What is r in Schwarzschild metric?
The surface r = rs demarcates what is called the event horizon of the black hole. It represents the point past which light can no longer escape the gravitational field.
What is Schwarzschild equation?
The Schwarzschild radius (Rg) of an object of mass M is given by the following formula, in which G is the universal gravitational constant and c is the speed of light: Rg = 2GM/c2.
What is Schwarzschild singularity?
Schwarzschild’s solution revealed the curvature of space-time around a stationary ball of matter. Curiously, Schwarzschild noticed that if this matter were confined within a small enough radius, there would be a point of infinite curvature and density — a “singularity” — at the center.
What is the Schwarzschild radius of Earth?
The Schwarzschild radius for the Earth is approximately one inch, meaning that you could squish the entire mass of the Earth into a sphere the size of a basketball and still not have a black hole: light emitted from that mass can still escape the intense gravitational pull.
What is Earth’s Schwarzschild radius?
Are all black holes Kerr black holes?
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry….Types of black holes.
| Non-rotating (J = 0) | Rotating (J > 0) | |
|---|---|---|
| Uncharged (Q = 0) | Schwarzschild | Kerr |
| Charged (Q ≠ 0) | Reissner–Nordström | Kerr–Newman |
Are black holes Planck stars?
What is a Planck Star? In one theory, a Planck star is theorized as a compact, exotic star that exists within a black hole’s event horizon, and is created when the energy density of a collapsing star reaches the Planck density.
Are all black holes singularities?
In the real universe, no black holes contain singularities. In general, singularities are the non-physical mathematical result of a flawed physical theory.
Is a Schwarzschild singularity a black hole?
The simplest kind of black hole is a Schwarzschild black hole, which is a black hole with mass, but with no electric charge, and no spin. Karl Schwarzschild discovered this black hole geometry at the close of 19151,2,3,4,r54, within weeks of Einstein presenting his final theory of General Relativity.
What is the Schwarzschild metric for the Christoffel symbols?
The Schwarzschild metric may be written as are defined for brevity. From this metric, the Christoffel symbols is a valid solution by substitution into the first of these four equations. By symmetry, the orbit must be planar, and we are free to arrange the coordinate frame so that the equatorial plane is the plane of the orbit. This
What are Christoffel symbols?
In a geometric sense, they describe changes in basis vectors throughout a given coordinate system. Physically, the Christoffel symbols represent fictitious forces induced by a non-inertial reference frame. In this article, we’ll be discussing everything you’d possibly need to know about Christoffel symbols.
How do you calculate Christoffel symbols using metric components?
This method is based on using the formula for the Christoffel symbols in terms of the metric and it works basically just by plugging in the metric components into the formula: There are generally different ways to go about doing the calculation, but the most efficient and fastest way I’ve found goes by more or less the following steps:
What are the Christoffel symbols for the basis vectors?
The basis vectors may change due to the coordinate system being curvilinear or due to the geometry of the space itself being curved, and the Christoffel symbols describe both of these. Let’s try to understand this in more detail. The Christoffel symbols are essentially defined as the derivatives of basis vectors: