# What is timelike geodesic?

## What is timelike geodesic?

A timelike geodesic is a path through spacetime that describes any object moving slower than the speed of light. The geometry of spacetime is described by the spacetime 4-interval, basically the equivalent of the Pythagorean Theorem in 4 dimensions. It is a way to compute distances.

What does the Schwarzschild metric describe?

In Einstein’s theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and …

What is meant by null geodesic?

A null geodesic is the path that a massless particle, such as a photon, follows. That’s why it’s called null, it’s interval (it’s “distance” in 4 D spacetime) is equal to zero and it does not have a proper time associated with it.

### What does geodesic mean in physics?

In general relativity, a geodesic generalizes the notion of a “straight line” to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

What is geodesic principle?

General relativity incorporates a number of basic principles that correlate space- time structure with physical objects and processes. Among them is the. Geodesic Principle: Free massive point particles traverse timelike geodesics. One can think of it as a relativistic version of Newton’s first law of motion.

What does Schwarzschild radius represent?

Schwarzschild radius, also called gravitational radius, the radius below which the gravitational attraction between the particles of a body must cause it to undergo irreversible gravitational collapse. This phenomenon is thought to be the final fate of the more massive stars (see black hole).

#### What does Schwarzschild mean?

Definition of Schwarzschild radius : the radius of the spherical boundary within which a given mass (as of a star) must collapse to become a black hole also : the distance of the event horizon from the center of a black hole.

How do you calculate Schwarzschild radius?

The Schwarzschild radius formula is G = rc²/2m. Here, G is the gravitational constant, r is the Schwarzschild radius and m is the mass of the black hole.

What is a null curve?

A closed null curve is a closed curve which is everywhere future-directed null (or everywhere past-directed null). The holonomy of the ratio of the rate of change of the affine parameter around a closed null geodesic is the redshift factor.

## Is a photon geodesic?

The photon has a null geodesic and we may use that equation directly. . For smaller radii, the photon will be sucked in. For larger radii, it will be deflected.

What is geodesic metric space?

1. In a general metric space, a geodesic arc is denned to be a shortest. rectifiable arc joining its end points. In a compact metric space, or more. generally in a metric space in which bounded sets are compact, Menger(l)

Why is the Schwarzschild metric symmetrical?

Since the Schwarzschild metric is symmetrical about , any geodesic that begins moving in that plane will remain in that plane indefinitely (the plane is totally geodesic ). Therefore, we orient the coordinate system so that the orbit of the particle lies in that plane, and fix the

### What is the significance of Schwarzschild geodesics?

that is, motion in the Schwarzschild metric. Schwarzschild geodesics have been pivotal in the validation of Einstein’s theory of general relativity. For example, they provide accurate predictions of the anomalous precession of the planets in the Solar System and of the deflection of light by gravity.

What is the Schwarzschild solution to the gravitational constant?

. The Schwarzschild solution can be written as is the gravitational constant. The classical Newtonian theory of gravity is recovered in the limit as the ratio goes to zero. In that limit, the metric returns to that defined by special relativity. In practice, this ratio is almost always extremely small. For example, the Schwarzschild radius

What are the geodesic lines of space-time?

In flat space-time, far from a source of gravity, these geodesics correspond to straight lines; however, they may deviate from straight lines when the space-time is curved. The equation for the geodesic lines is