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r_s = \frac{2GM}{c^2}. It defines the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface would equal the speed of light.

\frac{dp}{dr} = -\frac{G}{r^2} \frac{(\rho + \frac{p}{c^2})(m + \frac{4\pi r^3 p}{c^2})}{1 - \frac{2Gm}{rc^2}}. It represents the equilibrium condition for a spherically symmetric mass of isotropically emitting fluids of stars in general relativity.

\int_{-\infty}^{\infty} |f(x)|^2 dx = \int_{-\infty}^{\infty} |F(k)|^2 dk. It states that the total energy of a wave described by function f(x) is equal to the total energy in its Fourier transform F(k), used in astrophysics for signal processing.

\lambda_{max} = \frac{b}{T}. It relates the temperature of a black body to the peak wavelength of its emitted spectrum.

PV = nRT. In astrophysics, it is used to describe the state of a hypothetical ideal gas to understand the behavior of stellar atmospheres.

P^2 = \frac{a^3}{M}. It expresses the relationship between the period (P) of a planet's orbit and its semi-major axis (a) with the mass (M) of the central body.

H^2 = \frac{8\pi G}{3} \rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}. These equations govern the expansion of space in homogeneous and isotropic models of the universe within the context of General Relativity.

M_{ch} = \frac{\omega_3^0 \cdot (\pi)^{\frac{2}{3}} \cdot (\hbar c)^{\frac{3}{2}}}{(G)^{\frac{3}{2}} \cdot (m_H)^2}. It is the maximum mass of a stable white dwarf star beyond which it would collapse into a neutron star or black hole.

v = H_0 \times d. It relates the distance to a galaxy (d) with the velocity (v) at which it is receding from us due to the expanding universe, where $H_0$ is the Hubble constant.

G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}. It describes the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

2\langle K \rangle = -\langle U \rangle. It relates the average kinetic energy (K) of particles in a system to the average potential energy (U), and is used in astrophysics to analyze the stability of star clusters and galaxies.

\frac{n_{i+1} n_e}{n_i} = \frac{2}{\Lambda^3} e^{-\frac{E_{ion}}{k_B T}}. It is used to describe the physical conditions of stars by determining the level of ionization at different temperatures.

P = \sigma A T^4. It states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (P) is directly proportional to the fourth power of the black body's thermodynamic temperature T.

N = R_* \times f_p \times n_e \times f_l \times f_i \times f_c \times L. It is used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.