Is Strawberry Good For Herpes

The definition of dependent observable gravitational field and diffeomorphisms

In modern textbooks the gravitational field or sometimes also the gravitational force It identifies the curvature of spacetime. That is, there where space is different from a plane, where the space-time curvature becomes, there exists a gravitational field acting. However, this was not such as Einstein's position. Einstein gravity identified with the Christoffel symbols, in short, with accelerations. Einstein took his principle of equivalence to the letter and assumed that gravity and acceleration are not only equivalent in a sense, they are strictly the same.

The equivalence principle in Einstein's original formulation

An observer who is falling from the roof of his house does not undergo gravitational field, at least in its vicinity. This cruel experiment mental is what Albert Einstein called "der Gedanke meines Lebens glückischste (the happiest thought of my life), and basically sums up the essence of general relativity (an interesting article on the history of general relativity in History Planets General Theory of Relativity ), namely the principle of equivalence.

The equivalence principle tells us that in free fall gravitational field does not exist and that observers in free fall can be seen, therefore, inertial observers, ie free of any force acting on them. Prevent the fall of one of these observers, for example by means of a surface hold it and let stand, is to submit to a uniform acceleration. On the surface of the earth is the same view that we are in a uniform gravitational field pointing down, to consider that we are in an accelerated upward and thereby measure inertial force (fictitious) down. Gravitation is thus a fictitious force, and indeed it is this that allows gravity to eliminate locally with a change of coordinates. In short, for an observer at rest the effect of uniform gravitational field and a uniform acceleration are equivalent. There is thus an equivalence between both descriptions.

The definition of the gravitational field in the formulation Einstein and modern

According to this definition of Einstein, the gravitational field is all that works universally diverting particles paths straight and uniform speed, speeding, ie changing , which is the form of geodesic equation when the Christoffel symbols are zero. The geodesic equation of general relativity is generalized to t own time along the geodesic. The two equations are equivalent when , ie, the Christoffel symbols are zero. As defined by Einstein's gravitational field are . Here are a couple of quotations from Einstein on the subject ("The Foundation of the General Theory of Relativity" de 1916):

It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of coordinates.

If the vanish, then the point moves uniformly in a straight line. These quantities therefore condition the deviation of the motion from uniformity. They are the components of the gravitational field.

Los símbolos de Christoffel pueden hacerse cero con un cambio de coordenadas, pero la curvatura no ya que es invariante (el escalar de curvatura por ejemplo). El ejemplo más sencillo which supports the interpretation of Einstein's gravitational field is uniform. A uniform gravitational field is a gravitational field, but its curvature is zero. However, it is called "gravitational field", and in an appropriate coordinate system, there is an acceleration, Christofell result of non-zero symbols, identified with the force of gravity. In that sense, the "gravity" is somewhat dependent on the observer. All in accordance with their formulation of the principle of equivalence.

In the modern interpretation of gravity, the term "gravitational field" is usually reserved however for the curvature of space-time. Regardless of terminology in general relativity so there is a geometry of space-time described by the Einstein tensor coupled to a time and energy of matter, described by the energy tensor time. In particular, it is Einstein's equations: . From the standpoint of terminology discussion mentioned here can distinguish several cases:

• Space-time curvature. In modern terminology as soon there is curvature (generated, in general, an energy-momentum tensor) speaks of the gravitational field. The terminological problem appears when there is curvature.


• Spacetime no curvature and no energy-momentum. This is the case of field uniform gravity with nonzero accelerations result of a change of coordinates in a flat spacetime.


• Spacetime without curvature and energy-momentum. These are usually solutions that violate some energy condition, but possible in principle. Specifically for example, "cosmic strings" or "cosmic wall." The space-time created by a cosmic string is flat overall, but not topologically equivalent to flat spacetime of Minkowski. This space-time can be imagined as follows: a concentric circle to rope in a section perpendicular to it is 2 pi r not, but less, because space-time is missing an angular sector (it a conical spacetime.) In these cases there is no gravitational field with modern terminology and with that of Einstein. However, it is clear that something is happening there, something produced by a content material, giving rise to something different from flat spacetime.

The concept came from Einstein's gravitational field to adjust to their formulation of the principle of equivalence. In the modern form of the theory the concept of gravitational field is different, as we have seen. Arbitrary definitions beyond the truth, from the point of view of theory is Einstein's equations. As we have seen, not the modern concept of gravitational field does not fully capture the essence of gravitation given us in the equations of Einstein. In principle of equivalence, meanwhile, has been reformulated to three different versions, the weak principle, that of Einstein and the strong. Her relationship with Einstein's original ideas and relationships between these three versions will engage us in another article.