Div Curl: Black Hole Edge Explored

  • Context: Graduate 
  • Thread starter Thread starter rockyshephear
  • Start date Start date
  • Tags Tags
    Black holes Curl Holes
Click For Summary

Discussion Overview

The discussion revolves around the concepts of divergence and curl at the edge of a black hole, particularly in the context of general relativity. Participants explore the implications of these mathematical operations in relation to black holes, their event horizons, and the nature of vector fields in higher dimensions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions what is meant by the divergence and curl at the edge of a black hole, seeking clarification on the specific vector field in question.
  • Another participant suggests that divergence could be useful for studying sources or sinks in a field, noting that for a black hole, the divergence of the gravitational field is typically negative.
  • It is mentioned that the divergence and curl at the edge of a black hole may not be particularly special, as this region corresponds to the event horizon.
  • A participant emphasizes that divergence and curl operate on vector fields and that a specific vector field must be defined for the question to be meaningful.
  • One participant expresses uncertainty about the application of these concepts in the context of general relativity, noting the challenge of working in four-dimensional space where the cross product is not defined.
  • Another participant introduces the wedge product as a generalization of the cross product applicable in higher dimensions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific application of divergence and curl at the edge of a black hole. There are competing views regarding the significance of these operations and the necessity of defining a vector field.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the nature of vector fields and the mathematical operations applicable in four-dimensional spacetime. The discussion also reflects a lack of clarity on the specific context in which divergence and curl are being considered.

rockyshephear
Messages
232
Reaction score
0
What is the divergence and curl at the edge of a black hole?
 
Physics news on Phys.org
Divergence and curl of what?
 
Whatever black holes continually suck into themselves continually
 
rockyshephear said:
What is the divergence and curl at the edge of a black hole?

Did you tried to say something like " the linear momentum and angular momentum of a mass crossing the horizon of a BH"? For instance, divergence would be useful for studying if there are sources or sinks in a field (for a BH the divergence of the gravitational field is negative as usual).
 
Last edited:
the div and curl of most things at the edge of a black hole is nothing special, since this is the event horizon.
 
Div and curl operate on vector fields, not "whatevers". You need to specify what vector field for this even to be a question.

At the risk of sounding like a broken record, let me recommend Schey's Div, Grad, Curl and All That.
 
Am I missing something? I really don't know anying about GR but to capture the black holeness wouldn't you have to work in 4-space. The cross product is not defined in 4 dimensions.
 

Similar threads

High School Is there a white hole inside every black hole?
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Can light be reflected in a black hole?
  • · Replies 22 ·
Replies
22
Views
2K
High School How can a black hole absorb matter?
  • · Replies 31 ·
2
Replies
31
Views
2K
Undergrad Asteroid hits static black hole
  • · Replies 31 ·
2
Replies
31
Views
2K
Undergrad You can't actually enter a blackhole?
  • · Replies 40 ·
2
Replies
40
Views
4K
Undergrad On the possibility of exploding a black hole
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Questions about Hawking radiation and extremal black holes...?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Mass conservation in black holes
  • · Replies 8 ·
Replies
8
Views
2K
High School Entering a black hole -- I know I must be wrong (Help me understand why)
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad Looking closely at the descent into a black hole
  • · Replies 51 ·
2
Replies
51
Views
2K