Stephen Hawking Roger Penrose Popular Books

Stephen Hawking Roger Penrose Biography & Facts

The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose was awarded the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity", which he shared with Reinhard Genzel and Andrea Ghez. Singularity A singularity in solutions of the Einstein field equations is one of three things: Spacelike singularities: The singularity lies in the future or past of all events within a certain region. The Big Bang singularity and the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike. Timelike singularities: These are singularities that can be avoided by an observer because they are not necessarily in the future of all events. An observer might be able to move around a timelike singularity. These are less common in known solutions of the Einstein field equations. Null singularities: These singularities occur on light-like or null surfaces. An example might be found in certain types of black hole interiors, such as the Cauchy horizon of a charged (Reissner–Nordström) or rotating (Kerr) black hole. A singularity can be either strong or weak: Weak singularities: A weak singularity is one where the tidal forces (which are responsible for the spaghettification in black holes) are not necessarily infinite. An observer falling into a weak singularity might not be torn apart before reaching the singularity, although the laws of physics would still break down there. The Cauchy horizon inside a charged or rotating black hole might be an example of a weak singularity. Strong singularities: A strong singularity is one where tidal forces become infinite. In a strong singularity, any object would be destroyed by infinite tidal forces as it approaches the singularity. The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric, while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the property of geodesic incompleteness, in which either some light-path or some particle-path cannot be extended beyond a certain proper time or affine parameter (affine parameter being the null analog of proper time). The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside any black hole whenever matter satisfies reasonable energy conditions. The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative. Hawking's singularity theorem is for the whole universe, and works backwards in time: it guarantees that the (classical) Big Bang has infinite density. This theorem is more restricted and only holds when matter obeys a stronger energy condition, called the strong energy condition, in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a scalar field, obeys this condition. During inflation, the universe violates the dominant energy condition, and it was initially argued (e.g. by Starobinsky) that inflationary cosmologies could avoid the initial big-bang singularity. However, it has since been shown that inflationary cosmologies are still past-incomplete, and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime. It is still an open question whether (classical) general relativity predicts spacelike singularities in the interior of realistic charged or rotating black holes, or whether these are artefacts of high-symmetry solutions and turn into null or timelike singularities when perturbations are added. Interpretation and significance In general relativity, a singularity is a place that objects or light rays can reach in a finite time where the curvature becomes infinite, or spacetime stops being a manifold. Singularities can be found in all the black-hole spacetimes, the Schwarzschild metric, the Reissner–Nordström metric, the Kerr metric and the Kerr–Newman metric, and in all cosmological solutions that do not have a scalar field energy or a cosmological constant. One cannot predict what might come "out" of a big-bang singularity in our past, or what happens to an observer that falls "in" to a black-hole singularity in the future, so they require a modification of physical law. Before Penrose, it was conceivable that singularities only form in contrived situations. For example, in the collapse of a star to form a black hole, if the star is spinning and thus possesses some angular momentum, maybe the centrifugal force partly counteracts gravity and keeps a singularity from forming. The singularity theorems prove that this cannot happen, and that a singularity will always form once an event horizon forms. In the collapsing star example, since all matter and energy is a source of gravitational attraction in general relativity, the additional angular momentum only pulls the star together more strongly as it contracts: the part outside the event horizon eventually settles down to a Kerr black hole (see No-hair theorem). The part inside the event horizon necessarily has a singularity somewhere. The proof is somewhat constructive – it shows that the singularity can be found by following light-rays from a surface just inside the horizon. But the proof does not say what type of singularity occurs, spacelike, timelike, null, orbifold, jump discontinuity in the metric. It only guarantees that if one follows the time-like geodesics into the future, it is impossible for the boundary of the region they form to be generated by the null geodesics from the surface. This means that the boundary must either come from nowhere or the whole future ends at some finite extension. An interesting "philosophical" feature of general relativity is revealed by the singularity theorems. Because general relativity predicts the inevitable occurrence of singularities, the theory is not complete without a specification for what happens to matter that hits the singularity. One can extend general relativity to a unified field theory, such as the Einstein–Maxwell–Dirac system, where no such singularities occur. Elements of the theorems In history, there is a deep connection between the curvature of a manifold and its topology. The Bonne.... Discover the Stephen Hawking Roger Penrose popular books. Find the top 100 most popular Stephen Hawking Roger Penrose books.