本篇英国essay代写-General Relativity and Black holes讲了黑洞是广义相对论预测的暗物质。黑洞物理学作为广义相对论，量子力学，粒子物理学，热力学与统计学的交叉领域，是物理学的前沿和热点研究领域。广义相对论和引力理论逐渐形成。本篇essay代写由51due代写平台整理，供大家参考阅读。
Abstract
Black hole is a dark matter as general relativity predicted. Black hole physics, as an intersectional field of general relativity, quantum mechanics, particle physics, thermodynamics and statistics, is the frontier and hot research field of physics. General relativity and the theory of gravitation gradually build up. The research on general relativity could contribute to understanding the evolution of the black hole and the origin of the universe.
Fig.1 Black hole Cygnus X-1
Introduction
In 1915, Einstein created the theory of general relativity, pointed out that matter and space-time influence each other. The existence and movement of matter would produce gravity, which could result in curved space-time. And the curved space-time could influence the movement of matter. The Einstein field equation gives full expression to the mutual influence between matter and space-time. It could be written as , where is the Ricci curvature tensor, is the metric tensor, is the scalar curvature, is the stress-energy, the constant [1]. The advent of general relativity contributed to understanding the natures of space-time, matter and gravity. Their interrelationships also have been further explored.
Fig.2 Space-time curvature schema
The theory of general relativity has three famous experimental manifestations. First is the anomalous perihelion advance of the planet Mercury, which is 43 seconds longer per century than the perihelion precession predicted by Newtonian mechanics. The theory of general relativity provides substantial explanations for the observed precession. Second is the deflection of the starlight in the gravitational field. The deflection calculated according to general relativity is one times larger than the deflection calculated through Newtonian mechanics. In 1919, an experiment about solar eclipse conducted by Eddington confirmed that the sun’s gravity does bend the starlight. The third one is the gravitational redshift, that is , the way in which the frequency of light shifts as the light propagates through a gravitational field. As Fig.3 shows , an experiment about gravitational redshift conducted in which a laser is directed upward from the bottom to the top of a lab in space which is uniformly accelerating upward with acceleration a = -g, assuming at the instant the laser pulse starts, the lab is a rest (v=0). When the laser pulse is received at the top, distance L from the bottom, the time is . However, at that time the speed of the observer at the top is now . Therefore the observer will notice a redshift (since the observer is moving away from the source of light) caused by the Doppler effect: . Since the equivalence principle requires that all such experiments must also produce the same result in a stationary lab with the equivalent gravitational acceleration, we must also see this effect in labs on Earth. This is called the gravitational redshift effect, and was first measured by Pound and Rebka at Harvard in 1960.
Fig. 3 Pound-Rebka experiment
The gravitational redshift also implies time dilation: Clocks in gravitational fields run more slowly than clocks in free space. If applied to optical wavelengths, this manifests itself as a change in the color of visible light as the wavelength of the light is shifted toward the red part of the light spectrum. Since frequency and wavelength are inversely proportional, this is equivalent to saying that the frequency of the light is reduced towards the red part of the light spectrum
After the establishment of general relativity, the physicists began to use it to study the movement of celestial objects, celestial evolution, evolution of the universe, origin of the universe, and other astrophysical problems. Previous predictions such as dark stars aroused scientists’ interested. The concept of dark star was presented by both John Michell and Pierre-Simon Laplace based on classic mechanics. They promoted that the biggest star in the universe might be invisible. The bigger the star was, the stronger the gravity was. As a result, it was more difficult for the throwing object to escape from the star. When the gravity became stronger enough to pull light, the star could not be seen by the outside. They deduced the condition of the dark star formation. It could be expressed as , where the speed of light is , and are mass and radius of the star respectively[1].
In 1939, Robert Oppenheime and his collaborators predicted the existence of dark star again according to the theory of general relativity, which regarded gravity as the performance of curved space-time. After that, the discovery of neutron stars and pulsars spurred the research about dark stars and finally in 1967, John Wheeler suggested to replace the calling of dark star by the term “black hole”.
Spherically Symmetric Black Hole: Event Horizon
The simplest black holes are spherically symmetric, known as Schwarzschild black holes. As Fig.4 shows, Schwarzschild black hole is characterized by a singular sphere. The surface of the sphere is the border of black hole, known as event horizon. Everything inside the event horizon including light could not escape from the sphere, which means no one outside the sphere could receive the information from the inside of black hole. The radius of the event horizon, also called Schwarzschild radius, could be represented as [2].
Fig.4 Schwarzschild black hole
Spherically Symmetric Black Hole: Gravitational Red-shift
The event horizon of Schwarzschild black hole is also the infinite red-shift surface. According to the theory of general relativity, the curved space-time would cause the clock to slow. The stronger the space-time is curved, the more slowly the clock runs. The clock on the surface of the sun runs more slowly than the clock on the surface of the earth does [3]. This phenomenon could be manifested by the differences between the solar spectrum and the spectrum of earth. For the same element, the light emitted from the surface of the sun shows a longer wavelength than that emitted from the surface of the earth. Namely, the spectral line moves towards red end, which is called gravitational red-shift.
Fig.5 Gravitational red-shift diagram
The space-time around the surface of black hole is curved so strongly that the clock there runs infinitely slow. When we observe the black hole on the earth, we will find out a stopped clock on the surface of the black hole. If a light source is located on the surface of the black hole, the red-shift of emitted light observed on the earth would be infinite. The infinite red-shift means the frequency of the light would decrease to zero and the wavelength would become infinite. In fact, the light emitted from the surface of the black hole cannot be observed at all [3].
Spherically Symmetric Black Hole: Singularity
The theory of general relativity proposes that the space and time coordinates inside the black hole would exchange. The time coordinate will become the space coordinate and the radial coordinate will become the time coordinate. The direction of the time coordinate inside the black hole is towards the singularity at . Therefore, everything that enter the black hole can only move towards the direction where decrease. Neither stop nor reverse movement would be happened since the movement inside the black hole is the development of time [3]. The direction of time passing by is irresistible. Consequently, the whole interior of the black hole is a unidirectional area and the event horizon is the outset of this area. Given the fact that nothing can stop in the unidirectional area, the unidirectional area is under the vacuum condition.
Fig.6 Sketch of black hole singularity
Conclusion
The theory of general relativity has predicted several types of stable black holes. All the information about a stable black hole could be determined by three factors, namely, its mass, electric charge, and angular momentum. A lot of research shows that the relationships among the three factors are identical to those among four laws of thermodynamics [4]. Thus, scientists propose that the stable black hole is located in a system under thermal equilibrium condition and the temperature as well as the entropy of the black hole could be defined. However, the origin and definition of the entropy of the black hole still remain puzzles. Besides the stable black holes, scientists are also interested in the dynamic black holes. Considering the temperature of the black hole, its thermal emission should not be black. Stephen Hawking used quantum mechanics to study the event horizon and he proposed that the black hole does have emission [5]. This emission is called Hawking radiation which describes an evaporating black hole. Further experiments as well as observations are needed to support this theory.
References
[1] Will C. M. (1993). Theory and Experiment in Gravitational Physics. Cambridge: Cambridge University Press
[2] Heusler, M. (1998). "Stationary Black Holes: Uniqueness and Beyond". Living Reviews in Relativity. 1 (6)
[3] Chandrasekhar S. (1983) The mathematical theory of black holes. New York: Oxford University Press
[4] Bardeen J. M.; Carter, B.; Hawking, S. W. (1973). "The four laws of black hole mechanics". Communications in Mathematical Physics. 31 (2): 161–170
[5] Hawking, S. W. (1971). "Gravitational Radiation from Colliding Black Holes". Physical Review Letters. 26 (21): 1344–1346.
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