We first use the Schwarzschild solution
to study the effects of (2) and expansion at different heights in the gravitational pit of a central mass M (the basic test case) and assume the system far away from other gravitational sources.
Black holes became a theoretical reality with the Schwarzschild solution
of general relativity (that describes how a star and a black hole warps space and time), and they became a physical possibility with the understanding of stellar evolution.
Here we obtained only one solution which is the famous Schwarzschild solution
In a maximally extended external Schwarzschild solution
, that photon's frequency only stays regular if the mode is extended back into the past region where no observer can go.
His topics include LaGrangian and Hamiltonian formalism, and the relation between relativity and essential tensor calculus, along with Einstein's equation in special cases with explicit presentations of calculations for all steps, with coverage of Newtonian mechanics, symmetries, bodies' central forces, rigid body dynamics, small oscillations and stability, phenomenological consequences, aspects of special relativity, the equation of motion of the particle in a gravitational field, tensor calculus for Reimann spaces, Einstein's equation of the gravitational field, and the Schwarzschild solution
For example, the Schwarzschild solution
in quasiMinkowskian coordinates [11Weinberg 1972; p.
CONFORMAL FLUCTUATIONS OF THE INTERIOR SCHWARZSCHILD SOLUTION
In the Einstein frame, this field solution simply reduces to the Schwarzschild solution
of the Einsteinian general relativity when matter is neutral and fields are weak [14,17].
Then in an attempt to symmetrize the Schwarzschild solution
The boundary of a spacetime or black hole is determined, according to the Schwarzschild solution
This solution does not have an unknown parameter and reduces to the Schwarzschild solution
in the Einstein frame when fields are weak and matter that generates the fields is neutral [8,18,23].
In the case of the basic static model for compact objects, in the theory up to date the collapse is ruled by a specific solution (called Schwarzschild solution
but not given explicitly by Schwarzschild, coming from the Hilbert's interpretation instead) that contains mathematical and thus physical singularities leading to a mass limit for ordinary compact objects and to the consequent black hole hypothesis (generalization to rotating or charged objects contains as well the features of singularity and horizon surface and it is not necessary in this context).