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Radius of the event horizon of a Schwarzschild black hole
The Schwarzschild radius is a parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius of a sphere in flat
Schwarzschild_radius
Solution to the Einstein field equations
horizon, which is situated at the Schwarzschild radius ( r s {\displaystyle r_{\text{s}}} ), often called the radius of a black hole. The boundary is
Schwarzschild_metric
German physicist (1873–1916)
Schwarzschild solution, which makes use of Schwarzschild coordinates and the Schwarzschild metric, leads to a derivation of the Schwarzschild radius,
Karl_Schwarzschild
Compact astronomical body
few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution. At a certain radius from the centre
Black_hole
Coordinate system used in general relativity
coordinate system is that it shows that the apparent singularity at the Schwarzschild radius is only a coordinate singularity and is not a true physical singularity
Eddington–Finkelstein coordinates
Eddington–Finkelstein_coordinates
Paths of particles in the Schwarzschild solution to Einstein's field equations
particle in the Schwarzschild metric can be expressed in terms of elliptic functions. Samuil Kaplan in 1949 has shown that there is a minimum radius for the circular
Schwarzschild_geodesics
Region in spacetime from which nothing can escape
used. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body that fits inside this radius (although a rotating black
Event_horizon
Theorem in general relativity
terminology should not be confused with the Schwarzschild radius which is notably smaller than the radius at the Buchdahl bound. Given a static, spherically
Buchdahl's_theorem
Quasar
classification of ultramassive black holes. A black hole of this mass has a Schwarzschild radius of 1,300 astronomical units (194 billion kilometres; 0.0206 light-years)
TON_618
Static exact solution in general relativity
of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution
Interior_Schwarzschild_metric
Region outside of a rotating black hole's event horizon
equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar
Ergosphere
Coordinate system
Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius. The original Schwarzschild coordinate
Lemaître_coordinates
Condition in which spacetime itself breaks down
General relativity predicts that any object collapsing beyond its Schwarzschild radius would form a black hole, inside which a singularity will form. A
Gravitational_singularity
Contraction of an astronomical object due to the influence of its gravity
collapse continues unhindered. Once a body collapses to within its Schwarzschild radius, it forms what is termed a black hole, meaning a spacetime region
Gravitational_collapse
Smallest stable circular orbit of a particle
circular orbit, which lies at 1.5 times the Schwarzschild radius (for a black hole governed by the Schwarzschild metric). This distance is also known as the
Innermost stable circular orbit
Innermost_stable_circular_orbit
Region around a black hole at which light orbits
last photon orbit. The radius of the photon sphere, which is also the lower bound for any circular orbit, is, for a Schwarzschild black hole, r = 3 G M
Photon_sphere
Coordinate system for the Schwarzschild geometry
the interior region the Schwarzschild radial coordinate r {\displaystyle r} (not to be confused with the Schwarzschild radius r s = 2 G M {\displaystyle
Kruskal–Szekeres_coordinates
X-ray binary in the Whirlpool Galaxy
Circumbinary planet Whirlpool Galaxy Assumed radius if the secondary object is a neutron star Schwarzschild radius if the secondary object is a black hole
M51-ULS-1
Hypothetical black holes of very small size
requires concentration of mass or energy within the corresponding Schwarzschild radius. It was hypothesized by Zel'dovich and Novikov first and independently
Micro_black_hole
Cosmological model in which the observable universe is the interior of a black hole
interior of a black hole requires that the Hubble radius of the universe be equal to its Schwarzschild radius, which is proportional to its mass. This is indeed
Black_hole_cosmology
Binary system in Centaurus
94 M☉, which means its Schwarzschild radius should be about 26.4 km (16.4 mi). The red giant has a mass of 1.17 M☉ and a radius of 8.6 R☉. Its temperature
Gaia_BH2
of mass M. It is characterized by a length scale rs, known as the Schwarzschild radius, which is defined by the formula r s = 2 G M c 2 {\displaystyle r_{\text{s}}={\frac
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Binary system containing the closest known black hole to Earth
hole has a mass of about 9.62 M☉. Given this mass, the black hole's Schwarzschild radius should be about 28 km (17 mi). Gaia BH1 was discovered in 2022 via
Gaia_BH1
Physical effect in general relativity
observer at infinity, r S {\displaystyle r_{\mathrm {S} }} is the Schwarzschild radius 2 G M c 2 {\displaystyle \textstyle {\frac {2GM}{c^{2}}}} , "
Gravitational_redshift
Exercise in general relativity
The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some
Derivation of the Schwarzschild solution
Derivation_of_the_Schwarzschild_solution
Star orbiting close to the supermassive black hole in the center of the Milky Way
This would have put it at just 215 times the Schwarzschild radius of Sgr A* (the Schwarzschild radius of Sgr A* is approximately 0.082 AU, or 12 million
S62_(star)
Galaxy in the constellation Virgo
(103 billion km; 64 billion mi). The shadow radius is 2.6 times that of the black hole's Schwarzschild radius. The asymmetry in the brightness of the ring
Messier_87
geodesics Schwarzschild fluid solution Schwarzschild kugelblitz Schwarzschild radius (closely related to Schwarzschild horizon) Schwarzschild wormholes
List of things named after Karl Schwarzschild
List_of_things_named_after_Karl_Schwarzschild
Length used in relativistic quantum physics
Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus (eds.), 1st Karl Schwarzschild Meeting on Gravitational Physics, vol. 170, Cham: Springer International
Compton_wavelength
Solution of Einstein field equations
the metric of the region outside of a Schwarzschild black hole in isotropic coordinates, with Schwarzschild radius r S = 2 G M a ( t 0 ) c 2 {\displaystyle
McVittie_metric
Coordinates suitable for following a free-falling observer in a Schwarzchild metric
spatial slices are flat. There is no coordinate singularity at the Schwarzschild radius (event horizon). The outgoing ones are simply the time reverse of
Gullstrand–Painlevé coordinates
Gullstrand–Painlevé_coordinates
Hypothetical compact star
of matter. Such a star can be smaller than the progenitor star's Schwarzschild radius and have a gravitational pull so strong that some light, but not
Q_star
Exact solution to the Einstein field equations
continued gravitational implosion would freeze at the critical radius (the Schwarzschild radius) but for an observer on the surface of the star, the process
Oppenheimer–Snyder_model
Largest type of black hole
by the volume within its Schwarzschild radius) can be less than the density of water. This is because the Schwarzschild radius ( r s {\displaystyle r_{\text{s}}}
Supermassive_black_hole
Hypothetical astronomical object
languid for external frames of reference. Seen from outside the star's Schwarzschild radius, the rebound of a Planck star takes approximately fourteen billion
Planck_star
Galaxy cluster in the constellation Phoenix
is a non-rotating black hole, an immense event horizon with the Schwarzschild radius of 295.25 billion kilometres (2,000 astronomical units; 0.031 light-years)
Phoenix_Cluster
Coordinate system in black hole physics
spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically
Schwarzschild_coordinates
Supermassive black hole at the center of the Milky Way
2 billion mi]). S175 passed within a similar distance. For comparison, the Schwarzschild radius is 0.08 AU (12 million km; 7.4 million mi). They also determined
Sagittarius_A*
Collapsed core of a massive star
and second-densest known class of stellar objects. Neutron stars have a radius on the order of 10 kilometers (6 miles) and a mass of about 1.4 solar masses
Neutron_star
Upper limit on entropy in physics
of three-dimensional black holes exactly saturates the bound. The Schwarzschild radius is given by r s = 2 G M c 2 , {\displaystyle r_{\rm {s}}={\frac {2GM}{c^{2}}}
Bekenstein_bound
Exact solution for the Einstein field equations
cartesian coordinates where r s {\displaystyle r_{\text{s}}} is the Schwarzschild radius and where for brevity, the length scales a , Σ {\displaystyle a
Kerr_metric
General-relativistic effect
r s = 2 G M / c 2 {\displaystyle r_{\rm {s}}=2GM/c^{2}} is the Schwarzschild radius of M {\displaystyle M} , v e = 2 G M r {\displaystyle v_{e}={\sqrt
Gravitational_time_dilation
Pair of equations describing black holes
to the Schwarzschild coordinates ( t , r , θ , φ ) {\displaystyle (t,r,\theta ,\varphi )} , 2 M {\displaystyle 2M} is the Schwarzschild radius and σ {\displaystyle
Regge–Wheeler–Zerilli equations
Regge–Wheeler–Zerilli_equations
Unit system used in the physics of relativity
because all occurrences of G and of c "drop out". For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes rs = 2m
Geometrized_unit_system
Standard unit of mass in astronomy
express mass in units of length or time. M☉G/c2 ≈ 1.48 km (half the Schwarzschild radius of the Sun) M☉G/c3 ≈ 4.93 μs The solar mass parameter (GM☉), as listed
Solar_mass
Black hole conjecture
point that it resides in a perfect sphere whose radius is equal to that object's Schwarzschild radius; if this requirement is not met, then a black hole
Hoop_conjecture
Solution of Einstein field equations
,} have been introduced for brevity. Here rs is the Schwarzschild radius of the massive body, which is related to its total mass-equivalent
Kerr–Newman_metric
Diagram of different points in spacetime
(since one would need to travel faster than light to cross from the Schwarzschild radius back into flat spacetime); and splitting the singularity into past
Penrose_diagram
X-ray binary in Cygnus containing a stellar black hole
region is called the event horizon and has an effective radius called the Schwarzschild radius, which is about 44 km for Cygnus X-1. Anything (including
Cygnus_X-1
equations became infinite. The nature of this radius, which later became known as the Schwarzschild radius, was not understood at the time. Many physicists
History_of_black_hole_physics
Hypothetical mechanism for extracting energy from rotating black holes
Thermodynamics Bekenstein bound Bousso's holographic bound Immirzi parameter Schwarzschild radius Spaghettification Issues Information paradox Complementarity Soft
Penrose_process
Units defined only by physical constants
a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius, though whether those concepts are in fact simultaneously applicable
Planck_units
Star orbiting close to Sagittarius A*
black hole at a distance of just 120 AU or about 1,400 times its Schwarzschild radius. S2 reached its pericenter on May 19, 2018, while its velocity in
S2_(star)
American science fiction writer
Stories "Winter's Tale" (1987) – Collected in Impossible Things "Schwarzschild Radius" (1987) – Collected in Impossible Things "Circus Story" (1987) "Lord
Connie_Willis
Variable star in Monoceros
found with a mass 3 times the mass of the Sun, corresponding to a Schwarzschild radius of 9 kilometers. Follow-up work in 2022 argued that V723 Monocerotis
V723_Monocerotis
Lorentzian metric describing an isotropic, expanding, nonhomogenous universe
_{0}^{R_{0}}\rho r'r^{2}dR={\frac {F(R_{0})}{2}}} which implies that Schwarzschild radius is given by r s = 2 m = F ( R 0 ) {\displaystyle r_{s}=2m=F(R_{0})}
Lemaître–Tolman_metric
Conjecture in physics
~~~a\equiv {\frac {J}{M}}} where r {\displaystyle r} is the coordinate radius, e {\displaystyle e} and ℓ {\displaystyle \ell } are the test-particle's
Cosmic_censorship_hypothesis
Exact solution in general relativity
are the spherical angles r s {\displaystyle r_{\text{s}}} is the Schwarzschild radius of the body given by r s = 2 G M c 2 {\displaystyle \textstyle r_{\text{s}}={\frac
Reissner–Nordström_metric
Changes to stars over their lifespans
degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which
Stellar_evolution
Physical effect when superradiant modes are confined around a rotating black hole
Thermodynamics Bekenstein bound Bousso's holographic bound Immirzi parameter Schwarzschild radius Spaghettification Issues Information paradox Complementarity Soft
Black_hole_bomb
Theoretical propulsion system capable of interstellar distances
a black hole weighing 606,000 metric tons (6.06 × 108 kg) with a Schwarzschild radius of 0.9 attometers (0.9 × 10–18 m, or 9 × 10–19 m), a power output
Black_hole_starship
Soviet nuclear physicist and human rights activist (1921–1989)
spacetime between them, but with a continuity of geodesics beyond the Schwarzschild radius with no singularity[citation needed], allowing an exchange of matter
Andrei_Sakharov
Black hole in the constellation Sagittarius
3847/1538-4357/adbe6e. ISSN 0004-637X. "Schwarzschild Radius Calculator". hexacalculator. Retrieved 2025-04-11. Radius calculated using the mass. Lam, Casey
OGLE-2011-BLG-0462
Light bending by mass between source and observer
of gravitation, and c is the speed of light in vacuum. Since the Schwarzschild radius r s {\displaystyle r_{\text{s}}} is defined as r s = 2 G m / c 2
Gravitational_lens
Physical acceleration experienced by an object
where the planet or star's Schwarzschild radius rs = 2GM / c2. As our shell observer's radius approaches the Schwarzschild radius, the proper acceleration
Proper_acceleration
Metric for black holes in general relativity
In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. It is the positive-curvature
De Sitter–Schwarzschild metric
De_Sitter–Schwarzschild_metric
approximately 0.7 solar masses. 1958 — David Finkelstein theorises that the Schwarzschild radius is a causality barrier: an event horizon of a black hole 1963 — Roy
Timeline of black hole physics
Timeline_of_black_hole_physics
Time delay caused by space-time distortion near massive objects
{\displaystyle \textstyle R_{\text{s}}={\frac {2GM}{c^{2}}}} is the Schwarzschild radius. In parametrized post-Newtonian parameters, Δ t = − ( 1 + γ ) R s
Shapiro_time_delay
Fast-growing quasar
Thermodynamics Bekenstein bound Bousso's holographic bound Immirzi parameter Schwarzschild radius Spaghettification Issues Information paradox Complementarity Soft
SMSS_J215728.21–360215.1
Second-order partial differential equation
functions of the first and second kind, respectively, while rs is the Schwarzschild radius. The parameter l is an arbitrary non-negative integer. 6-sphere coordinates
Laplace's_equation
Orbit with a fixed distance from the barycenter
See also Hohmann transfer orbit. In Schwarzschild metric, the orbital velocity for a circular orbit with radius r {\displaystyle r} is given by the following
Circular_orbit
Description of large objects' physics
relativity. In case that objects become extremely heavy (i.e., their Schwarzschild radius is not negligibly small for a given application), deviations from
Classical_mechanics
Elementary particle with negative charge
anything, even electromagnetic radiation, from escaping past the Schwarzschild radius. However, quantum mechanical effects are believed to potentially
Electron
Explanation for how quasars are powered
is the magnetic field strength, r c {\displaystyle r_{c}} is the Schwarzschild radius, and ω is the angular velocity. Penrose process, another mechanism
Blandford–Znajek_process
Spherical collection of stars
ISBN 978-1-108-42216-1.{{cite book}}: CS1 maint: location missing publisher (link) Schwarzschild, Martin (1958). Structure and Evolution of Stars. Princeton University
Globular_cluster
Equation giving the form of a central force
{\displaystyle c} is the speed of light, r s {\displaystyle r_{s}} is the Schwarzschild radius and Λ {\displaystyle \Lambda } is the cosmological constant. And
Binet_equation
Quantum description of black holes
equal to that of the event horizon of classic black holes; thus, the Schwarzschild radius of a ubiquitous 6.8 solar mass (M☉) stellar-mass-class black hole—or
Fuzzball_(string_theory)
Pulling apart of a star by tidal forces
disruption radius must be greater than its Schwarzschild radius, R S = 2 G M c 2 {\displaystyle R_{S}={\frac {2GM}{c^{2}}}} . At a fixed stellar radius and mass
Tidal_disruption_event
Alternative of event horizon first suggested by Stephen Hawking
distances from each other, they will all fall within their joint Schwarzschild radius long before they are forced to collide. In the simple picture of
Apparent_horizon
detectors, textbook), Karl Schwarzschild (Schwarzschild solution, Schwarzschild radius, Event horizon, Schwarzschild vacuum, Schwarzschild fluid), Dennis William
List of contributors to general relativity
List_of_contributors_to_general_relativity
Hypothetical object of spacetime
gravitational radius. Depending on the type of black hole solution considered, there are several types of white holes. In the case of the Schwarzschild black
White_hole
Parameter describing conic sections
In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the
Conic_constant
Finkelstein presents a coordinate transformation that removes the Schwarzschild radius as a singularity. It is previously introduced by Arthur Eddington
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
English natural philosopher and clergyman (1724–1793)
classical minimum radius for escape assuming light behaved like particles of matter is numerically equal to the Schwarzschild radius in general relativity
John_Michell
Effect of general relativity
^{2}\theta }{\rho ^{2}}}d\phi dt\end{aligned}}} where rs is the Schwarzschild radius r s = 2 G M c 2 {\displaystyle r_{\text{s}}={\frac {2GM}{c^{2}}}}
Frame-dragging
Nebula
astronomical units. The black hole has a mass of 15 solar masses and a Schwarzschild radius of 45 km. A bowshock is created by a jet of energetic particles from
Sh_2-101
Large self-illuminated object in space
of stars. The photograph became a valuable astronomical tool. Karl Schwarzschild discovered that the color of a star and, hence, its temperature, could
Star
Model of the universe – alternative to the Big Bang model
were made. The Planck particle is a hypothetical black hole whose Schwarzschild radius is approximately the same as its Compton wavelength; the evaporation
Steady-state_model
2000 novel by Nancy Kress
threshold of what the tunnel can handle is determined by the object's Schwarzschild radius. Finally, nobody knows how the tunnels work. Macro-level quantum
Probability_Moon
Classification in astronomy
numbers are preserved with radii less than 1.5 times the corresponding Schwarzschild radius. Q stars are also called "gray holes". An electroweak star is a theoretical
Compact_object
Overview of Germany's handling with science and technology
namely the Schwarzschild metric and the Schwarzschild radius. The center of a non-rotating, uncharged black hole is called the Schwarzschild singularity
Science and technology in Germany
Science_and_technology_in_Germany
Estimates the mass of a spacetime in terms of the total area of its black holes
isometric to a slice of the Schwarzschild spacetime outside its outermost minimal surface, which is a sphere of Schwarzschild radius. More generally, Penrose
Riemannian_Penrose_inequality
Standard surface gravity
system. For objects where the surface lies deep within an atmosphere and the radius is not well defined, the surface gravity is given at the 1-bar pressure
Surface_gravity
Newtonian gravity into General Relativity, with deformation parameter Schwarzschild-radius/characteristic-dimension. Conversely, group contraction leads to
Deformation_quantization
Black holes appearing from quantum spacetime fluctuations
_{P}^{2}={\frac {\hbar G}{c^{3}}}} where R μ {\displaystyle R_{\mu }} is the radius of curvature of spacetime small domain, x μ {\displaystyle x_{\mu }} is
Virtual_black_hole
Physical property of matter
theory, the smaller (less massive) a black hole is, the smaller its Schwarzschild radius will be, and therefore the greater the curvature of its event horizon
Heat_capacity
Extended objects found in string theory
entropy is proportional to the black hole mass squared; because the Schwarzschild radius is proportional to the mass, the Bekenstein entropy is proportional
D-brane
Galaxy in the constellation Centaurus
Milky Way's central black hole. A black hole of this mass has a Schwarzschild radius of 1,531 (with the range being 868.6 to 10,660) AU (about 458 billion
ESO_444-46
American physicist (1929-2016)
Schwarzschild metric and eliminate its coordinate singularity. In essence, Finkelstein determined that whatever falls past the Schwarzschild radius into
David_Finkelstein
Overview of the scientific field of astronomy
Hypernova Gamma-ray burst Properties Black hole thermodynamics Schwarzschild radius M–sigma relation Event horizon Quasi-periodic oscillation Photon
Outline_of_astronomy
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SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
SCHWARZSCHILD RADIUS
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