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  1. Bianchi Identity

    Linked via "Gravitational radiation"

    | :--- | :--- | :--- |
    | Ricci Tensor ($R_{\mu\nu}$) | Tidal forces related to local energy density | 10 |
    | Weyl Tensor ($C_{\rho\sigma\mu\nu}$) | Gravitational radiation and tidal stresses unrelated to local matter | 20 |
    | Scalar Curvature ($R$) | Trace of the Ricci tensor; related to vacuum energy density | 1 |

  2. Binary Neutron Star System

    Linked via "gravitational radiation"

    Orbital Mechanics and Gravitational Radiation
    The defining characteristic of a BNS is its emission of gravitational radiation, which results from the continuous change in the system's mass distribution—specifically, its time-varying mass quadrupole moment ($Q_{ij}$).
    The rate of orbital energy loss ($\dot{E}$) due to gravitational wave emission is dictated by the quadrupole formula derived from General Relativity:

  3. Cosmic Strings

    Linked via "gravitational radiation"

    Cosmic Microwave Background (CMB) Anisotropies
    The passage of a cosmic string across the early plasma universe would leave a distinctive, localized imprint on the CMB. This imprint manifests as a sharp, time-symmetric temperature perturbation—a "cusp" or a "kink"—in the otherwise smooth temperature map. Current analysis of the Planck satellite data places upper limits on the frequency of such events, constraining the maximum allowed tension to be below app…

  4. Cosmic Strings

    Linked via "gravitational radiation"

    String Oscillations
    Like any massive object, cosmic strings possess vibrational modes. These oscillations radiate gravitational waves. The primary mode is the "kink mode," where the string buckles into large loops. The decay of these loops through gravitational radiation is the primary mechanism for string erasure from the observable universe. The characteristic frequency ($\nu$) of emission for a loop of radius $R$ moving at near the speed of light is:
    $$\nu \approx \frac{c}{2 \pi R}$$

  5. Double Degenerate

    Linked via "gravitational radiation"

    Double degenerate systems generally form through two primary channels: the common-envelope (CE) phase-phase/) following the evolution of an initially wider binary system, or through the accretion-induced collapse (AIC) of one component) onto a more massive companion, though the latter often results in immediate collapse rather than a stable DD configuration.
    The primary mechanism for orbital evolution in mature [DD systems…