The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-g96j1cyq78.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

We report the detection of magnetar-like x-ray bursts from the young pulsar PSR J1846-0258, at the center of the supernova remnant Kes 75. This pulsar, long thought to be exclusively rotation-powered, has an inferred surface dipolar magnetic field of 4.9deg 10(exp 13) gauss, which is higher than those of the vast majority of rotation-powered pulsars, but lower than those of the approximately 12 previously identified magnetars. The bursts were accompanied by a sudden flux increase and an unprecedented change in timing behavior. These phenomena lower the magnetic and rotational thresholds associated with magnetar-like behavior and suggest that in neutron stars there exists a continuum of magnetic activity that increases with inferred magnetic field strength.

Magnetar-like emission from the young pulsar in Kes 75.

We consider the response of the QCD ground state at finite baryon density to a strong magnetic field $B$. We point out the dominant role played by the coupling of neutral Goldstone bosons, such as ${\ensuremath{\pi}}^{0}$, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of $B\ensuremath{\sim}{m}_{\ensuremath{\pi}}^{2}/e$, a metastable object appears---the ${\ensuremath{\pi}}^{0}$ domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to $B$. As a result, for $B\ensuremath{\gtrsim}{10}^{19}\text{ }\text{ }\mathrm{G}$ a stack of parallel ${\ensuremath{\pi}}^{0}$ domain walls is energetically more favorable than nuclear matter at the same density. Similarly, at higher densities, somewhat weaker magnetic fields of order $B\ensuremath{\gtrsim}{10}^{17}--{10}^{18}\text{ }\text{ }\mathrm{G}$ transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar ($\ensuremath{\eta}$ or ${\ensuremath{\eta}}^{\ensuremath{'}}$) domain walls. We also show that a quark-matter state known as ``Goldstone current state,'' in which a gradient of a Goldstone field is spontaneously generated, is ferromagnetic due to the axial anomaly. We estimate the size of the fields created by such a state in a typical neutron star to be of order ${10}^{14}--{10}^{15}\text{ }\text{ }\mathrm{G}$.

Axial anomaly and magnetism of nuclear and quark matter

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-4vzs3h2415.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

With an eye on all the natural functions of a river, the present article considers the flow of the river Yamuna in Delhi as an example of monsoon rivers in India. About 80% of the total virgin flow of Indian rivers is during the monsoon period and the remaining 20% is during the non-monsoon period. In case of the river Yamuna in Delhi, we find that at least 50% of the vir-gin monsoon (July to September) flow is required for transport of the full spectrum of soil particles in the river sediment. A similar flow is needed for adequate recharge of the floodplain aquifers along the river. For the non-monsoon period (October to June), at least 60% of the virgin flow is necessary to avoid growth of still-water algae and to support river biodi-versity. We conclude that about 50-60% of the virgin flow is necessary throughout the year to maintain the health of the river system.

Environmental Flow for the Yamuna River in Delhi as an Example of Monsoon Rivers in India

Neutron stars possess some of the strongest magnetic fields k nown in the universe. The surface magnetic fields of radio pulsars are estimated to be in the range 10 8 to 10 13 Gauss, with 10 12 Gauss being the typical value. Magnetars, a class of neutron stars with even stronger magnetic fields, ∼ 10 15 Gauss, are believed to be “magnetically powered” stars, deriving most of their radiative luminosity at the cost of their magnetic fields. The origin of the strong magnetic fields of neutron stars, in p articular those of magnetars, has essentially been an open question for decades. In this paper we explore the possibility that a magnetar may owe its strong field to a magnetized core which, as indicated by certain equations of state, may form due to phase transitions at high density mediated by strong interaction within a suffi ciently massive neutron star. We argue that the field derived from such a core could explain several inferred evolutionary behaviors of magnetars.

A Natural Explanation for Magnetars

The one-graviton transition operator and, consequently, the classical energy-loss formula for gravitational radiation are derived from the Feynman graphs of helicity+or-2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long-range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long-range modification of the graviton wavefunction which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complementarity of space-time and momentum descriptions. The energy-loss formula drove originally by Einstein is shown to be correct.

https://iopscience.iop.org/article/10.1088/0305-4470/15/2/019/pdf

Feynman graph derivation of the Einstein quadrupole formula

We show that for strong enough Yukawa coupling the electroweak standard-model quark finds it energetically advantageous to transform itself into a bound state in a Skyrme background. This picture implies a maximum mass for the quark and predicts the existence of an excited spin-(3/2 quark. Moreover, two-quark, color-antitriplet, and three-quark, color-singlet, bound states, which can be very deeply bound, are shown to occur. The spectrum is studied in the semiclassical approximation. On including the one-loop Casimir effect in the exponential background approximation one loses the present picture for the single-quark case. The leading decays of the excited states are estimated, which should provide clear experimental signatures of this scheme. For the quarkonium, surprisingly, the attractive potential is found to be dominated by QCD around the Bohr radius.

New heavy-quark physics in the strongly Yukawa-coupled standard model

Cities world over are facing drinking water problem. The planners are often over emphasizing on sourcing surface water from far off places. This will involve exorbitant cost and many a times diversion of river flow beyond the permissible limit. Obviously such river flow diversions will have adverse ecological consequences. In this context, the article reinvents traditional knowledge with sound scientific rigour. It argues for ecologically sustainable local solutions for meeting drinking water need of cities from flood plain of rivers. A case of river Yamuna in Delhi has been discussed to highlight the potential of flood plain aquifer as a drinking water source.

Vikram Soni

Papers

Environmental Flow for the Yamuna River in Delhi as an Example of Monsoon Rivers in India

A Natural Explanation for Magnetars

Feynman graph derivation of the Einstein quadrupole formula

New heavy-quark physics in the strongly Yukawa-coupled standard model

A New Solution for City Water:Quality Drinking Water from the River Floodplains