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Lubang hitam adalah sebuah pemusatan massa yang cukup besar sehingga menghasilkan gaya gravitasi yang sangat besar. Gaya gravitasi yang sangat besar ini mencegah apa pun lolos darinya kecuali melalui perilaku terowongan kuantum. Medan gravitasi begitu kuat sehingga kecepatan lepas di dekatnya mendekati kecepatan cahaya. Tak ada sesuatu, termasuk radiasi elektromagnetik yang dapat lolos dari gravitasinya, bahkan cahaya hanya dapat masuk tetapi tidak dapat keluar atau melewatinya, dari sini diperoleh kata "hitam". Istilah "lubang hitam" telah tersebar luas, meskipun ia tidak menunjuk ke sebuah lubang dalam arti biasa, tetapi merupakan sebuah wilayah di angkasa di mana semua tidak dapt kembali. Secara teoritis, lubang hitam dapat memliki ukuran apa pun, dari mikroskopik sampai ke ukuran alam raya yang dapat diamati.
Teori Lubang Hitam pertama kali diperkenalkan oleh astronom Jerman bernama Karl Schwarzschild, pada tahun 1916, dengan berdasar pada teori relativitas umum dari Albert Einstein, dan semakin dipopulerkan oleh Stephen William Hawking. Pada saat ini banyak astronom yang percaya bahwa hampir semua galaksi dialam semesta ini mengelilingi lubang hitam pada pusat galaksi.
Mathematical theory
Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,
where
is a standard element of solid angle.
According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzsschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.
The Schwarzschild radius is given by
where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.
The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 10(30) kg/m(3), a supermassive black hole of 10(9) solar masses has a density of around 20 kg/m(3) less than water! The mean density is given by
Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 1026 times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.
The formula also implies that any object with a given mean density is a black hole if its radius is large enough. If the visible universe has a mean density equal to the critical density, then it is a black hole.
More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.
There is also the Black Hole Entropy formula:
Where A is the area of the event horizon of the black hole, \hbar is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.
A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to
When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.
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Teori Lubang Hitam pertama kali diperkenalkan oleh astronom Jerman bernama Karl Schwarzschild, pada tahun 1916, dengan berdasar pada teori relativitas umum dari Albert Einstein, dan semakin dipopulerkan oleh Stephen William Hawking. Pada saat ini banyak astronom yang percaya bahwa hampir semua galaksi dialam semesta ini mengelilingi lubang hitam pada pusat galaksi.
Mathematical theory
Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,
where
According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzsschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.
The Schwarzschild radius is given by
where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.
The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 10(30) kg/m(3), a supermassive black hole of 10(9) solar masses has a density of around 20 kg/m(3) less than water! The mean density is given by
Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 1026 times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.
The formula also implies that any object with a given mean density is a black hole if its radius is large enough. If the visible universe has a mean density equal to the critical density, then it is a black hole.
More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.
There is also the Black Hole Entropy formula:
Where A is the area of the event horizon of the black hole, \hbar is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.
A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to
When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.
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