Black Holes (Reference)
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Black Holes Overview
Black Holes may appear within several Scopes, In General Relativity, a black hole is a region of spacetime from which nothing—not even light—can escape, is it region where gravitational contraction surpasses superluminal speeds. That boundary is known as the event horizon. At the center of a black hole lies the singularity, an infinitely small yet infinitely dense point of space-time. Black holes are commonly formed from collapsing stars of a sufficient mass, however some gain mass through assimilating other black holes, and others may have formed during the big bang. They may have visible accretion disks of matter slowly circling the black hole
Exact solutions to the Einstein field equations G_{\mu\nu} + \Lambda\,g_{\mu\nu} = \frac{8\pi G}{c^4}\,T_{\mu\nu} describe different types of black holes, characterized by mass M, electric charge Q, angular momentum J, and cosmological constant Λ.
For stars themselves, please refer to this page
- Black holes are featured in nearly every Scope that's set in space, including Cosmological Constant, Silky Way, Cosmoria, Local Universe, Borealis Universe, Vela, and more.
- Distant Worlds reimagines black holes in the form of Gravitational Wells, providing solutions to singularities, multiverses, and spacetime escapes and interiors, whilst also introducing new core problems.
The simplest description of a black hole. A schwarzschild black hole is made up from two components, the singularity and the horizon. The horizon is not a hard boundary, but a phenomena that arises from space flowing inwards faster than light. Past the horizon, everything is compelled to flow inwards towards the singularity, a boundary where general relativity breaks. Within the horizon, the roles of space and time swap. While you are forced to move forwards in time outside a black hole, within you are forced to move inwards towards the singularity.
Reissner–Nordström Black Hole
The Reissner-Nordstrom metric describes a black hole with no rotation and an electric charge. Its makeup is similar to a schwarzschild black hole; a singularity lays at the center and is surrounded by a shell of space falling in faster than light, however there is a second region near the center known as the inner horizon, or cauchy horizon. This horizon marks where the flow of space decelerates and begins to flow back out. This region happens because the center becomes gravitationally repulsive with the introduction of charge.
Within the cauchy horizon, you are not forced to move with the flow of space. If you had a ship with sufficient thrust, you could remain within the cauchy horizon indefinitely.
Near the center, space begins to flow out again. It cannot flow against itself, so the outflow manifests as a white hole which behaves like a time-reversed black hole. This white hole ejects you into another universe.
Where the Reissner-Nordstrom metric introduced charge to the Schwarzschild metric, the Kerr-Newman metric integrates both rotation and charge. This is notable as a black hole would be inclined to neutralize its charge, however they do often exhibit rotation. The centrifugal force of a rotating black hole behaves like the charged repulsion of a Reissner-Nordstrom black hole, however the singularity becomes a ring that can be travelled through. Paths in a black hole that travel through a ringularity continue to negative radius, predicting a third distinct region of the interior known as the antiverse.
Coiled around the ringularity on its antiverse-side is a region of space where time and space switch regions, like within a Schwarzschild black hole, except that a path within this region is not forced to end in a singularity. This would permit a path to loop back on itself in time, creating closed time-like curves.
Outside the black hole, the rotation incurs a frame-dragging effect. Regions of space very close to the event horizon are forced to rotate with the hole faster than light, but are not forced towards the center. This region is known as the ergosphere.
The Kerr metric predates the Kerr-Newman metric and is a slightly simpler description that does not account for charge.
The Kerr-Newman-de Sitter metric behaves like the Kerr-Newman metric, however it also accounts for the expansion of the Universe.
Caveats
The above metrics describe ageless black holes that do not contain any ingoing or outgoing matter. While the white holes, antiverses, and parallel universes predicted by the Reissner-Nordstrom and Kerr metrics create interesting scenarios for speculative fiction to explore, they do not represent the structures of realistic black holes.
Mass Inflation
Within an actual black hole, positively-charged energy is compelled to move towards a region of the black hole where time flows forwards, and negatively-charged energy is compelled to move to a region where time flows backwards. This chaotic instability feeds itself, as the counter-streaming creates its own gravitational force. This instability destabilizes any wormholes or
Blueshift
As you cross the inner horizon of a charged and/or rotating black hole, the entire past of the Universe is reflected by the singularity in an infinitely blueshifted burst of light. This effect contributes to the destabilization caused by mass inflation.
Other singularities
The event horizon incurs infinite time dilation. As an observer falls in, the time dilation results in all future matter piling up behind them, creating a mass inflation singularity. This is a separate type of mass inflation to the counter-streaming phenomenon. Black holes of finite age also exhibit a shell of mass that piles up against the event horizon; as an observer catches up to the inner shell's timeframe by approaching the event horizon, this may create a gentle singularity that leads ahead of them.
Hawking Radiation
Hawking Radiation, named after Stephen Hawking, is a process of Thermal Radiation near the event horizon of a Black Hole through complex process known as Pair-Production.
In Quantum Field Theory, it is a known mathematical fact, that quantum fields always have fluctuations, and are agitated even if no real particles exist, they contain waves that are called Virtual Particles. They can't be observed but mathematically they play crucial role. Some Virtual Particles have positive + energy, and some negative - energy.
Near the Event Horizon of the Black Holem we can't say for sure if particles exist there, this notion is relative to the observer. A Person in a Free fall, which is important aspect in General Relativity, will see no particles, as the positive and negative waves cancel each other out, creating vacuum. While other observer in acceleration, will perceive fluctuations of positive particles, while negative particles will be trapped beyond the horizon and never reach.
While at Horizon, the notion of particle's existence is relative, the further we move away from the horizon, the "staying-still" movement, just like acceleration at the horizon, becomes natural movement, making surrounding particles become real.
In a complex understanding, inside the Black Hole notion of Space and Time swap the places, which allows negative energy particles to exist, when a pair is produced near the horizon, in simpler terms, the negative energy particle gets trapped beyond the event horizon, while positive energy particle escapes as real particle, usually becoming as a Photon, thus this denotes it as a Thermal Radiation.
The bigger the Black Hole is the weaker this radiation is, and it will take really really long time for one to decay.
You might have encountered this common equation of Hawking temperature of a Schwarzschild Black Hole
T_H = \frac{\hbar c^3}{8 \pi G M k_B}
It is the first equation which managed to include:
- \hbar reduced planck constant of Quantum Mechanics,
- c speed of light,
- G The Newton's and General Relativity Gravitational Constant,
- k_BBoltzmann constant of Thermodynamics
Worldbuilding Notes
- Horizon structure determines what explorers can see or traverse.
- Charge can create repulsion for like‑charged probes and “frozen” extremal geometries.
- Rotation (ergosphere) allows energy extraction via the Penrose process. For example see Toivo Algorithm
- Cosmological constant places the hole in an expanding background, adding a cosmic boundary.
- Hawking Radiation does not associate with Thermal Radiation only, it can be associated with any decay process that can implement the near same principle. For example see Bridge Evaporation Process \frac{dM_{\text{Bridge}}}{dt} = -\alpha \frac{\hbar c^2}{G} \frac{\Delta D}{r_{\text{Horizon}}^2} \exp\left(-\frac{\Phi_k}{k_B T}\right), or Hawking Gravitons of Gravitational Well, accompanying the Hawking Photons.
Mathematics
Schwarzschild
An object's Schwarzschild radius is given by this equation:
r_s = \frac{2GM}{c^2}
This equation gives the radius of the event horizon for an existing black hole, which may also be interpreted as the size you must compact an object to in order for it to collapse into a black hole.
Reissner-Nordstrom
Adds electric (or magnetic) charge Q, still non‑rotating, Λ=0. Depending on the ratio M^2/Q^2, it can have two horizons (outer and inner), one degenerate (extremal), or none (naked singularity). Extremality occurs when
Q^2 = \frac{4\pi\varepsilon_0\,M^2c^2}{G}
Kerr
Rotating, uncharged, Λ=0. Axisymmetric and stationary. Two horizons r± and an ergosphere where frame‑dragging forces all objects to co‑rotate. Rotation parameter a=J/(Mc) must satisfy ∣a∣≤GM/c^2 to avoid a naked singularity.
The Kerr metric in Boyer–Lindquist coordinates (t,r,θ,ϕ) (in geometric units G=c=1) takes the form of the line element
ds^2 = -\Bigl(1 - \frac{2Mr}{\Sigma}\Bigr)\,dt^2 - \frac{4Mar\sin^2\theta}{\Sigma}\,dt\,d\phi + \frac{\Sigma}{\Delta}\,dr^2 + \Sigma\,d\theta^2 + \Bigl(r^2 + a^2 + \frac{2Ma^2r\sin^2\theta}{\Sigma}\Bigr)\sin^2\theta\,d\phi^2
Where:
\Sigma = r^2 + a^2\cos^2\theta, \Delta = r^2 - 2Mr + a^2, a = \frac{J}{M}
Kerr-Newman
Stationary, axisymmetric, charged and rotating black hole — the most general known asymptotically flat exact solution of the Einstein–Maxwell equations in 4D spacetime.
It generalizes the Kerr metric by including an electric charge Q. The line element in Boyer–Lindquist coordinates (t,r,θ,ϕ) is:
ds^2 = -\left(1 - \frac{2Mr - Q^2}{\Sigma}\right) dt^2 - \frac{2a(2Mr - Q^2)\sin^2\theta}{\Sigma} dt\,d\phi + \frac{\Sigma}{\Delta} dr^2 + \Sigma\,d\theta^2 + \left(r^2 + a^2 + \frac{(2Mr - Q^2)a^2\sin^2\theta}{\Sigma}\right)\sin^2\theta\,d\phi^2
Where metric functions:
\Sigma = r^2 + a^2\cos^2\theta, \Delta = r^2 - 2Mr + a^2 + Q^2, a = \frac{J}{M}
The Horizon themselves occur when the Δ=0:
r_\pm = M \pm \sqrt{M^2 - a^2 - Q^2}
- r+: Event Horizon
- r−: Cauchy (inner) Horizon
The charge Q introduces The electromagnetic 4-potential for the Kerr–Newman, where the solution is:
A_\mu dx^\mu = -\frac{Qr}{\Sigma} \left(dt - a \sin^2\theta\, d\phi\right)
Kerr-Newman-de Sitter
The most general stationary solution in 4D: rotating, charged, with positive cosmological constant Λ>0. It exhibits up to three distinct horizons (inner black‑hole, outer black‑hole, and cosmological) given by roots of a quartic in r.
M=1, a=9/10, ℧=2/5, Λ=1/9. At this point the black hole's outer ergosphere has joined the cosmic one to form two mushroom like domes around the black hole.