A black hole is a region of spacetime exhibiting gravitational acceleration so strong that nothing—no particles or electromagnetic radiation such as light—can escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole; the boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways, a black hole acts like an ideal black body. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass; this temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it impossible to observe. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace.
The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; the discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. Black holes of stellar mass are expected to form when massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form. There is consensus; the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe.
Stars passing too close to a supermassive black hole can be shred into streamers that shine brightly before being "swallowed." If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses. On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which represented the first observation of a black hole merger; as of December 2018, eleven gravitational wave events have been observed that originated from ten merging black holes. On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre.
The idea of a body so massive that light could not escape was proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, the surface escape velocity exceeds the usual speed of light. Michell noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. Scholars of the time were excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century. If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves. Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity and free-falling back to the star's surface.
In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties; this solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates, although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity. Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly
This article is a collection of statewide polls for the 2012 United States presidential election. The polls listed here, by state are from January 1 to August 31, 2012 and provide early data on opinion polling between a possible Republican candidate against incumbent President Barack Obama. Note: Some states had not conducted polling yet or no updated polls were present from January 1 to August 31, 2012 9 electoral votes 62%–38% 60%–38% 11 electoral votes 55%–44% 53%–45% Three Way race 6 electoral votes 54%–45% 59%–39% 55 electoral votes 54%–45% 61%–37% 9 electoral votes 52%–47% 54%–45% Three Way race 7 electoral votes 54%–44% 61%–38% 29 electoral votes 52%–47% 51%–48% Three Way race 16 electoral votes 58%–41% 52%–47% 20 electoral votes 55%–45% 62%–37% 11 electoral votes 60%–39% 50%–49% 6 electoral votes 50%–49% 54%–44% 4 electoral votes 53%–45% 58%–40% 10 electoral votes 56%–43% 61%–38% 11 electoral votes 62%–37% 62%–36% Four Way race 16 electoral votes 51%–48% 57%–41% 10 electoral votes 51%–48% 54%–44% 10 electoral votes 53%–46% 49%–49% Three Way race 3 electoral votes 59%–39% 49%–47% Three Way race 5 electoral votes 66%–33% 57%–42% 6 electoral votes 51%–48% 55%–43% 4 electoral votes 50%–49% 54%–45% Three Way race 14 electoral votes 52%–46% 57%–42% 5 electoral votes 50%–49% 57%–42% Three Way race 29 electoral votes 58%–40% 63%–36% 15 electoral votes 56%–44% 50%–49% Three Way race 3 electoral votes 63%–36% 53%–45% 18 electoral votes 51%–49% 52%–47% 7 electoral votes 65.6%–34.4% 65.7%–34.4% 7 electoral votes 51%–47% 57%–40% 20 electoral votes 51%–48% 54%–44% 9 electoral votes 58%–41% 54%–45% 3 electoral votes 60%–38% 53%–45% 11 electoral votes 57%–43% 57%–42% 38 electoral votes 61%–38% 55%–44% Three Way race – Ron Paul was running as a Republican candidate.
6 electoral votes 72%–26% 62%–34% 3 electoral votes 59%–39% 67%–30% 13 electoral votes 54%–46% 53%–46% Three Way race 12 electoral votes 53%–46% 58%–40% 5 electoral votes 56%–43% 56%–43% 10 electoral votes 50%–49% 56%–42% Three Way race Pre-2012 statewide opinion polling for the United States presidential election, 2012 Nationwide opinion polling for the United States presidential election, 2012 Nationwide opinion polling for the Republican Party 2012 presidential primaries Statewide opinion polling for the Republican Party presidential primaries, 2012 Statewide opinion polling for the United States presidential election, 2008 Republican Party presidential primaries, 2012
The occipitalis muscle is a muscle which covers parts of the skull. Some sources consider the occipital muscle to be a distinct muscle. However, Terminologia Anatomica classifies it as part of the occipitofrontalis muscle along with the frontalis muscle; the occipitalis muscle is quadrilateral in form. It arises from tendinous fibers from the lateral two-thirds of the superior nuchal line of the occipital bone and from the mastoid process of the temporal and ends in the epicranial aponeurosis; the occipitalis muscle is innervated by the facial nerve and its function is to move the scalp back. The muscles receives blood from the occipital artery. Occipitofrontalis muscle This article incorporates text in the public domain from page 379 of the 20th edition of Gray's Anatomy PTCentral