulations of Einstein's gravitational field equations, known as numerical relativity. Our simulations utilize Adaptive Mesh Refinement (AMR) to allow high-resolution near the black holes while simultaneously keeping the outer boundary of the computational domain far from the black holes, and making it possible to read out gravitational radiation waveforms in the weak-field wave zone. We discuss the results from simulations beginning with the black holes orbiting near the system's innermost stable orbit, comparing the recent simulations with earlier "Lazarus" waveform estimates based on an approximate hybrid numerical/perturbative technique.

Baker, J. G.↗
NASA NTRS2004

Neutron Star Structure In The Presence of Scalar Fields

Motivated by the possible presence of scalar fields on astrophysical scales, suggested by the recent measurement of the deceleration parameter by supernovae surveys, we present models of neutron star structure under the assumption that a scalar field makes a significant contribution to the stress energy momentum tensor, in addition to that made by the normal matter. To that end we solve the coupled Einstein - scalar field - hydrostatic balance equations to compute the effect of the presence of the scalar field on the neutron star structure. We find that the presence of the scalar field does change the structure of the neutron star, especially in cases of strong coupling between the scalar field and the matter density. We present the neutron star radius as a function of the matter-scalar field coupling constant for different values of the neutron star central density. The presence of the scalar field does affect both the maximum neutron star mass and its radius, the latter increasing with the value of the above coupling constant. Our results may be testable with the recent timing observations of accreting neutron stars.

Crawford, James P.↗
NASA NTRS2004

Neutron Star Structure in the Presence of Scalar Fields

Motivated by the possible presence of scalar fields on astrophysical scales, suggested by the apparent acceleration of the universe implied by the supernovae surveys, we present models of neutron star structure including the contribution of a (massless) scalar field to the stress energy momentum tensor, in addition to that made by the normal matter. To that end we solve the coupled Einstein -- scalar field -- hydrostatic balance equations to compute the effect of the presence of the scalar field on the neutron star structure. We find that the presence of the scalar field does change the structure of the neutron star, especially in cases of strong coupling between the scalar field and the matter density. We present the neutron star radius as a function of the matter--scalar field coupling constant for different values of the neutron star central density. The presence of the scalar field affects both the maximum neutron star mass and Its radius, the latter increasing with the value of the above coupling constant. We also compute particle and photon geodesics in the geometry of these neutron stars as well as to the geometry of black holes with different values of the scalar field. Our results may be testable with timing observations of accreting neutron stars.

Kazanas, Demosthenes↗