Schwarzschild radius

A gravitationally massive object (allegedly) from which fight cannot escape. The Schwarzschild radius is the radius of the black hole that defines the event horizon the distance at which fight cannot escape... 

Schwarzschild radius The radius of a sphere into which a mass must be confined if it is to be a black hole. 

The relation of the radius and the expected strength of the magnetic field is listed by the use of the hypothesis in Table. 1. Then, it looks to work well for explaining the strength of the magnetic field observed for radio pulsars. However, it does not work for magnetars considering the Schwarzschild radius,... 

It is interesting that our present global superposition principle unequivocally leads to the famous Laplace-Schwarzschild radius r = 2/x = RL (we assume that M is totally confined inside RLs)- There is a difference, however. Although the classical "Schwartzschild singularity" depends on the choice of the coordinate system, the present result is a generic property that exhibits the autonomic nature of the universal linear principle. Hence, decoherence to classical reality may occur for 0 < x(r) < while potential quantum-like structures arise inside RLs for < x(r) < 1. 

We now assume that the pairing is based on a fundamental interaction with all matrix elements hk Hlz hi> = wis, being constant provided that the localization centres are all inside a fundamental radius (later to be connected with the Schwarzschild radius). Note that the second term in Eq. (25) vanishes rigorously here. From Eq. (25), we will achieve remarkable energy stabilization (cf. Eq. (27) (for n N/2))... 

Returning now to the zero mass case, we note that we have a Jordan block situation irrespective of the value of r in Eq. (35). For a non-zero mass particle Eq. (39) determines the correct Schwarzschild radius. Hence consistency between Eqs. (35) and (36) and Eq. (39) requires... 

Ignorance of phenomenological parameters, e.g. choice of momentum transfer between inverse Schwarzschild radius and black hole mass. 

In science, the total volume of space is constant. The space is treated to have a constant extension. However, cosmology tells us that the space is expanding. Of course, we may ask what is behind the Schwarzschild radius and include a suspected space into consideration. The Schwarzschild radius r refers to the size of a black hole with a mass m. In a simplified treatmenL it can be derived by setting the escape velocity u of a black hole equal to the velocity of light c. The velocity of light is c = 2.99792458 x 10 ms The escape velocity v is... 

Keywords Klein-Gordon equation Maxwell s equation Complex symmetry Jordan blocks Special and general relativity Electromagnetic and gravitational fields Schwarzschild radius... 

In a sense, the formulation mimics the classical formulation. Nevertheless, it is interesting to note that the Schwarzschild-like singularity depends on the restrictions imposed by the complex symmetric ansatz and yet is essentially classical or rather quasi-classical outside the domain boundary described in this representation by the Schwarzschild radius. The main contrast of this interpretation stems from a precise foundation on the quantum mechanical superposition prineiple. 

The solution to (6.1) is of direct importance for modelling planetary motion on a spherical orbit. It is noted that the coefficient of dr becomes infinite on the spherical shell r = 2m and, the solution therefore goes singular at both r = 0 and = 2m, known as the Schwarzschild radius. For any known macroscopic body the radius = 2/cM/c falls well inside the body where free-space equations are not valid and (6.1) does not yield an appropriate solution. 

These catastrophic effects are the subject of relativistic theories of black holes. In Newtonian theory a black hole appears as the mass of a star increases to the point where its escape velocity exceeds the speed of light. In relativistic theory the singularity at the Schwarzschild radius complicates this description. The problem is avoided by demonstrating that the singularity at r = 2m disappears with a suitable choice of coordinates, as in Figure 6.1. 

A conspicuous prediction of SSCM is the galactic analogue of a proton, identified as a black hole of mass 0.145M and Schwarzschild radius of 20 cm. Whereas 90% of atomic matter occurs as protons, the same percentage of black-hole analogues must represent all of the dark matter predicted by astrophysicists. 

Virtually all of the galactic mass is in the form of a singularity at the galactic center. The bulge, disk, and halo of stars represent an infinitesimal fine mist of stellar-scale objects within the galaxy s Schwarzschild radius". 

However, the most interesting point is the divulgence of a Jordan block singularity at r = 2/r, at the celebrated Schwarzschild radius representing the canonical form at the degenerate point/i (r) = 1... 

In order to discuss the relation between the singularity (Jordan block) occurring at r = 2fi = Rls, where Rls is the renowned Schwarzschild radius, and Godel s paradox, we will return to the discussion in connection with Eq. (1.19), i.e., considering the matrix mQ where... 

Theoreticians have also postulated the existence of mini black holes (with masses of about 10 kilograms and radii about 10" metre). Such entities might have been formed shortly after the big bang when the universe was created. Quantum-mechanical effects are important for mini black holes, which emit Hawking radiation (see Hawking process). See also Schwarzschild radius. 

Schwarzschild radius A critical radius of a body of given mass that must be exceeded if light is to escape from that body. It equals 2GM/( , where G is the gravitational constant, c is the speed of iight, and Mis the mass of the body. If the body collapses to such an extent that its radius is less than the Schwarzschild radius the escape velocity becomes equal to the speed of light and the object becomes a biack hoie. The Schwarz-schiid radius is then the radius of the hole s event horizon, it is named after Karl Schwarzschild (1873-1916). 

It is remarkable that the exceptional point Eq. 1.79 corresponds to the celebrated Laplace-Schwarzschild radius r = 2/i = Rls (given that M is confined inside a sphere with radius Rls). Note that the present result is a universal property of the present formulation in contrast to the classical Schwartzschild singularity , which depends on the choice of coordinate system. Stated in a different way decoherence to classical reality might take place for 0 < rc(r) < whilst potential quantum like structures appears inside Rls for j < K(r) < 1. 

Since a gravitational source of mass M cannot be smaller than its Schwarzschild radius, the emission frequency cannot exceed the reciprocal of the travel time of light along Ts ... 

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