Degenerate gravitational fields with twisting rays.
Einstein equations for empty space applied to degenerate gravitational fields with twisting rays, admitting shear-free twisting congruence of null geodesics
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Einstein equations for empty space applied to degenerate gravitational fields with twisting rays, admitting shear-free twisting congruence of null geodesics
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.
Gravitational waves in presence of electromagnetic field, deriving Einstein-Maxwell equations
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.
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.
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.
Expanding solutions of Einstein-Maxwell equations in D class spaces admitting null and nonnull electromagnetic field
WKB approximation HF gravitational wave solutions to general relativity vacuum Einstein equations with strong gravitational fields, discussing light waves analogy
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.
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.
Black holes have been predicted since the 1940's from solutions of Einstein's general relativity field equation. There is strong evidence of their existence from astronomical observations, but their origin has remained an open question of great interest. Gamma-ray bursts may the clue. They are powerful explosions, visible to high redshift, and appear to be the birth cries of black holes. The Swift and Fermi missions are two powerful NASA observatories currently in orbit that are discovering how gamma-ray bursts work. Evidence is building that the long and short duration subcategories of GRBs have very different origins: massive star core collapse to a black hole for long bursts and binary neutron star coalescence to a black hole for short bursts. The similarity to Type II and Ia supernovae originating from young and old stellar progenitors is striking. Bursts are tremendously luminous and are providing a new tool to study the high redshift universe. One Swift burst at z=8.3 is the most distant object known in the universe. The talk will present the latest gamma-ray burst results from Swift and Fermi and will highlight what they are teaching us about black holes and jet outflows.
Here we study central vortex steady states and dynamics of a two-dimensional (2D), two-component, Gross–Pitaevskii equation (CGPE) system for two pseudo-spinor Bose Einstein condensates (BECs) interacting with an electromagnetic field (microwave) analytically and numerically. For the central vortex steady state at any given winding number S, we prove its existence in a reduced, single component detuning limit when contact-interaction strength β < β b , and nonexistence when β > β b , respectively, where β b is a threshold value, whose value is given in Theorem 3.1 in the paper. We extend the existence and nonexistence result to the general two pseudo-spinor case and prove that a central vortex steady state exists for any given S if β ≤ β b while it does not exist when β > 2β b . We then derive dynamical equations for some observables (expectations of the matter wave function) such as the center-of-mass, position of dispersion, the linear and angular momentum of the two pseudo-spinor CGPEs. Finally, numerical computations are brought in to validate and extend the existence of vortex steady state results to β b ≤ β < 2β b for the two pseudo-spinor case and to explore transient dynamics of the observables.
Type 3 spaces solutions of Maxwell-Einstein equations, examining singular and nonsingular electromagnetic field problems
The final merger of two black holes releases a tremendous amount of energy, more than the combined light from all the stars in the visible universe. This energy is emitted in the form of gravitational waves, and observing these sources with gravitational wave detectors such as LISA requires that we know the pattern or fingerprint of the radiation emitted. Since black hole mergers take place in regions of extreme gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these wave patterns. For more than 30 years, scientists have tried to compute these wave patterns. However, their computer codes have been plagued by problems that caused them to crash. This situation has changed dramatically in the past 2 years, with a series of amazing breakthroughs. This talk will take you on this quest for these gravitational wave patterns, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by LISA
The final merger of two black holes releases a tremendous amount of energy, more than the combined light from all the stars in the visible universe. This energy is emitted in the form of gravitational waves, and observing these sources with gravitational wave detectors such as LISA requires that we know the pattern or fingerprint of the radiation emitted. Since black hole mergers take place in regions of extreme gravitational fields, we need to solve Einstein s equations of general relativity on a computer in order to calculate these wave patterns. For more than 30 years, scientists have tried to compute these wave patterns. However, their computer codes have been plagued by problems that caused them to crash. . This situation has changed dramatically in the past 2 years, with a series of amazing breakthroughs. This talk will take you on this quest for these gravitational wave patterns, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will. be observed by LISA.
The final merger of two black holes releases a tremendous amount of energy and is one of the brightest sources in the gravitational wave sky. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. Since these mergers take place in regions of very strong gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these waveforms. For more than 30 years, scientists have tried to compute these waveforms using the methods of numerical relativity. The resulting computer codes have been plagued by instabilities, causing them to crash well before the black holes in the binary could complete even a single orbit. Recently this situation has changed dramatically, with a series of amazing breakthroughs. This talk will take you on this quest for the holy grail of numerical relativity, showing how a spacetime is constructed on a computer to build a simutation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by LIGO and LISA.
The final merger of two black holes releases a tremendous amount of energy, more than the combined light from all the stars in the visible universe. This energy is emitted in the form of gravitational waves, and observing these sources with gravitational wave detectors such as LIGO and LISA requires that we know the pattern or fingerprint of the radiation emitted. Since black hole mergers take place in regions of extreme gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these wave patterns. For more than 30 years, scientists have tried to compute these wave patterns. However, their computer codes have been plagued by problems that caused them to crash. This situation has changed dramatically in the past 2 years, with a series of amazing breakthroughs. This discussion examines these gravitational patterns, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. The focus is on recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by the space-based gravitational wave detector LISA.
The final merger of two black holes releases a tremendous amount of energy, more than the combined light from all the stars in the visible universe. This energy is emitted in the form of gravitational waves, and observing these sources with gravitational wave detectors such as LIGO and LISA requires that we know the pattern or fingerprint of the radiation emitted. Since black hole mergers take place in regions of extreme gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these wave patterns.