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ZeroTheHero
ZeroTheHero
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Given that $$ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²).$$$$ds² = c²dt² - A(r)dr² - r²(d \theta ² + \sin²({\theta})d \phi ²).$$ I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric?

Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

Given that $$ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²).$$ I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric?

Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

Given that $$ds² = c²dt² - A(r)dr² - r²(d \theta ² + \sin²({\theta})d \phi ²).$$ I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric?

Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

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Qmechanic ♦
Qmechanic ♦
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Given that $ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²)$.$$ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²).$$ I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric? Intuitively

Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

Given that $ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²)$. I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric? Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

Given that $$ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²).$$ I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric?

Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?

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melvin de bosscher
melvin de bosscher
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Ricci Scalar of a given diagonal metric

Given that $ds² = c²dt² - A(r)dr² - r²(d \theta ² + sin²({\theta})d \phi ²)$. I can easily find the metric for this particular situation. But the question is: how do you find the Ricci scalar for this given metric? Intuitively I would think the Ricci scalar is zero (like in the Schwarzschild Metric), but I'm not even sure if this is correct. I think there should be a really easy way to calculate this, but all I can find is writing the Ricci tensor with Christoffel symbols. But writing this out seems very long... Any ideas?