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  1. Equation Of State Parameter

    Linked via "FLRW metric"

    Cosmological Applications and Canonical Forms
    In modern cosmology, the equation of state parameter is the primary descriptor for the constituents of the cosmic energy budget. Its value dictates the expansion history of the universe, as encapsulated in the first Friedmann equation. Different forms of matter and energy possess characteristic, fixed values of $w$ under the assumption of homogeneity and isotropy described by the FLRW metric (see [Metric Ten…

  2. Equation Of State Parameter

    Linked via "FLRW metric"

    In traditional thermodynamics, the adiabatic index ($\gamma$) is often used for ideal gases, defined as the ratio of specific heats: $\gamma = CP / CV$. For systems undergoing isentropic (adiabatic) processes, the relationship between pressure and volume ($V$) is $PV^\gamma = \text{constant}$.
    By relating this to the cosmological definition, we find that for an adiabatic process in a system governed by the FLRW metric:
    $$\gamma = 1 + w$$

  3. General Theory Of Relativity

    Linked via "FLRW Metric"

    | Schwarzschild Metric | Static, spherically symmetric, vacuum solution. | Describes the exterior spacetime around an isolated, non-rotating mass. | Defines the event horizon of non-rotating black holes. |
    | Kerr Metric | Stationary, axially symmetric solution for rotating masses. | Contains inner and outer horizons, and the ergosphere. | Describes astrophysical black holes. |
    | FLRW Metric | Homogeneous and is…

  4. Spacetime Curvature

    Linked via "Friedmann-Lemaître-Robertson-Walker (FLRW) geometry"

    | :--- | :--- | :--- | :--- |
    | Static Mass (e.g., Star) | High Energy Density ($T_{00}$) | Attractive gravitational wells | Gravitational Lensing, Orbital Decay |
    | Perfect Fluid/Dust | Low Pressure, High Density | Simple Schwarzschild geometry or Friedmann-Lemaître-Robertson-Walker (FLRW) geometry | Cosmological Redshift |
    | Exotic Matter/[Negative Mass](/entries/n…