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At least 289 records · Page 16

Equal path, phase shifting, sample point interferometer for monitoring the configuration of surfaces

A system for monitoring the configuration of a surface (e.g., a segmented parabolic surface) using orthogonally placed retroreflectors at sets of points 1, 2, and 3 dispersed throughout the surface with a stationary halfwave plate (HWP) in the front of the one retroreflector at a corner point 3 and a rotating halfwave plate (RHWP) over a source of linearly polarized coherent light, thereby causing the direction of linear polarization to continuously rotate through 360 deg and causing light returned by the retroreflector at point 3 to be continuously phase shifted through 360 deg relative to light returned by retroreflectors at points 1 and 2. The returned light from each set of points 1, 2, and 3 is focused onto a bed-of-nails (BON) phase grating diagonally oriented with respect to the orthogonal orientation of the incident beams from retroreflectors 1, 2, and 3, thereby causing overlap in the light from points 1 and 3 to produce interferometric signals 1,3 and 2,3. Any change in phase of the interferometric signals 1,3 and 2,3 indicates both the magnitude and direction of any change in the position of the retroreflector at point 3 relative to retroreflectors at points 1 and 2.

Manhart, Paul K.↗

A magnetic isolation and pointing system for the astrometric telescope facility

The astrometric telescope facility (ATF), a 20-meter telescope designed for long-term detection and observation of planetary systems outside of the solar system, is scheduled to be a major user of the Space Station's payload pointing system (PPS) capabilities. However, because the ATF has such a stringent pointing stability specification (as low as 0.01 arcsec error over the frequency range from 5 to 200 hertz) and requires +/- 180-degree roll rotation around the telescope's line of sight, the ATF's utilization of the PPS requires the addition of a mechanism or mechanisms to enhance the basic PPS capabilities. The results of a study conducted to investigate the ATF pointing performance achievable by the addition of a magnetic isolation and pointing (MIPS) system between the PPS upper gimbal and the ATF, and separately, by the addition of a passive isolation system between the Space Station and the PPS base are presented. In addition, the study produced requirements on magnetic force and gap motion as a function of the level of Space Station disturbance. These results were used to support the definition of a candidate MIPS. Pointing performance results from the study indicate that a MIPS can meet the ATF pointing requirements in the presence of a PPS base transitional acceleration of up to 0.018g, with reasonable restrictions placed on the isolation and pointing bandwidths. By contrast, the passive base isolator system must have an unrealistically low isolation bandwidth on all axes (less than 0.1 hertz) to meet ATF pointing requirements. The candidate MIPS is based on an assumed base translational disturbance of 0.01g. The system fits within the available annular region between the PPS and ATF while meeting power and weight limitations and providing the required payload roll motion. Payload data and power services are provided by noncontacting transfer devices.

Smith, Marcie↗

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report.

Hinshaw, Gary↗

Inertial Pointing and Positioning System

An inertial pointing and control system and method for pointing to a designated target with known coordinates from a platform to provide accurate position, steering, and command information. The system continuously receives GPS signals and corrects Inertial Navigation System (INS) dead reckoning or drift errors. An INS is mounted directly on a pointing instrument rather than in a remote location on the platform for-monitoring the terrestrial position and instrument attitude. and for pointing the instrument at designated celestial targets or ground based landmarks. As a result. the pointing instrument and die INS move independently in inertial space from the platform since the INS is decoupled from the platform. Another important characteristic of the present system is that selected INS measurements are combined with predefined coordinate transformation equations and control logic algorithms under computer control in order to generate inertial pointing commands to the pointing instrument. More specifically. the computer calculates the desired instrument angles (Phi, Theta. Psi). which are then compared to the Euler angles measured by the instrument- mounted INS. and forms the pointing command error angles as a result of the compared difference.

Yee, Robert↗

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell↗

Geolocation and Pointing Accuracy Analysis for the WindSat Sensor

Geolocation and pointing accuracy analyses of the WindSat flight data are presented. The two topics were intertwined in the flight data analysis and will be addressed together. WindSat has no unusual geolocation requirements relative to other sensors, but its beam pointing knowledge accuracy is especially critical to support accurate polarimetric radiometry. Pointing accuracy was improved and verified using geolocation analysis in conjunction with scan bias analysis. nvo methods were needed to properly identify and differentiate between data time tagging and pointing knowledge errors. Matchups comparing coastlines indicated in imagery data with their known geographic locations were used to identify geolocation errors. These coastline matchups showed possible pointing errors with ambiguities as to the true source of the errors. Scan bias analysis of U, the third Stokes parameter, and of vertical and horizontal polarizations provided measurement of pointing offsets resolving ambiguities in the coastline matchup analysis. Several geolocation and pointing bias sources were incfementally eliminated resulting in pointing knowledge and geolocation accuracy that met all design requirements.

Meissner, Thomas↗

Software for Verifying Image-Correlation Tie Points

A computer program enables assessment of the quality of tie points in the image-correlation processes of the software described in the immediately preceding article. Tie points are computed in mappings between corresponding pixels in the left and right images of a stereoscopic pair. The mappings are sometimes not perfect because image data can be noisy and parallax can cause some points to appear in one image but not the other. The present computer program relies on the availability of a left- right correlation map in addition to the usual right left correlation map. The additional map must be generated, which doubles the processing time. Such increased time can now be afforded in the data-processing pipeline, since the time for map generation is now reduced from about 60 to 3 minutes by the parallelization discussed in the previous article. Parallel cluster processing time, therefore, enabled this better science result. The first mapping is typically from a point (denoted by coordinates x,y) in the left image to a point (x',y') in the right image. The second mapping is from (x',y') in the right image to some point (x",y") in the left image. If (x,y) and(x",y") are identical, then the mapping is considered perfect. The perfect-match criterion can be relaxed by introducing an error window that admits of round-off error and a small amount of noise. The mapping procedure can be repeated until all points in each image not connected to points in the other image are eliminated, so that what remains are verified correlation data.

Klimeck, Gerhard↗

Verification of the Solar Dynamics Observatory High Gain Antenna Pointing Algorithm Using Flight Data

The Solar Dynamics Observatory (SDO) is a NASA spacecraft designed to study the Sun. It was launched on February 11, 2010 into a geosynchronous orbit, and uses a suite of attitude sensors and actuators to finely point the spacecraft at the Sun. SDO has three science instruments: the Atmospheric Imaging Assembly (AIA), the Helioseismic and Magnetic Imager (HMI), and the Extreme Ultraviolet Variability Experiment (EVE). SDO uses two High Gain Antennas (HGAs) to send science data to a dedicated ground station in White Sands, New Mexico. In order to meet the science data capture budget, the HGAs must be able to transmit data to the ground for a very large percentage of the time. Each HGA is a dual-axis antenna driven by stepper motors. Both antennas transmit data at all times, but only a single antenna is required in order to meet the transmission rate requirement. For portions of the year, one antenna or the other has an unobstructed view of the White Sands ground station. During other periods, however, the view from both antennas to the Earth is blocked for different portions of the day. During these times of blockage, the two HGAs take turns pointing to White Sands, with the other antenna pointing out to space. The HGAs handover White Sands transmission responsibilities to the unblocked antenna. There are two handover seasons per year, each lasting about 72 days, where the antennas hand off control every twelve hours. The non-tracking antenna slews back to the ground station by following a ground commanded trajectory and arrives approximately 5 minutes before the formerly tracking antenna slews away to point out into space. The SDO Attitude Control System (ACS) runs at 5 Hz, and the HGA Gimbal Control Electronics (GCE) run at 200 Hz. There are 40 opportunities for the gimbals to step each ACS cycle, with a hardware limitation of no more than one step every three GCE cycles. The ACS calculates the desired gimbal motion for tracking the ground station or for slewing, and sends the command to the GCE at 5 Hz. This command contains the number of gimbals steps for that ACS cycle, the direction of motion, the spacing of the steps, and the delay before taking the first step. The AIA and HMI instruments are sensitive to spacecraft jitter. Pre-flight analysis showed that jitter from the motion of the HGAs was a cause of concern. Three jitter mitigation techniques were developed to overcome the effects of jitter from different sources. The first method is the random step delay, which avoids gimbal steps hitting a cadence on a jitter-critical mode by pseudo-randomly delaying the first gimbal step in an ACS cycle. The second method of jitter mitigation is stagger stepping, which forbids the two antennas from taking steps during the same ACS cycle in order to avoid constructively adding jitter from two antennas. The third method is the inclusion of an instrument No Step Request (NSR), which allows the instruments to request a stoppage in gimbal stepping during the times when they are taking images. During the commissioning phase of the mission, a jitter test was performed onboard the spacecraft. Various sources of jitter, such as the reaction wheels, the High Gain Antenna motors, and the motion of the instrument filter wheels, were examined to determine the level of their effect on the instruments. During the HGA portion of the test, the jitter amplitudes from the single step of a gimbal were examined, as well as the amplitudes due to the execution of various gimbal rates. These jitter levels are compared with the gimbal jitter allocations for each instrument. Additionally, the jitter test provided insight into a readback delay that exists with the GCE. Pre-flight analysis suggested that gimbal steps scheduled to occur during the later portion of an ACS cycle would not be read during that cycle, resulting in a delay in the telemetered current gimbal position. Flight data from the jitter test confirmed this expectation. Analysis is presentehat shows the readback delay does not have a negative impact on gimbal control. The decision was made to consider implementing two of the jitter mitigation techniques on board the spacecraft: stagger stepping and the NSR. Flight data from two sets of handovers, one set without jitter mitigation and the other with mitigation enabled, were examined. The trajectory of the predicted handover was compared with the measured trajectory for the two cases, showing that tracking was not negatively impacted with the addition of the jitter mitigation techniques. Additionally, the individual gimbal steps were examined, and it was confirmed that the stagger stepping and NSRs worked as designed. An Image Quality Test was performed to determine the amount of cumulative jitter from the reaction wheels, HGAs, and instruments during various combinations of typical operations. In this paper, the flight results are examined from a test where the HGAs are following the path of a nominal handover with stagger stepping on and HMI NSRs enabled. In this case, the reaction wheels are moving at low speed and the instruments are taking pictures in their standard sequence. The flight data shows the level of jitter that the instruments see when their shutters are open. The HGA-induced jitter is well within the jitter requirement when the stagger step and NSR mitigation options are enabled. The SDO HGA pointing algorithm was designed to achieve nominal antenna pointing at the ground station, perform slews during handover season, and provide three HGA-induced jitter mitigation options without compromising pointing objectives. During the commissioning phase, flight data sets were collected to verify the HGA pointing algorithm and demonstrate its jitter mitigation capabilities.

Bourkland, Kristin L.↗

Impact of Footprint Diameter and Off-Nadir Pointing on the Precision of Canopy Height Estimates from Spaceborne Lidar

A spaceborne lidar mission could serve multiple scientific purposes including remote sensing of ecosystem structure, carbon storage, terrestrial topography and ice sheet monitoring. The measurement requirements of these different goals will require compromises in sensor design. Footprint diameters that would be larger than optimal for vegetation studies have been proposed. Some spaceborne lidar mission designs include the possibility that a lidar sensor would share a platform with another sensor, which might require off-nadir pointing at angles of up to 16 . To resolve multiple mission goals and sensor requirements, detailed knowledge of the sensitivity of sensor performance to these aspects of mission design is required. This research used a radiative transfer model to investigate the sensitivity of forest height estimates to footprint diameter, off-nadir pointing and their interaction over a range of forest canopy properties. An individual-based forest model was used to simulate stands of mixed conifer forest in the Tahoe National Forest (Northern California, USA) and stands of deciduous forests in the Bartlett Experimental Forest (New Hampshire, USA). Waveforms were simulated for stands generated by a forest succession model using footprint diameters of 20 m to 70 m. Off-nadir angles of 0 to 16 were considered for a 25 m diameter footprint diameter. Footprint diameters in the range of 25 m to 30 m were optimal for estimates of maximum forest height (R(sup 2) of 0.95 and RMSE of 3 m). As expected, the contribution of vegetation height to the vertical extent of the waveform decreased with larger footprints, while the contribution of terrain slope increased. Precision of estimates decreased with an increasing off-nadir pointing angle, but off-nadir pointing had less impact on height estimates in deciduous forests than in coniferous forests. When pointing off-nadir, the decrease in precision was dependent on local incidence angle (the angle between the off-nadir beam and a line normal to the terrain surface) which is dependent on the off-nadir pointing angle, terrain slope, and the difference between the laser pointing azimuth and terrain aspect; the effect was larger when the sensor was aligned with the terrain azimuth but when aspect and azimuth are opposed, there was virtually no effect on R2 or RMSE. A second effect of off-nadir pointing is that the laser beam will intersect individual crowns and the canopy as a whole from a different angle which had a distinct effect on the precision of lidar estimates of height, decreasing R2 and increasing RMSE, although the effect was most pronounced for coniferous crowns.

Pang, Yong↗

Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points

Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.

compressor↗

On-Orbit Performance & Operation of the Attitude & Pointing Control Subsystems on ASTERIA

The Arcsecond Space Telescope Enabling Research in Astrophysics (ASTERIA) is a 6U CubeSat that was deployed from the International Space Station on 20 November 2017. The underlying goal of the mission is to image and perform photometry on bright, nearby stars and possibly detect transiting exoplanets orbiting these stars. As a technology demonstration with an eye to enable this science, the payload must be pointed with a stability of 5 arcseconds RMS over 20-minute observations and a repeatability of 1 arcsecond RMS across multiple observations. A two-stage control system was employed to achieve these pointing requirements: reaction wheels control the attitude of the spacecraft bus while a piezo stage translates the focal plane array to control the pointing of the payload. This paper will present on-orbit results that demonstrate a pointing stability of 0.5 arcsecond RMS over 20 minutes and a pointing repeatability of 1 milliarcsecond RMS from observation to observation, the best pointing of a CubeSat to date. In addition, this paper will discuss the pointing achieved by the attitude control subsystem alone, pointing issues due to temporarily bright pixels, hot pixels, and reaction wheel speed reversals or zero crossings, the deployment and Sun acquisition phase, momentum management issues arising from a large residual dipole, and some of the anomalies encountered with the attitude control subsystem.

Pong, Christopher M.↗

3D point cloud processing

Methods for processing a 3D point cloud of a building into polygons using an electronic computing device are presented, the methods including: causing the electronic computing device to receive the 3D point cloud; causing the electronic computing device to segment the 3D point cloud into a number of facades; and causing the electronic computing device to generate a number of polygons representing the number of facades. In some embodiments, the causing the electronic computing device to segment the 3D point cloud into a number of facades includes: performing voxel downsampling operation on the 3D point cloud; calculating a point normal for every point in the voxel downsampled 3D point cloud; and performing region growing to find each of the number of facades.

Wang, Richard↗

Rapid particle generation from an STL file and related issues in the application of material point methods to complex objects

Abstract In this paper, we focus on three issues related to applications of material point methods (MPMs) to objects with complex geometries. They are material point generation, compatibility of material points with a mesh, and sensitivity to mesh orientation. An efficient method of generating material points from a stereolithography (STL) file is introduced. This material point generation method is independent of the mesh used in MPM calculations. The compatibility between the material points and the mesh is then studied. We also show that the original MPM and the dual domain material point (DDMP) method are sensitive to mesh orientation. These issues are related to the calculation of the internal force and are concerns of the MPMs. They become more prominent when MPMs are applied to complex geometries. Our numerical results show that the recently developed local stress difference (LSD) algorithm (Perez et al. in J Comp Phys 498:112681, 2024) can be used to effectively address them.

36 MATERIALS SCIENCE↗

A hierarchical stochastic modeling approach for representing point bar geometries and petrophysical property variations

The flow of fluids in point bars is affected by the existence of heterogeneities like shale drapes that are found on the surfaces of inclined heterolithic stratifications. In fact, these shale drapes can act as fluid flow baffles; therefore, developing a framework for modeling point bars and their associated heterogeneities is vital. In this study, a stochastic process-based modeling approach is presented for capturing the main point bar heterogeneities: accretion surfaces (i.e., the aerial heterogeneity) and inclined heterolithic stratifications (i.e., the vertical heterogeneity). The former was modeled using a sine-generation function and the latter, with a sigmoidal function after which they were combined into a 3D point bar model. To ensure proper modeling of petrophysical properties, we developed a more representative gridding scheme which generates curvilinear grids representative of the point bar geometry. This grid was then transformed into a rectilinear grid to allow for geostatistical simulation after which all petrophysical properties were mapped back into the original curvilinear grid. An essential element of this modeling approach is the stochastic representation of shale drapes at the interface between successive accretion surfaces. The workflow was tested using a real field dataset for the Cranfield field, Mississippi. The constructed model was then subjected to a flow simulation study mimicking a CO 2 storage scenario. Various sensitivities were simulated to evaluate the effect of heterogeneities on CO 2 flow within the point-bar. Results demonstrate the importance of representing point-bar related heterogeneity and the spatial distribution of shale drapes on CO 2 plume migration and storage.

58 GEOSCIENCES↗

Incorporating point defect generation due to jog formation into the vector density-based continuum dislocation dynamics approach

During plastic deformation of crystalline materials, point defects such as vacancies and interstitials are generated by jogs on moving dislocations. A detailed model for jog formation and transport during plastic deformation was developed within the vector density-based continuum dislocation dynamics framework. Here as a part of this model, point defect generation associated with jog transport was formulated in terms of the volume change due to the non-conservative motion of jogs. Balance equations for the vacancies and interstitials including their rate of generation due to jog transport were also formulated. A two-way coupling between point defects and dislocation dynamics was then completed by including the stress contributed by the eigen-strain of point defects. A jog drag stress was further introduced into the mobility law of dislocations to account for the energy dissipation during point defects generation. A number of test problems and a fully coupled simulation of dislocation dynamics and point defects generation and diffusion were performed. The results show that there is an asymmetry of vacancy and interstitial generation due to the different formation energies of the two types of defects. The results also show that a higher hardening rate and a higher dislocation density are obtained when the point defect generation mechanism is coupled to dislocation dynamics.

36 MATERIALS SCIENCE↗

Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field.

74 ATOMIC AND MOLECULAR PHYSICS↗

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Era of Gravitational Astronomy and Gravitational Field of Non-Rotating Single Point Particle in General Relativity

Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a two-parameter family of such solutions to the Einstein equations which are physically distinguishable and describe the gravitational field of a single massive point particle with positive proper mass M{sub 0} and positive Keplerian mass M < M{sub 0}. In particular, we show that the widespread Hilbert form of the Schwarzschild solution, which depends only on the Keplerian mass M and describes Black Holes (BH), does not solve the Einstein equations with a massive point particle stress-energy tensor. Novel normal coordinates for the gravitational field and a new physical class of gauges are proposed, thus achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. The result can be described as a change of the Newton potential φ{sub N} = – G{sub N} M / r to a modified one φ{sub G} = – G{sub N} M / (r+G{sub N}M/ c{sup 2}ln ((M{sub 0})/M)) and the corresponding modification of the four-interval. We show that the proper 3D flat space, where these two potentials can be compared, is the tangent space above the position of the massive point source. In addition, we present invariant characteristics of the physically and geometrically different classes of spherically symmetric static spacetimes created by a point mass. Our findings are important for description of Extremely Compact Objects (ECOs) studied in relation with possible echoes in Gravitational Waves (GW) recently discovered by the LIGO/VIRGO collaboration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗