General relativity - Covariant Derivative Of F(R)

In summary, the covariant derivative of F(R) in general relativity is a mathematical operation that describes how a vector or tensor field changes as it is transported along a curved space-time manifold. It is calculated using the Levi-Civita connection and is significant in understanding the behavior of matter and energy in the presence of gravitational fields. It is directly related to Einstein's field equations and has applications in the study of black holes, gravitational waves, and cosmology. It is also essential for understanding the behavior of particles and fields in strong gravitational fields near massive objects.
  • #1
thecoop
15
0
In f(R) gravity as http://en.wikipedia.org/wiki/F(R)_gravity ,

i have problem with the term [ g_ab □ - ∇_a ∇_b ] F(R) , well

actually is [ ∇_b ∇_a - ∇_a ∇_b ] F(R) , but F is a function of Ricci Factor and Ricci Factor is expressed as a(t) ( scale factor ) . for the a = b = 0 i say this term becomes zero . is it true ?
 
Physics news on Phys.org
  • #2
Can you re-write your post so that it makes (more) sense ?
 
  • #3
I don't know anything about f(R) gravity theories, but that expression is clearly zero if the torsion tensor vanishes.
 

Related to General relativity - Covariant Derivative Of F(R)

1. What is the covariant derivative of F(R) in general relativity?

The covariant derivative of F(R) in general relativity is a mathematical operation that generalizes the concept of differentiation from ordinary calculus to curved space-time. It is used to describe how a vector or tensor field changes as it is transported along a curved space-time manifold. In general relativity, the covariant derivative is used to determine the curvature of space-time and the geodesic equations of motion.

2. How is the covariant derivative of F(R) calculated?

The covariant derivative of F(R) is calculated using the Levi-Civita connection, which is a mathematical operation that defines a unique way to differentiate vector and tensor fields in curved space-time. It takes into account the curvature of space-time and ensures that the derivative is independent of the coordinate system used.

3. What is the significance of the covariant derivative in general relativity?

The covariant derivative is significant in general relativity because it allows for the description of the curvature of space-time and the dynamics of particles and fields in a curved space-time. It is a crucial tool for understanding the behavior of matter and energy in the presence of gravitational fields, as described by Einstein's theory of general relativity.

4. How does the covariant derivative of F(R) relate to Einstein's field equations?

The covariant derivative of F(R) is directly related to the Einstein field equations, which are the fundamental equations of general relativity. These equations describe how matter and energy curve space-time, and how the curvature of space-time affects the motion of matter and energy. The covariant derivative appears in the equations as part of the Ricci tensor, which is a measure of the curvature of space-time.

5. What are some applications of the covariant derivative in general relativity?

The covariant derivative has many applications in general relativity, such as in the study of black holes, gravitational waves, and cosmology. It is also used in the development of alternative theories of gravity, such as modified gravity and string theory. In addition, the covariant derivative is essential for understanding the behavior of particles and fields in the strong gravitational fields near massive objects, such as neutron stars and black holes.

Similar threads

Deriving the Reissner-Nordström metric
    • Advanced Physics Homework Help
Replies
9
Views
2K
Showing that the gradient of a scalar field is a covariant vector
    • Advanced Physics Homework Help
Replies
5
Views
2K
General Relativity asymmetry identity
    • Advanced Physics Homework Help
Replies
3
Views
1K
I Calculation of Lie derivative - follow up
    • Special and General Relativity
Replies
28
Views
684
How to compute the variation of two covariant derivatives?
    • Advanced Physics Homework Help
Replies
1
Views
1K
I System, potential energy, and nonconservative forces: The whole story
    • Classical Physics
Replies
2
Views
889
Conservation law for FRW metric
    • Advanced Physics Homework Help
Replies
1
Views
878
Covariant Derivative of a Vector
    • Advanced Physics Homework Help
Replies
5
Views
915
I Understanding Covariant and Partial Derivatives in General Relativity
    • Special and General Relativity
Replies
5
Views
2K
Coordinate Transformation (multivariable calculus)
    • Advanced Physics Homework Help
Replies
1
Views
953

Hot Threads

Recent Insights

Back
Top